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  Large language model

  A large language model (LLM) is a neural network trained on a vast amount of text for natural language processing tasks, especially language generation. LLMs can typically generate, summarize, translate and analyze text in many contexts, and are a foundational technology behind modern chatbots. Biased or inaccurate training data can make an LLM's output less reliable. As of 2026, the most capable LLMs are based on transformer architectures, which, according to the 2017 paper "Attention Is All You Need", can be more efficient and parallelizable than earlier statistical and recurrent neural network models. Benchmark evaluations for LLMs attempt to measure model reasoning, factual accuracy, alignment, and safety. == History == Before the emergence of transformer-based models in 2017, some language models were considered large relative to the computational and data constraints of their time. In the early 1990s, IBM's statistical models pioneered word alignment techniques for machine translation, laying the groundwork for corpus-based language modeling. In 2001, a smoothed n-gram model, such as those employing Kneser–Ney smoothing, trained on 300 million words, achieved state-of-the-art perplexity on benchmark tests. During the 2000s, with the rise of widespread internet access, researchers began compiling massive text datasets from the web ("web as corpus") to train statistical language models. Moving beyond n-gram models, researchers started in 2000 to use neural networks as language models. Following the breakthrough of deep neural networks in image classification around 2012, similar architectures were adapted for language tasks. This shift was marked by the development of word embeddings (e.g., Word2Vec by Mikolov in 2013) and sequence-to-sequence (seq2seq) models using LSTM. In 2016, Google transitioned its translation service to neural machine translation (NMT), replacing statistical phrase-based models with deep recurrent neural networks. These early NMT systems used LSTM-based encoder-decoder architectures, as they preceded the invention of transformers. At the 2017 NeurIPS conference, Google researchers introduced the transformer architecture in their landmark paper "Attention Is All You Need". This paper's goal was to improve upon 2014 seq2seq technology, and was based mainly on the attention mechanism developed by Bahdanau et al. in 2014. The following year in 2018, BERT was introduced and quickly became "ubiquitous". Though the original transformer has both encoder and decoder blocks, BERT is an encoder-only model. Academic and research usage of BERT began to decline in 2023, following rapid improvements in the abilities of decoder-only models (such as GPT) to solve tasks via prompting. Although decoder-only GPT-1 was introduced in 2018, it was GPT-2 in 2019 that caught widespread attention because OpenAI claimed to have initially deemed it too powerful to release publicly, out of fear of malicious use. GPT-3 in 2020 went a step further and as of 2025 is available only via API with no offering of downloading the model to execute locally. But it was the consumer-facing chatbot ChatGPT in late 2022 that received extensive media coverage and public attention by 2023. The 2023 GPT-4 was praised for its increased accuracy and as a "holy grail" for its multimodal capabilities. OpenAI did not reveal the high-level architecture and the number of parameters of GPT-4. The release of ChatGPT led to an uptick in LLM usage across several research subfields of computer science, including robotics, software engineering, and societal impact work. In 2024, OpenAI released the reasoning model OpenAI o1, which generates long chains of thought before returning a final answer. Many LLMs with parameter counts comparable to those of OpenAI's GPT series have been developed. Since 2022, weights-available models have been gaining popularity, especially at first with BLOOM and LLaMA, though both have restrictions on usage and deployment. Mistral AI's open-weight models Mistral 7B and Mixtral 8x7B have a more permissive Apache License. In January 2025, DeepSeek released DeepSeek R1, a 671-billion-parameter open-weight model that performs comparably to OpenAI o1 but at a much lower price per token for users. Since 2023, many LLMs have been trained to be multimodal, having the ability to also process or generate other types of data, such as images, audio, or 3D meshes. Open-weight LLMs have become more influential since 2023. Per Vake et al. (2025), community-driven contributions to open-weight models improve their efficiency and performance via collaborative platforms such as Hugging Face. == Dataset preprocessing == === Tokenization === As machine learning algorithms process numbers rather than text, the text must be converted to numbers. In the first step, a vocabulary is decided upon, then integer indices are arbitrarily but uniquely assigned to each vocabulary entry, and finally, an embedding is associated with the integer index. Algorithms include byte-pair encoding (BPE) and WordPiece. There are also special tokens serving as control characters, such as [MASK] for masked-out token (as used in BERT), and [UNK] ("unknown") for characters not appearing in the vocabulary. Also, some special symbols are used to denote special text formatting. For example, "Ġ" denotes a preceding whitespace in RoBERTa and GPT and "##" denotes continuation of a preceding word in BERT. For example, the BPE tokenizer used by the legacy version of GPT-3 would split tokenizer: texts -> series of numerical "tokens" as Tokenization also compresses the datasets. Because LLMs generally require input to be an array that is not jagged, the shorter texts must be "padded" until they match the length of the longest one. ==== Byte-pair encoding ==== As an example, consider a tokenizer based on byte-pair encoding. In the first step, all unique characters (including blanks and punctuation marks) are treated as an initial set of n-grams (i.e. initial set of uni-grams). Successively the most frequent pair of adjacent characters is merged into a bi-gram and all instances of the pair are replaced by it. All occurrences of adjacent pairs of (previously merged) n-grams that most frequently occur together are then again merged into even lengthier n-gram, until a vocabulary of prescribed size is obtained. After a tokenizer is trained, any text can be tokenized by it, as long as it does not contain characters not appearing in the initial-set of uni-grams. === Dataset cleaning === In the context of training LLMs, datasets are typically cleaned by removing low-quality, duplicated, or toxic data. Cleaned datasets can increase training efficiency and lead to improved downstream performance. A trained LLM can be used to clean datasets for training a further LLM. With the increasing proportion of LLM-generated content on the web, data cleaning in the future may include filtering out such content. LLM-generated content can pose a problem if the content is similar to human text (making filtering difficult) but of lower quality (degrading performance of models trained on it). === Synthetic data === Training of largest language models might need more linguistic data than naturally available, or that the naturally occurring data is of insufficient quality. In these cases, synthetic data might be used. == Training == An LLM is a type of foundation model (large X model) trained on language. LLMs can be trained in different ways. In particular, GPT models are first pretrained to predict the next word on a large amount of data, before being fine-tuned. === Cost === Substantial infrastructure is necessary for training the largest models. The tendency towards larger models is visible in the list of large language models. For example, the training of GPT-2 (i.e. a 1.5-billion-parameter model) in 2019 cost $50,000, while training of the PaLM (i.e. a 540-billion-parameter model) in 2022 cost $8 million, and Megatron-Turing NLG 530B (in 2021) cost around $11 million. The qualifier "large" in "large language model" is inherently vague, as there is no definitive threshold for the number of parameters required to qualify as "large". === Fine-tuning === Before being fine-tuned, most LLMs are next-token predictors. The fine-tuning shapes the LLM's behavior via techniques like reinforcement learning from human feedback (RLHF) or constitutional AI. Instruction fine-tuning is a form of supervised learning used to teach LLMs to follow user instructions. In 2022, OpenAI demonstrated InstructGPT, a version of GPT-3 similarly fine-tuned to follow instructions. Reinforcement learning from human feedback (RLHF) involves training a reward model to predict which text humans prefer. Then, the LLM can be fine-tuned through reinforcement learning to better satisfy this reward model. Since humans typically prefer truthful, helpful and harmless answers, RLHF favors such answers. == Architecture == LLMs are generally based on the tra

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  Scale-invariant feature operator

  In the fields of computer vision and image analysis, the scale-invariant feature operator (or SFOP) is an algorithm to detect local features in images. The algorithm was published by Förstner et al. in 2009. == Algorithm == The scale-invariant feature operator (SFOP) is based on two theoretical concepts: spiral model feature operator Desired properties of keypoint detectors: Invariance and repeatability for object recognition Accuracy to support camera calibration Interpretability: Especially corners and circles, should be part of the detected keypoints (see figure). As few control parameters as possible with clear semantics Complementarity to known detectors scale-invariant corner/circle detector. == Theory == === Maximize the weight === Maximize the weight w {\displaystyle w} = 1/variance of a point p {\displaystyle p} w ( p , α , τ , σ ) = ( N ( σ ) − 2 ) λ m i n ( M ( p , α , τ , σ ) ) Ω ( p , α , τ , σ ) {\displaystyle w(\mathbf {p} ,\alpha ,\tau ,\sigma )=\left(N(\sigma )-2\right){\frac {\lambda _{min}(M(\mathbf {p} ,\alpha ,\tau ,\sigma ))}{\Omega (\mathbf {p} ,\alpha ,\tau ,\sigma )}}} comprising: 1. the image model Ω ( p , α , τ , σ ) = ∑ n = 1 N ( σ ) [ ( q n − p ) T R α ∇ T g ( q n ) ] 2 G σ ( q n − p ) = N ( σ ) t r { R α ∇ τ ∇ τ T R α T ∗ p p T G σ ( p ) } {\displaystyle {\begin{aligned}\Omega (\mathbf {p} ,\alpha ,\tau ,\sigma )&=\sum _{n=1}^{N(\sigma )}[(\mathbf {q} _{n}-\mathbf {p} )^{T}\mathbf {R} _{\alpha }\mathbf {\nabla } _{T}g(\mathbf {q} _{n})]^{2}G_{\sigma }(\mathbf {q} _{n}-\mathbf {p} )\\&=N(\sigma )\mathbf {tr} \left\{R_{\alpha }\mathbf {\nabla } _{\tau }\mathbf {\nabla } _{\tau }^{T}R_{\alpha }^{T}\mathbf {p} \mathbf {p} ^{T}G_{\sigma }(\mathbf {p} )\right\}\end{aligned}}} 2. the smaller eigenvalue of the structure tensor M ( p , α , τ , σ ) ⏟ structure tensor = G σ ( p ) ⏟ weighted summation ∗ ( R σ ∇ τ ∇ τ T R σ T ) ⏟ squared rotated gradients {\displaystyle \underbrace {M(\mathbf {p} ,\alpha ,\tau ,\sigma )} _{\text{structure tensor}}=\underbrace {G_{\sigma }(\mathbf {p} )} _{\text{weighted summation}}\underbrace {(R_{\sigma }\nabla _{\tau }\nabla _{\tau }^{T}R_{\sigma }^{T})} _{\text{squared rotated gradients}}} === Reduce the search space === Reduce the 5-dimensional search space by linking the differentiation scale τ {\displaystyle \tau } to the integration scale τ = σ / 3 {\displaystyle \tau =\sigma /3} solving for the optimal α ^ {\displaystyle {\hat {\alpha }}} using the model Ω ( α ) = a − b cos ⁡ ( 2 α − 2 α 0 ) {\displaystyle \Omega (\alpha )=a-b\cos(2\alpha -2\alpha _{0})} and determining the parameters from three angles, e. g. Ω ( 0 ∘ ) , Ω ( 60 ∘ ) , Ω ( 120 ∘ ) → a , b , α 0 → α ^ {\displaystyle \Omega (0^{\circ }),\Omega (60^{\circ }),\Omega (120^{\circ })\quad \rightarrow \quad a,b,\alpha _{0}\quad \rightarrow \quad {\hat {\alpha }}} pre-selection possible: α = 0 ∘ → junctions , α = 90 ∘ → circular features {\displaystyle \alpha =0^{\circ }\,\rightarrow \,{\mbox{junctions}},\quad \alpha =90^{\circ }\,\rightarrow \,{\mbox{circular features}}} === Filter potential keypoints === non-maxima suppression over scale, space and angle thresholding the isotropy λ 2 ( M ) {\displaystyle \lambda _{2(M)}} :eigenvalues characterize the shape of the keypoint, smallest eigenvalue has to be larger than threshold T λ {\displaystyle T_{\lambda }} derived from noise variance V ( n ) {\displaystyle V(n)} and significance level S {\displaystyle S} : T λ ( V ( n ) , τ , σ , S ) = N ( σ ) 16 π τ 4 V ( n ) χ 2 , S 2 {\displaystyle T_{\lambda }(V(n),\tau ,\sigma ,S)={\frac {N(\sigma )}{16\pi \tau ^{4}}}V(n)\chi _{2,S}^{2}} == Algorithm == == Results == === Interpretability of SFOP keypoints ===

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  Nearest neighbor search

  Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values. Formally, the nearest neighbor (NN) search problem is defined as follows: given a set S of points in a space M and a query point q ∈ M {\displaystyle q\in M} , find the closest point in S to q. Donald Knuth in volume 3 of The Art of Computer Programming (1973) called it the post-office problem, referring to an application of assigning to a residence the nearest post office. A direct generalization of this problem is a k-NN search, where we need to find the k closest points. Most commonly M is a metric space and dissimilarity is expressed as a distance metric, which is symmetric and satisfies the triangle inequality. Even more common, M is taken to be the d-dimensional vector space where dissimilarity is measured using the Euclidean distance, Manhattan distance or other distance metric. However, the dissimilarity function can be arbitrary. One example is asymmetric Bregman divergence, for which the triangle inequality does not hold. == Applications == The nearest neighbor search problem arises in numerous fields of application, including: Pattern recognition – in particular for optical character recognition Statistical classification – see k-nearest neighbor algorithm Computer vision – for point cloud registration Computational geometry – see Closest pair of points problem Cryptanalysis – for lattice problem Databases – e.g. content-based image retrieval Coding theory – see maximum likelihood decoding Semantic search Vector databases, where nearest-neighbor lookup over embeddings is used to retrieve semantically similar records Retrieval-augmented generation systems, where nearest-neighbor retrieval over embeddings is used to fetch candidate passages or documents before generation Data compression – see MPEG-2 standard Robotic sensing Recommendation systems, e.g. see Collaborative filtering Internet marketing – see contextual advertising and behavioral targeting DNA sequencing Spell checking – suggesting correct spelling Plagiarism detection Similarity scores for predicting career paths of professional athletes. Cluster analysis – assignment of a set of observations into subsets (called clusters) so that observations in the same cluster are similar in some sense, usually based on Euclidean distance Chemical similarity Sampling-based motion planning == Methods == Various solutions to the NNS problem have been proposed. The quality and usefulness of the algorithms are determined by the time complexity of queries as well as the space complexity of any search data structures that must be maintained. The informal observation usually referred to as the curse of dimensionality states that there is no general-purpose exact solution for NNS in high-dimensional Euclidean space using polynomial preprocessing and polylogarithmic search time. === Exact methods === ==== Linear search ==== The simplest solution to the NNS problem is to compute the distance from the query point to every other point in the database, keeping track of the "best so far". This algorithm, sometimes referred to as the naive approach, has a running time of O(dN), where N is the cardinality of S and d is the dimensionality of S. There are no search data structures to maintain, so the linear search has no space complexity beyond the storage of the database. Naive search can, on average, outperform space partitioning approaches on higher dimensional spaces. The absolute distance is not required for distance comparison, only the relative distance. In geometric coordinate systems the distance calculation can be sped up considerably by omitting the square root calculation from the distance calculation between two coordinates. The distance comparison will still yield identical results. ==== Space partitioning ==== Since the 1970s, the branch and bound methodology has been applied to the problem. In the case of Euclidean space, this approach encompasses spatial index or spatial access methods. Several space-partitioning methods have been developed for solving the NNS problem. Perhaps the simplest is the k-d tree, which iteratively bisects the search space into two regions containing half of the points of the parent region. Queries are performed via traversal of the tree from the root to a leaf by evaluating the query point at each split. Depending on the distance specified in the query, neighboring branches that might contain hits may also need to be evaluated. For constant dimension query time, average complexity is O(log N) in the case of randomly distributed points, worst case complexity is O(kN^(1-1/k)) Alternatively the R-tree data structure was designed to support nearest neighbor search in dynamic context, as it has efficient algorithms for insertions and deletions such as the R tree. R-trees can yield nearest neighbors not only for Euclidean distance, but can also be used with other distances. In the case of general metric space, the branch-and-bound approach is known as the metric tree approach. Particular examples include vp-tree and BK-tree methods. Using a set of points taken from a 3-dimensional space and put into a BSP tree, and given a query point taken from the same space, a possible solution to the problem of finding the nearest point-cloud point to the query point is given in the following description of an algorithm. (Strictly speaking, no such point may exist, because it may not be unique. But in practice, usually we only care about finding any one of the subset of all point-cloud points that exist at the shortest distance to a given query point.) The idea is, for each branching of the tree, guess that the closest point in the cloud resides in the half-space containing the query point. This may not be the case, but it is a good heuristic. After having recursively gone through all the trouble of solving the problem for the guessed half-space, now compare the distance returned by this result with the shortest distance from the query point to the partitioning plane. This latter distance is that between the query point and the closest possible point that could exist in the half-space not searched. If this distance is greater than that returned in the earlier result, then clearly there is no need to search the other half-space. If there is such a need, then you must go through the trouble of solving the problem for the other half space, and then compare its result to the former result, and then return the proper result. The performance of this algorithm is nearer to logarithmic time than linear time when the query point is near the cloud, because as the distance between the query point and the closest point-cloud point nears zero, the algorithm needs only perform a look-up using the query point as a key to get the correct result. === Approximation methods === An approximate nearest neighbor search algorithm is allowed to return points whose distance from the query is at most c {\displaystyle c} times the distance from the query to its nearest points. The appeal of this approach is that, in many cases, an approximate nearest neighbor is almost as good as the exact one. In particular, if the distance measure accurately captures the notion of user quality, then small differences in the distance should not matter. ==== Greedy search in proximity neighborhood graphs ==== Proximity graph methods (such as navigable small world graphs and HNSW) are considered the current state-of-the-art for the approximate nearest neighbors search. The methods are based on greedy traversing in proximity neighborhood graphs G ( V , E ) {\displaystyle G(V,E)} in which every point x i ∈ S {\displaystyle x_{i}\in S} is uniquely associated with vertex v i ∈ V {\displaystyle v_{i}\in V} . The search for the nearest neighbors to a query q in the set S takes the form of searching for the vertex in the graph G ( V , E ) {\displaystyle G(V,E)} . The basic algorithm – greedy search – works as follows: search starts from an enter-point vertex v i ∈ V {\displaystyle v_{i}\in V} by computing the distances from the query q to each vertex of its neighborhood { v j : ( v i , v j ) ∈ E } {\displaystyle \{v_{j}:(v_{i},v_{j})\in E\}} , and then finds a vertex with the minimal distance value. If the distance value between the query and the selected vertex is smaller than the one between the query and the current element, then the algorithm moves to the selected vertex, and it becomes new enter-point. The algorithm stops when it reaches a local minimum: a vertex whose neighborhood does not contain a vertex that is closer to the query than the vertex itself. The idea of proximity neighborhood graphs was exploited in multiple publications, including the seminal paper by Arya and Mount, in the VoroNet syst

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  Distributional Soft Actor Critic

  Distributional Soft Actor Critic (DSAC) is a suite of model-free off-policy reinforcement learning algorithms, tailored for learning decision-making or control policies in complex systems with continuous action spaces. Distinct from traditional methods that focus solely on expected returns, DSAC algorithms are designed to learn a Gaussian distribution over stochastic returns, called value distribution. This focus on Gaussian value distribution learning notably diminishes value overestimations, which in turn boosts policy performance. Additionally, the value distribution learned by DSAC can also be used for risk-aware policy learning. From a technical standpoint, DSAC is essentially a distributional adaptation of the well-established soft actor-critic (SAC) method. To date, the DSAC family comprises two iterations: the original DSAC-v1 and its successor, DSAC-T (also known as DSAC-v2), with the latter demonstrating superior capabilities over the Soft Actor-Critic (SAC) in Mujoco benchmark tasks. The source code for DSAC-T can be found at the following URL: Jingliang-Duan/DSAC-T. Both iterations have been integrated into an advanced, Pytorch-powered reinforcement learning toolkit named GOPS: GOPS (General Optimal control Problem Solver).

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  Contract management software

  Contract management software constitutes software and associated data management used to support contract management, contract lifecycle management, and contractor management on projects in the procurement of goods and services. It may be used together with project management software. == History == Historically, contract management was seen as a "paper-intensive" process. Early steps from the early 2000's reported by the Aberdeen Group required extensive data conversion work to enable documents to be handled electronically. With the adoption of the European Union's General Data Protection Regulation (GDPR) in 2016, companies needed to take additional steps in regards to contract management. Each data responsible entity was obliged to sign data processing agreements (DPAs) with the various vendors, who treat personal data on behalf of the data responsible. DPAs need to be regularly controlled, adjusted and renewed, which adds an extra agreement to such vendors or at least an extra DPA addendum to each agreement. By 2018, Ardent Partner's research had found that software used for automating contract management activities was being more extensively used among major companies or businesses with "Best-in-Class" procurement teams. Contract management process automation was found to be closely linked with more effective internal business collaboration, standardization and risk management. == Advantages and key functions == Using contract management software can have multiple benefits compared to manually managing paper contracts. This software can help keep track of multiple activities and can have features for automating administration, ensuring compliance, monitoring risk, running reports and triggering alerts. In addition to these types of features, contract management software systems provide a centralized repository for employees to quickly access all contracts worldwide in one place. Contract management software is produced by many companies, working on a range of scales and offering varying degrees of customizability. Basic functions should include the ability to store contract documents, track changes to contract documents, search documents for a particular criterion, send key date alerts and to report required aspects of the contract. Other functions include managing a new contract request, capturing related data, following a document through a review and approval process, and collecting digital signatures. Contract management software may also be an aid to project portfolio management and spend analysis, and may also monitor KPIs. Leading contract management software provides contract visibility, monitoring, and compliance to automate and streamline the contract lifecycle process. Contract management software which uses artificial intelligence (AI) can identify contract types based on pattern recognition. AI contracting software trains its algorithms on a set of contract data to recognize patterns and extract variables such as clauses, dates, and parties. It also offers simple prediction capabilities, by sorting through a large volume of contracts and flagging individual contracts based on specified criteria. AI software can also read contracts in multiple formats and languages, extract contract data, and provide analytics. It can reduce the risk of human error in contract drafting and review. A centralized repository provides a critical advantage allowing for all contract documents to be stored within one location. Having contracts stored in multiple locations can delay and interrupt the contracting process. == Contract risk management software (CRMS) for capital projects == Very large enterprises, such as capital expenditure (capex) projects, involve multiple parties and high risk and uncertainty. They are unlike traditional operating contracts in that they are subject to shared deadlines in unique situations. As the complexity of these unique projects increases, the relationships between parties become more important. This requires contract management software, or contract risk management software (CRMS), to become more dynamic and responsive. The terms of these capex contracts necessarily involve assumptions at the start of the process and are likely to change over the lifetime of the project lifecycle. For this reason, CRMS must be capable of recording one single instance of agreed changes to contract terms and incorporating these changes in an auditable and legally robust way. With multiple decision makers involved, CRMS should also make accountability more transparent and enable faster decisions about variation proposals.

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  VITAL (machine learning software)

  VITAL (Validating Investment Tool for Advancing Life Sciences) was a Board Management Software machine learning proprietary software developed by Aging Analytics, a company registered in Bristol (England) and dissolved in 2017. Andrew Garazha (the firm's Senior Analyst) declared that the project aimed "through iterative releases and updates to create a piece of software capable of making autonomous investment decisions." According to Nick Dyer-Witheford, VITAL 1.0 was a "basic algorithm". On 13 May 2014, Deep Knowledge Ventures, a Hong Kong venture capital firm, claimed to have appointed VITAL to its board of directors in order to prove that artificial intelligence could be an instrument for investment decision-making. The announcement received great press coverage despite the fact commentators consider this a publicity stunt. Fortune reported in 2019 that VITAL is no longer used. == Criticism == Academics and journalists viewed VITAL's board appointment with skepticism. University of Sheffield computer science professor Noel Sharkey called it "a publicity hype". Michael Osborne, a University of Oxford associate professor in machine learning, found it is "a gimmick to call that an actual board member". Simon Sharwood of The Register, wrote there is "a strong whiff of stunt and/or promotion about this". In a 2019 speech, the Chief Scientist of Australia, Alan Finkel, commented, "At the time, most of us probably dismissed Vital as a PR exercise. I admit, I used her story three years ago to get a laugh in one of my speeches." Florian Möslein, a law professor at the University of Marburg, wrote in 2018 that "Vital has widely been acknowledged as the 'world's first artificial intelligence company director'". Vice journalist Jason Koebler suggested that the software did not have any article intelligence capabilities and concluded "VITAL can’t talk, and it can’t hear, and it can’t be a real, functional executive of a company." Sharwood of The Register noted that because VITAL was not a natural person, it could not be a board member under Hong Kong's corporate governance laws. However, in a 2017 interview to The Nikkei, Dmitry Kaminskiy, managing partner of Deep Knowledge Ventures, stated that VITAL had observer status on the board and no voting rights. University of Sheffield computer science professor Noel Sharkey said of VITAL, "On first sight, it looks like a futuristic idea but on reflection it is really a little bit of publicity hype." Vice journalist Jason Koebler said "this is a gimmick" and said "There is literally nothing to suggest that VITAL has any sort of capabilities beyond any other proprietary analysis software". Michael Osborne, a University of Oxford associate professor in machine learning, found VITAL's appointment to be noncredible, saying it is "a bit of a gimmick to call that an actual board member". Osborne said that a core duty of board members to converse with each other, which the algorithm is incapable of doing, so its more likely functionality is to serve as a springboard for conversation among other board members. In a 2019 speech, the Chief Scientist of Australia, Alan Finkel, commented, "At the time, most of us probably dismissed Vital as a PR exercise. I admit, I used her story three years ago to get a laugh in one of my speeches." == Machine intelligence as board member == VITAL was created by a group of programmers employed by Aging Analytics According to Andrew Garazh, Aging Analytics Senior Analyst, VITAL was not a machine learning algorithm as the necessary datasets on investment rounds, intellectual property and clinical trial outcomes are generally not disclosed. Rather, VITAL used fuzzy logic based on 50 parameters to assess risk factors. Aging Analytics licensed the software to Deep Knowledge Ventures. It was used to help the human board members of Deep Knowledge Venture make investment decisions in biotechnology companies. For instance, it supported investments in Insilico Medicine, which creates ways for computers to help find drugs in research into aging. VITAL also supported investing in Pathway Pharmaceuticals, which uses the OncoFinder algorithm to choose and appraise cancer treatments. According to Dmitry Kaminskiy, managing partner of Deep Knowledge Ventures, the motivation for using VITAL was the large number of failed investments in the biotechnology sector and the desire to avoid investing in companies likely to fail. == Ethical and legal implications == Scholars addressed questions around the safety, privacy, accountability transparency and bias in algorithms. Writing in the philosophical journal Multitudes, the academic Ariel Kyrou raised questions about the consequences of a mistake made by an algorithm recommending a dangerous investment. He raised the hypothetical where VITAL was able to persuade the board to invest in a startup that had the facade of doing research into treatment for age-associated ills, but in actuality was run by terrorists who were raising funds. Kyrou raised a series of questions about who society would fault for VITAL's mistake. As the owner of VITAL, should Deep Knowledge Ventures be held accountable, or rather should the companies that supplied data to VITAL or the people who created VITAL be held liable? Simon Sharwood of The Register wrote that because the appointment of a software program to the board directors is not legally feasible in Hong Kong, there is "a strong whiff of stunt and/or promotion about this". Quoting a Thomson Reuters website describing Hong Kong legislation related to corporate governance, Sharwood pointed out that in Hong Kong "the board comprises all of the directors of the company" and "a director must normally be a natural person, except that a private company may have a body corporate as its director if the company is not a member of a listed group." He concluded that since VITAL cannot be considered a "natural person", it is merely a "cosmetic" appointment to the board and that "this software is no more a Board member than Caligula's horse was a senator". Sharwood further argued that corporations frequently purchase directors and officers liability insurance but that it would be practically impossible to get such insurance for VITAL. Sharwood also wrote that were VITAL to be hacked, any misinformation it outputs could be considered "false and misleading communications". In the book Research Handbook on the Law of Artificial Intelligence, Florian Mölein wrote that VITAL could not become a director as defined in Hong Kong's corporate laws, so the other directors just were approaching it as "a member of [the] board with observer status". Lin Shaowei raised concerns in a Journal of East China University of Political Science and Law article about how the software's appearance inspired a complex question about the relationship between corporate law and artificial intelligence. VITAL could be considered either a board director who has voting rights or an observer who does not. Lin said either choice raised questions about whether VITAL is subject to corporate law and who would be held accountable if VITAL recommends a choice that turns out to be damaging to the company. David Theo Goldberg in the Critical Times, a peer reviewed journal in Critical Global Theory, argues that VITAL processed a dataset to predict the most remunerative investment opportunities. Drawing his analysis on an article from Business Insider, Goldberg describes VITAL's decision-making predictiveness based "on surface pattern recognition and the identification of regularities and/or irregularities". In other words, Goldberg asserts that "the normativity of the surface" explains algorithmic knowledge of a "product" like VITAL. In Homo Deus, Yuval Noah Harari mentions VITAL as an example of the future risks that humankind faces. Harari argues that the human mind is being replaced by a world in which algorithms and data make the decisions. Specifically, it is argued that "as algorithms push humans out of the job market," executive boards driven by artificial intelligence are more likely to give priority to algorithms over the humans.

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  Log-linear model

  A log-linear model is a mathematical model that takes the form of a function whose logarithm equals a linear combination of the parameters of the model, which makes it possible to apply (possibly multivariate) linear regression. That is, it has the general form exp ⁡ ( c + ∑ i w i f i ( X ) ) {\displaystyle \exp \left(c+\sum _{i}w_{i}f_{i}(X)\right)} , in which the fi(X) are quantities that are functions of the variable X, in general a vector of values, while c and the wi stand for the model parameters. The term may specifically be used for: A log-linear plot or graph, which is a type of semi-log plot. Poisson regression for contingency tables, a type of generalized linear model. The specific applications of log-linear models are where the output quantity lies in the range 0 to ∞, for values of the independent variables X, or more immediately, the transformed quantities fi(X) in the range −∞ to +∞. This may be contrasted to logistic models, similar to the logistic function, for which the output quantity lies in the range 0 to 1. Thus the contexts where these models are useful or realistic often depends on the range of the values being modelled.

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  Yooreeka

  Yooreeka is a library for data mining, machine learning, soft computing, and mathematical analysis. The project started with the code of the book "Algorithms of the Intelligent Web". Although the term "Web" prevailed in the title, in essence, the algorithms are valuable in any software application. It covers all major algorithms and provides many examples. Yooreeka 2.x is licensed under the Apache License rather than the somewhat more restrictive LGPL (which was the license of v1.x). The library is written 100% in the Java language. == Algorithms == The following algorithms are covered: Clustering Hierarchical—Agglomerative (e.g. MST single link; ROCK) and Divisive Partitional (e.g. k-means) Classification Bayesian Decision trees Neural Networks Rule based (via Drools) Recommendations Collaborative filtering Content based Search PageRank DocRank Personalization

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  Optical sorting

  Optical sorting (sometimes called digital sorting) is the automated process of sorting solid products using cameras and/or lasers. Depending on the types of sensors used and the software-driven intelligence of the image processing system, optical sorters can recognize an object's color, size, shape, structural properties and chemical composition. The sorter compares objects to user-defined accept/reject criteria to identify and remove defective products and foreign material (FM) from the production line, or to separate product of different grades or types of materials. Optical sorters are in widespread use in the food industry worldwide, with the highest adoption in processing harvested foods such as potatoes, fruits, vegetables and nuts where it achieves non-destructive, 100 percent inspection in-line at full production volumes. The technology is also used in pharmaceutical manufacturing and nutraceutical manufacturing, tobacco processing, waste recycling and other industries. Compared to manual sorting, which is subjective and inconsistent, optical sorting helps improve product quality, maximize throughput and increase yields while reducing labor costs. == History == Optical sorting is an idea that first came out of the desire to automate industrial sorting of agricultural goods like fruits and vegetables. Before automated optical sorting technology was conceived in the 1930s, companies like Unitec were producing wooden machinery to assist in the mechanical sorting of fruit processing. In 1931, a company known as “the Electric Sorting Company” was incorporated and began the creation of the world’s first color sorters, which were being installed and used in Michigan’s bean industry by 1932. In 1937, optical sorting technology had advanced to allow for systems based on a two-color principle of selection. The next few decades saw the installation of new and improved sorting mechanisms, like gravity feed systems and the implementation of optical sorting in more agricultural industries. In the late 1960s, optical sorting began to be implemented to new industries beyond agriculture, like the sorting of ferrous and non-ferrous metals. By the 1990s, optical sorting was being used heavily in the sorting of solid wastes. With the large technological revolution happening in the late 1990s and early 2000s, optical sorters were being made more efficient via the implementation of new optical sensors, like CCD, UV, and IR cameras. Today, optical sorting is used in a wide variety of industries and, as such, is implemented with a varying selection of mechanisms to assist in that specific sorter’s task. == The sorting system == In general, optical sorters feature four major components: the feed system, the optical system, image processing software, and the separation system. The objective of the feed system is to spread products into a uniform monolayer so products are presented to the optical system evenly, without clumps, at a constant velocity. The optical system includes lights and sensors housed above and/or below the flow of the objects being inspected. The image processing system compares objects to user-defined accept/reject thresholds to classify objects and actuate the separation system. The separation system — usually compressed air for small products and mechanical devices for larger products, like whole potatoes — pinpoints objects while in-air and deflects the objects to remove into a reject chute while the good product continues along its normal trajectory. The ideal sorter to use depends on the application. Therefore, the product's characteristics and the user's objectives determine the ideal sensors, software-driven capabilities and mechanical platform. == Sensors == Optical sorters require a combination of lights and sensors to illuminate and capture images of the objects so the images can be processed. The processed images will determine if the material should be accepted or rejected. There are camera sorters, laser sorters and sorters that feature a combination of the two on one platform. Lights, cameras, lasers and laser sensors can be designed to function within visible light wavelengths as well as the infrared (IR) and ultraviolet (UV) spectrums. The optimal wavelengths for each application maximize the contrast between the objects to be separated. Cameras and laser sensors can differ in spatial resolution, with higher resolutions enabling the sorter to detect and remove smaller defects. === Cameras === Monochromatic cameras detect shades of gray from black to white and can be effective when sorting products with high-contrast defects. Sophisticated color cameras with high color resolution are capable of detecting millions of colors to better distinguish more subtle color defects. Trichromatic color cameras (also called three-channel cameras) divide light into three bands, which can include red, green and/or blue within the visible spectrum as well as IR and UV. The interaction of different materials with parts of the electromagnetic spectrum make these contrasts more evident than how they appear to the naked human eye. Coupled with intelligent software, sorters that feature cameras are capable of recognizing each object's color, size and shape; as well as the color, size, shape and location of a defect on a product. Some intelligent sorters even allow the user to define a defective product based on the total defective surface area of any given object. === Lasers === While cameras capture product information based primarily on material reflectance, lasers and their sensors are able to distinguish a material's structural properties along with their color. This structural property inspection allows lasers to detect a wide range of organic and inorganic foreign material such as insects, glass, metal, sticks, rocks and plastic; even if they are the same color as the good product. Lasers can be designed to operate within specific wavelengths of light; whether on the visible spectrum or beyond. For example, lasers can detect chlorophyll by stimulating fluorescence using specific wavelengths; which is a process that is very effective for removing foreign material from green vegetables. === Camera/laser combinations === Sorters equipped with cameras and lasers on one platform are generally capable of identifying the widest variety of attributes. Cameras are often better at recognizing color, size and shape while laser sensors identify differences in structural properties to maximize foreign material detection and removal. === Hyperspectral Imaging === Driven by the need to solve previously impossible sorting challenges, a new generation of sorters that feature multispectral and hyperspectral imaging Optical Sorters. Like trichromatic cameras, multispectral and hyperspectral cameras collect data from the electromagnetic spectrum. Unlike trichromatic cameras, which divide light into three bands, hyperspectral systems can divide light into hundreds of narrow bands over a continuous range that covers a vast portion of the electromagnetic spectrum. This opens the door for more detailed analysis that leads to a more consistent product. Using IR alone might detect some defects, but combining it with a broader range of the spectrum makes it more effective. Compared to the three data points per pixel collected by trichromatic cameras, hyperspectral cameras can collect hundreds of data points per pixel, which are combined to create a unique spectral signature (also called a fingerprint) for each object. When complemented by capable software intelligence, a hyperspectral sorter processes those fingerprints to enable sorting on the chemical composition of the product. This is an emerging area of chemometrics. == Software-driven intelligence == Once the sensors capture the object's response to the energy source, image processing is used to manipulate the raw data. The image processing extracts and categorizes information about specific features. The user then defines accept/reject thresholds that are used to determine what is good and bad in the raw data flow. The art and science of image processing lies in developing algorithms that maximize the effectiveness of the sorter while presenting a simple user-interface to the operator. Object-based recognition is a classic example of software-driven intelligence. It allows the user to define a defective product based on where a defect lies on the product and/or the total defective surface area of an object. It offers more control in defining a wider range of defective products. When used to control the sorter's ejection system, it can improve the accuracy of ejecting defective products. This improves product quality and increases yields. New software-driven capabilities are constantly being developed to address the specific needs of various applications. As computing hardware becomes more powerful, new software-driven advancements become possible. Some of these advancements enhance the effectivene

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  Multispectral pattern recognition

  Multispectral remote sensing is the collection and analysis of reflected, emitted, or back-scattered energy from an object or an area of interest in multiple bands of regions of the electromagnetic spectrum (Jensen, 2005). Subcategories of multispectral remote sensing include hyperspectral, in which hundreds of bands are collected and analyzed, and ultraspectral remote sensing where many hundreds of bands are used (Logicon, 1997). The main purpose of multispectral imaging is the potential to classify the image using multispectral classification. This is a much faster method of image analysis than is possible by human interpretation. == Multispectral remote sensing systems == Remote sensing systems gather data via instruments typically carried on satellites in orbit around the Earth. The remote sensing scanner detects the energy that radiates from the object or area of interest. This energy is recorded as an analog electrical signal and converted into a digital value though an A-to-D conversion. There are several multispectral remote sensing systems that can be categorized in the following way: === Multispectral imaging using discrete detectors and scanning mirrors === Landsat Multispectral Scanner (MSS) Landsat Thematic Mapper (TM) NOAA Geostationary Operational Environmental Satellite (GOES) NOAA Advanced Very High Resolution Radiometer (AVHRR) NASA and ORBIMAGE, Inc., Sea-viewing Wide field-of-view Sensor (SeaWiFS) Daedalus, Inc., Aircraft Multispectral Scanner (AMS) NASA Airborne Terrestrial Applications Sensor (ATLAS) === Multispectral imaging using linear arrays === SPOT 1, 2, and 3 High Resolution Visible (HRV) sensors and Spot 4 and 5 High Resolution Visible Infrared (HRVIR) and vegetation sensor Indian Remote Sensing System (IRS) Linear Imaging Self-scanning Sensor (LISS) Space Imaging, Inc. (IKONOS) Digital Globe, Inc. (QuickBird) ORBIMAGE, Inc. (OrbView-3) ImageSat International, Inc. (EROS A1) NASA Terra Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) NASA Terra Multiangle Imaging Spectroradiometer (MISR) === Imaging spectrometry using linear and area arrays === NASA Jet Propulsion Laboratory Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) Compact Airborne Spectrographic Imager 3 (CASI 3) NASA Terra Moderate Resolution Imaging Spectrometer (MODIS) NASA Earth Observer (EO-1) Advanced Land Imager (ALI), Hyperion, and LEISA Atmospheric Corrector (LAC) === Satellite analog and digital photographic systems === Russian SPIN-2 TK-350, and KVR-1000 NASA Space Shuttle and International Space Station Imagery == Multispectral classification methods == A variety of methods can be used for the multispectral classification of images: Algorithms based on parametric and nonparametric statistics that use ratio-and interval-scaled data and nonmetric methods that can also incorporate nominal scale data (Duda et al., 2001), Supervised or unsupervised classification logic, Hard or soft (fuzzy) set classification logic to create hard or fuzzy thematic output products, Per-pixel or object-oriented classification logic, and Hybrid approaches == Supervised classification == In this classification method, the identity and location of some of the land-cover types are obtained beforehand from a combination of fieldwork, interpretation of aerial photography, map analysis, and personal experience. The analyst would locate sites that have similar characteristics to the known land-cover types. These areas are known as training sites because the known characteristics of these sites are used to train the classification algorithm for eventual land-cover mapping of the remainder of the image. Multivariate statistical parameters (means, standard deviations, covariance matrices, correlation matrices, etc.) are calculated for each training site. All pixels inside and outside of the training sites are evaluated and allocated to the class with the more similar characteristics. === Classification scheme === The first step in the supervised classification method is to identify the land-cover and land-use classes to be used. Land-cover refers to the type of material present on the site (e.g. water, crops, forest, wet land, asphalt, and concrete). Land-use refers to the modifications made by people to the land cover (e.g. agriculture, commerce, settlement). All classes should be selected and defined carefully to properly classify remotely sensed data into the correct land-use and/or land-cover information. To achieve this purpose, it is necessary to use a classification system that contains taxonomically correct definitions of classes. If a hard classification is desired, the following classes should be used: Mutually exclusive: there is not any taxonomic overlap of any classes (i.e., rain forest and evergreen forest are distinct classes). Exhaustive: all land-covers in the area have been included. Hierarchical: sub-level classes (e.g., single-family residential, multiple-family residential) are created, allowing that these classes can be included in a higher category (e.g., residential). Some examples of hard classification schemes are: American Planning Association Land-Based Classification System United States Geological Survey Land-use/Land-cover Classification System for Use with Remote Sensor Data U.S. Department of the Interior Fish and Wildlife Service U.S. National Vegetation and Classification System International Geosphere-Biosphere Program IGBP Land Cover Classification System === Training sites === Once the classification scheme is adopted, the image analyst may select training sites in the image that are representative of the land-cover or land-use of interest. If the environment where the data was collected is relatively homogeneous, the training data can be used. If different conditions are found in the site, it would not be possible to extend the remote sensing training data to the site. To solve this problem, a geographical stratification should be done during the preliminary stages of the project. All differences should be recorded (e.g. soil type, water turbidity, crop species, etc.). These differences should be recorded on the imagery and the selection training sites made based on the geographical stratification of this data. The final classification map would be a composite of the individual stratum classifications. After the data are organized in different training sites, a measurement vector is created. This vector would contain the brightness values for each pixel in each band in each training class. The mean, standard deviation, variance-covariance matrix, and correlation matrix are calculated from the measurement vectors. Once the statistics from each training site are determined, the most effective bands for each class should be selected. The objective of this discrimination is to eliminate the bands that can provide redundant information. Graphical and statistical methods can be used to achieve this objective. Some of the graphic methods are: Bar graph spectral plots Cospectral mean vector plots Feature space plots Cospectral parallelepiped or ellipse plots === Classification algorithm === The last step in supervised classification is selecting an appropriate algorithm. The choice of a specific algorithm depends on the input data and the desired output. Parametric algorithms are based on the fact that the data is normally distributed. If the data is not normally distributed, nonparametric algorithms should be used. The more common nonparametric algorithms are: One-dimensional density slicing Parallelipiped Minimum distance Nearest-neighbor Expert system analysis Convolutional neural network == Unsupervised classification == Unsupervised classification (also known as clustering) is a method of partitioning remote sensor image data in multispectral feature space and extracting land-cover information. Unsupervised classification require less input information from the analyst compared to supervised classification because clustering does not require training data. This process consists in a series of numerical operations to search for the spectral properties of pixels. From this process, a map with m spectral classes is obtained. Using the map, the analyst tries to assign or transform the spectral classes into thematic information of interest (i.e. forest, agriculture, urban). This process may not be easy because some spectral clusters represent mixed classes of surface materials and may not be useful. The analyst has to understand the spectral characteristics of the terrain to be able to label clusters as a specific information class. There are hundreds of clustering algorithms. Two of the most conceptually simple algorithms are the chain method and the ISODATA method. === Chain method === The algorithm used in this method operates in a two-pass mode (it passes through the multispectral dataset two times. In the first pass, the program reads through the dataset and sequentially builds clusters (groups of p

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  Win–stay, lose–switch

  In psychology, game theory, statistics, and machine learning, win–stay, lose–switch (also win–stay, lose–shift or Pavlov, named after Ivan Pavlov) is a heuristic learning strategy used to model learning in decision situations. It was first invented as an improvement over randomization in bandit problems. It was later applied to the prisoner's dilemma in order to model the evolution of altruism. In most versions, it starts either with a cooperate, then proceeds as always, or starts with a "probe" of cooperate-defect-cooperate to determine the other player's strategy. A mutual cooperation is regarded as a win. The learning rule bases its decision only on the outcome of the previous play. Outcomes are divided into successes (wins) and failures (losses). If the play on the previous round resulted in a success, then the agent plays the same strategy on the next round. Alternatively, if the play resulted in a failure the agent switches to another action. A large-scale empirical study of players of the game rock, paper, scissors shows that a variation of this strategy is adopted by real-world players of the game, instead of the Nash equilibrium strategy of choosing entirely at random between the three options.

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  Expectation–maximization algorithm

  In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step. It can be used, for example, to estimate a mixture of gaussians, or to solve the multiple linear regression problem. == History == The EM algorithm was explained and given its name in a classic 1977 paper by Arthur Dempster, Nan Laird, and Donald Rubin. They pointed out that the method had been "proposed many times in special circumstances" by earlier authors. One of the earliest is the gene-counting method for estimating allele frequencies by Cedric Smith. Another was proposed by H.O. Hartley in 1958, and Hartley and Hocking in 1977, from which many of the ideas in the Dempster–Laird–Rubin paper originated. Another one by S.K Ng, Thriyambakam Krishnan and G.J McLachlan in 1977. Hartley's ideas can be broadened to any grouped discrete distribution. A very detailed treatment of the EM method for exponential families was published by Rolf Sundberg in his thesis and several papers, following his collaboration with Per Martin-Löf and Anders Martin-Löf. The Dempster–Laird–Rubin paper in 1977 generalized the method and sketched a convergence analysis for a wider class of problems. The Dempster–Laird–Rubin paper established the EM method as an important tool of statistical analysis. See also Meng and van Dyk (1997). The convergence analysis of the Dempster–Laird–Rubin algorithm was flawed and a correct convergence analysis was published by C. F. Jeff Wu in 1983. Wu's proof established the EM method's convergence also outside of the exponential family, as claimed by Dempster–Laird–Rubin. == Introduction == The EM algorithm is used to find (local) maximum likelihood parameters of a statistical model in cases where the equations cannot be solved directly. Typically these models involve latent variables in addition to unknown parameters and known data observations. That is, either missing values exist among the data, or the model can be formulated more simply by assuming the existence of further unobserved data points. For example, a mixture model can be described more simply by assuming that each observed data point has a corresponding unobserved data point, or latent variable, specifying the mixture component to which each data point belongs. Finding a maximum likelihood solution typically requires taking the derivatives of the likelihood function with respect to all the unknown values, the parameters and the latent variables, and simultaneously solving the resulting equations. In statistical models with latent variables, this is usually impossible. Instead, the result is typically a set of interlocking equations in which the solution to the parameters requires the values of the latent variables and vice versa, but substituting one set of equations into the other produces an unsolvable equation. The EM algorithm proceeds from the observation that there is a way to solve these two sets of equations numerically. One can simply pick arbitrary values for one of the two sets of unknowns, use them to estimate the second set, then use these new values to find a better estimate of the first set, and then keep alternating between the two until the resulting values both converge to fixed points. It's not obvious that this will work, but it can be proven in this context. Additionally, it can be proven that the derivative of the likelihood is (arbitrarily close to) zero at that point, which in turn means that the point is either a local maximum or a saddle point. In general, multiple maxima may occur, with no guarantee that the global maximum will be found. Some likelihoods also have singularities in them, i.e., nonsensical maxima. For example, one of the solutions that may be found by EM in a mixture model involves setting one of the components to have zero variance and the mean parameter for the same component to be equal to one of the data points. == Description == === The symbols === Given the statistical model which generates a set X {\displaystyle \mathbf {X} } of observed data, a set of unobserved latent data or missing values Z {\displaystyle \mathbf {Z} } , and a vector of unknown parameters θ {\displaystyle {\boldsymbol {\theta }}} , along with a likelihood function L ( θ ; X , Z ) = p ( X , Z ∣ θ ) {\displaystyle L({\boldsymbol {\theta }};\mathbf {X} ,\mathbf {Z} )=p(\mathbf {X} ,\mathbf {Z} \mid {\boldsymbol {\theta }})} , the maximum likelihood estimate (MLE) of the unknown parameters is determined by maximizing the marginal likelihood of the observed data L ( θ ; X ) = p ( X ∣ θ ) = ∫ p ( X , Z ∣ θ ) d Z = ∫ p ( X ∣ Z , θ ) p ( Z ∣ θ ) d Z {\displaystyle {\begin{aligned}L({\boldsymbol {\theta }};\mathbf {X} )=p(\mathbf {X} \mid {\boldsymbol {\theta }})&=\int p(\mathbf {X} ,\mathbf {Z} \mid {\boldsymbol {\theta }})\,d\mathbf {Z} \\&=\int p(\mathbf {X} \mid \mathbf {Z} ,{\boldsymbol {\theta }})p(\mathbf {Z} \mid {\boldsymbol {\theta }})\,d\mathbf {Z} \end{aligned}}} However, this quantity is often intractable since Z {\displaystyle \mathbf {Z} } is unobserved and the distribution of Z {\displaystyle \mathbf {Z} } is unknown before attaining θ {\displaystyle {\boldsymbol {\theta }}} . === The EM algorithm === The EM algorithm seeks to find the maximum likelihood estimate of the marginal likelihood by iteratively applying these two steps: More succinctly, we can write it as one equation: θ ( t + 1 ) = arg ⁡ max θ ⁡ E Z ∼ p ( ⋅ | X , θ ( t ) ) ⁡ [ log ⁡ p ( X , Z | θ ) ] {\displaystyle {\boldsymbol {\theta }}^{(t+1)}=\mathop {\arg \max } _{\boldsymbol {\theta }}\operatorname {E} _{\mathbf {Z} \sim p(\cdot |\mathbf {X} ,{\boldsymbol {\theta }}^{(t)})}\left[\log p(\mathbf {X} ,\mathbf {Z} |{\boldsymbol {\theta }})\right]\,} === Interpretation of the variables === The typical models to which EM is applied use Z {\displaystyle \mathbf {Z} } as a latent variable indicating membership in one of a set of groups: The observed data points X {\displaystyle \mathbf {X} } may be discrete (taking values in a finite or countably infinite set) or continuous (taking values in an uncountably infinite set). Associated with each data point may be a vector of observations. The missing values (aka latent variables) Z {\displaystyle \mathbf {Z} } are discrete, drawn from a fixed number of values, and with one latent variable per observed unit. The parameters are continuous, and are of two kinds: Parameters that are associated with all data points, and those associated with a specific value of a latent variable (i.e., associated with all data points whose corresponding latent variable has that value). However, it is possible to apply EM to other sorts of models. The motivation is as follows. If the value of the parameters θ {\displaystyle {\boldsymbol {\theta }}} is known, usually the value of the latent variables Z {\displaystyle \mathbf {Z} } can be found by maximizing the log-likelihood over all possible values of Z {\displaystyle \mathbf {Z} } , either simply by iterating over Z {\displaystyle \mathbf {Z} } or through an algorithm such as the Viterbi algorithm for hidden Markov models. Conversely, if we know the value of the latent variables Z {\displaystyle \mathbf {Z} } , we can find an estimate of the parameters θ {\displaystyle {\boldsymbol {\theta }}} fairly easily, typically by simply grouping the observed data points according to the value of the associated latent variable and averaging the values, or some function of the values, of the points in each group. This suggests an iterative algorithm, in the case where both θ {\displaystyle {\boldsymbol {\theta }}} and Z {\displaystyle \mathbf {Z} } are unknown: First, initialize the parameters θ {\displaystyle {\boldsymbol {\theta }}} to some random values. Compute the probability of each possible value of ⁠ Z {\displaystyle \mathbf {Z} } ⁠, given ⁠ θ {\displaystyle {\boldsymbol {\theta }}} ⁠. Then, use the just-computed values of Z {\displaystyle \mathbf {Z} } to compute a better estimate for the parameters ⁠ θ {\displaystyle {\boldsymbol {\theta }}} ⁠. Iterate steps 2 and 3 until convergence. The algorithm as just described monotonically approaches a local minimum of the cost function. == Properties == Although an EM iteration does increase the observed data (i.e., marginal) likelihood function, no guarantee exists that the sequence converges to a maximum likelihood estimator. For multimodal distributions, this means that an EM algorithm may co

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  Predictive text

  Predictive text is an input technology used where one key or button represents many letters, such as on the physical numeric keypads of mobile phones and in accessibility technologies. Each key press results in a prediction rather than repeatedly sequencing through the same group of "letters" it represents, in the same, invariable order. Predictive text could allow for an entire word to be input by a single keypress. Predictive text makes efficient use of fewer device keys to input writing into a text message, an e-mail, an address book, a calendar, and the like. The most widely used, general, predictive text systems are T9, iTap, eZiText, and LetterWise/WordWise. There are many ways to build a device that predicts text, but all predictive text systems have initial linguistic settings that offer predictions that are re-prioritized to adapt to each user. This learning adapts, by way of the device memory, to a user's disambiguating feedback that results in corrective key presses, such as pressing a "next" key to get to the intention. Most predictive text systems have a user database to facilitate this process. Theoretically the number of keystrokes required per desired character in the finished writing is, on average, comparable to using a keyboard. This is approximately true provided that all words used are in its database, punctuation is ignored, and no input mistakes are made when typing or spelling. The theoretical keystrokes per character, KSPC, of a keyboard is KSPC=1.00, and of multi-tap is KSPC=2.03. Eatoni's LetterWise is a predictive multi-tap hybrid, which when operating on a standard telephone keypad achieves KSPC=1.15 for English. The choice of which predictive text system is the best to use involves matching the user's preferred interface style, the user's level of learned ability to operate predictive text software, and the user's efficiency goal. There are various levels of risk in predictive text systems, versus multi-tap systems, because the predicted text that is automatically written provides the speed and mechanical efficiency benefit, which, if the user is not careful to review, results in transmitting misinformation. Predictive text systems take time to learn to use well, and so generally, a device's system has user options to set up the choice of multi-tap or any one of several schools of predictive text methods. == Background == Short message service (SMS) permits a mobile phone user to send text messages (also called messages, SMSes, texts, and txts) as a short message. The most common system of SMS text input is referred to as "multi-tap". Using multi-tap, a key is pressed multiple times to access the list of letters on that key. For instance, pressing the "2" key once displays an "a", twice displays a "b" and three times displays a "c". To enter two successive letters that are on the same key, the user must either pause or hit a "next" button. A user can type by pressing an alphanumeric keypad without looking at the electronic equipment display. Thus, multi-tap is easy to understand and can be used without any visual feedback. However, multi-tap is not very efficient, requiring potentially many keystrokes to enter a single letter. In ideal predictive text entry, all words used are in the dictionary, punctuation is ignored, no spelling mistakes are made, and no typing mistakes are made. The ideal dictionary would include all slang, proper nouns, abbreviations, URLs, foreign-language words and other user-unique words. This ideal circumstance gives predictive text software a reduction in the number of key strokes a user is required to enter a word. The user presses the number corresponding to each letter. As long as the word exists in the predictive text dictionary or is correctly disambiguated by non-dictionary systems, it will appear. For instance, pressing "4663" will typically be interpreted as the word good, provided that a linguistic database in English is currently in use, though alternatives such as home, hood and hoof are also valid interpretations of the sequence of key strokes. The most widely used systems of predictive text are Tegic's T9, Motorola's iTap, and the Eatoni Ergonomics' LetterWise and WordWise. T9 and iTap use dictionaries, but Eatoni Ergonomics' products use a disambiguation process, a set of statistical rules to recreate words from keystroke sequences. All predictive text systems require a linguistic database for every supported input language. == Dictionary vs. non-dictionary systems == Traditional disambiguation works by referencing a dictionary of commonly used words, though Eatoni offers a dictionaryless disambiguation system. In dictionary-based systems, as the user presses the number buttons, an algorithm searches the dictionary for a list of possible words that match the keypress combination and offers up the most probable choice. The user can then confirm the selection and move on, or use a key to cycle through the possible combinations. A non-dictionary system constructs words and other sequences of letters from the statistics of word parts. To attempt predictions of the intended result of keystrokes not yet entered, disambiguation may be combined with a word completion facility. Either system (disambiguation or predictive) may include a user database, which can be further classified as a "learning" system when words or phrases are entered into the user database without direct user intervention. The user database is for storing words or phrases that are not well disambiguated by the pre-supplied database. Some disambiguation systems further attempt to correct spelling, format text or perform other automatic rewrites, with the risky effect of either enhancing or frustrating user efforts to enter text. == History == The predictive text and autocomplete technology was invented out of necessities by Chinese scientists and linguists in the 1950s to solve the input inefficiency of the Chinese typewriter, as the typing process involved finding and selecting thousands of logographic characters on a tray, drastically slowing down the word processing speed. The actuating keys of the Chinese typewriter created by Lin Yutang in the 1940s included suggestions for the characters following the one selected. In 1951, the Chinese typesetter Zhang Jiying arranged Chinese characters in associative clusters, a precursor of modern predictive text entry, and broke speed records by doing so. Predictive entry of text from a telephone keypad has been known at least since the 1970s (Smith and Goodwin, 1971). Predictive text was mainly used to look up names in directories over the phone until mobile phone text messaging came into widespread use. == Example == On a typical phone keypad, if users wished to type the in a "multi-tap" keypad entry system, they would need to: Press 8 (tuv) once to select t. Press 4 (ghi) twice to select h. Press 3 (def) twice to select e. Meanwhile, in a phone with predictive text, they need only: Press 8 once to select the (tuv) group for the first character. Press 4 once to select the (ghi) group for the second character. Press 3 once to select the (def) group for the third character. The system updates the display as each keypress is entered, to show the most probable entry. In this example, prediction reduced the number of button presses from five to three. The effect is even greater with longer words and those composed of letters later in each key's sequence. A dictionary-based predictive system is based on the hope that the desired word is in the dictionary. That hope may be misplaced if the word differs in any way from common usage—in particular, if the word is not spelled or typed correctly, is slang, or is a proper noun. In these cases, some other mechanism must be used to enter the word. Furthermore, the simple dictionary approach fails with agglutinative languages, where a single word does not necessarily represent a single semantic entity. == Companies and products == Predictive text is developed and marketed in a variety of competing products, such as Nuance Communications's T9. Other products include Motorola's iTap; Eatoni Ergonomic's LetterWise (character, rather than word-based prediction); WordWise (word-based prediction without a dictionary); EQ3 (a QWERTY-like layout compatible with regular telephone keypads); Prevalent Devices's Phraze-It; Xrgomics' TenGO (a six-key reduced QWERTY keyboard system); Adaptxt (considers language, context, grammar and semantics); Lightkey (a predictive typing software for Windows); Clevertexting (statistical nature of the language, dictionaryless, dynamic key allocation); and Oizea Type (temporal ambiguity); Intelab's Tauto; WordLogic's Intelligent Input Platform™ (patented, layer-based advanced text prediction, includes multi-language dictionary, spell-check, built-in Web search); Google's Gboard. == Textonyms == Words produced by the same combination of keypresses have been called "textonyms"; also "txtonyms"; or "T9o

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  Triplet loss

  Triplet loss is a machine learning loss function widely used in one-shot learning, a setting where models are trained to generalize effectively from limited examples. It was conceived by Google researchers for their prominent FaceNet algorithm for face detection. Triplet loss is designed to support metric learning. Namely, to assist training models to learn an embedding (mapping to a feature space) where similar data points are closer together and dissimilar ones are farther apart, enabling robust discrimination across varied conditions. In the context of face detection, data points correspond to images. == Definition == The loss function is defined using triplets of training points of the form ( A , P , N ) {\displaystyle (A,P,N)} . In each triplet, A {\displaystyle A} (called an "anchor point") denotes a reference point of a particular identity, P {\displaystyle P} (called a "positive point") denotes another point of the same identity in point A {\displaystyle A} , and N {\displaystyle N} (called a "negative point") denotes a point of an identity different from the identity in point A {\displaystyle A} and P {\displaystyle P} . Let x {\displaystyle x} be some point and let f ( x ) {\displaystyle f(x)} be the embedding of x {\displaystyle x} in the finite-dimensional Euclidean space. It shall be assumed that the L2-norm of f ( x ) {\displaystyle f(x)} is unity (the L2 norm of a vector X {\displaystyle X} in a finite dimensional Euclidean space is denoted by ‖ X ‖ {\displaystyle \Vert X\Vert } .) We assemble m {\displaystyle m} triplets of points from the training dataset. The goal of training here is to ensure that, after learning, the following condition (called the "triplet constraint") is satisfied by all triplets ( A ( i ) , P ( i ) , N ( i ) ) {\displaystyle (A^{(i)},P^{(i)},N^{(i)})} in the training data set: ‖ f ( A ( i ) ) − f ( P ( i ) ) ‖ 2 2 + α < ‖ f ( A ( i ) ) − f ( N ( i ) ) ‖ 2 2 {\displaystyle \Vert f(A^{(i)})-f(P^{(i)})\Vert _{2}^{2}+\alpha <\Vert f(A^{(i)})-f(N^{(i)})\Vert _{2}^{2}} The variable α {\displaystyle \alpha } is a hyperparameter called the margin, and its value must be set manually. In the FaceNet system, its value was set as 0.2. Thus, the full form of the function to be minimized is the following: L = ∑ i = 1 m max ( ‖ f ( A ( i ) ) − f ( P ( i ) ) ‖ 2 2 − ‖ f ( A ( i ) ) − f ( N ( i ) ) ‖ 2 2 + α , 0 ) {\displaystyle L=\sum _{i=1}^{m}\max {\Big (}\Vert f(A^{(i)})-f(P^{(i)})\Vert _{2}^{2}-\Vert f(A^{(i)})-f(N^{(i)})\Vert _{2}^{2}+\alpha ,0{\Big )}} == Intuition == A baseline for understanding the effectiveness of triplet loss is the contrastive loss, which operates on pairs of samples (rather than triplets). Training with the contrastive loss pulls embeddings of similar pairs closer together, and pushes dissimilar pairs apart. Its pairwise approach is greedy, as it considers each pair in isolation. Triplet loss innovates by considering relative distances. Its goal is that the embedding of an anchor (query) point be closer to positive points than to negative points (also accounting for the margin). It does not try to further optimize the distances once this requirement is met. This is approximated by simultaneously considering two pairs (anchor-positive and anchor-negative), rather than each pair in isolation. == Triplet "mining" == One crucial implementation detail when training with triplet loss is triplet "mining", which focuses on the smart selection of triplets for optimization. This process adds an additional layer of complexity compared to contrastive loss. A naive approach to preparing training data for the triplet loss involves randomly selecting triplets from the dataset. In general, the set of valid triplets of the form ( A ( i ) , P ( i ) , N ( i ) ) {\displaystyle (A^{(i)},P^{(i)},N^{(i)})} is very large. To speed-up training convergence, it is essential to focus on challenging triplets. In the FaceNet paper, several options were explored, eventually arriving at the following. For each anchor-positive pair, the algorithm considers only semi-hard negatives. These are negatives that violate the triplet requirement (i.e, are "hard"), but lie farther from the anchor than the positive (not too hard). Restated, for each A ( i ) {\displaystyle A^{(i)}} and P ( i ) {\displaystyle P^{(i)}} , they seek N ( i ) {\displaystyle N^{(i)}} such that: The rationale for this design choice is heuristic. It may appear puzzling that the mining process neglects "very hard" negatives (i.e., closer to the anchor than the positive). Experiments conducted by the FaceNet designers found that this often leads to a convergence to degenerate local minima. Triplet mining is performed at each training step, from within the sample points contained in the training batch (this is known as online mining), after embeddings were computed for all points in the batch. While ideally the entire dataset could be used, this is impractical in general. To support a large search space for triplets, the FaceNet authors used very large batches (1800 samples). Batches are constructed by selecting a large number of same-category sample points (40), and randomly selected negatives for them. == Extensions == Triplet loss has been extended to simultaneously maintain a series of distance orders by optimizing a continuous relevance degree with a chain (i.e., ladder) of distance inequalities. This leads to the Ladder Loss, which has been demonstrated to offer performance enhancements of visual-semantic embedding in learning to rank tasks. In Natural Language Processing, triplet loss is one of the loss functions considered for BERT fine-tuning in the SBERT architecture. Other extensions involve specifying multiple negatives (multiple negatives ranking loss).

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  Structured kNN

  Structured k-nearest neighbours (SkNN) is a machine learning algorithm that generalizes k-nearest neighbors (k-NN). k-NN supports binary classification, multiclass classification, and regression, whereas SkNN allows training of a classifier for general structured output. For instance, a data sample might be a natural language sentence, and the output could be an annotated parse tree. Training a classifier consists of showing many instances of ground truth sample-output pairs. After training, the SkNN model is able to predict the corresponding output for new, unseen sample instances; that is, given a natural language sentence, the classifier can produce the most likely parse tree. == Training == As a training set, SkNN accepts sequences of elements with class labels. The type of element does not matter; the only requirement is a defined metric function that gives a distance between each pair of elements of a set. SkNN is based on idea of creating a graph, with each node representing a class label. There is an edge between a pair of nodes if there is a sequence of two elements in the training set with corresponding classes. The first step of SkNN training is the construction of such a graph from training sequences. There are two special nodes in the graph corresponding to sentence beginnings and ends: if a sequence starts with class C, the edge between node START and node C should be created. Like regular k-NN, the second part of SkNN training consists of storing the elements of a training sequence in a certain way. Each element of the training sequences is stored in the node related to the class of the previous element in the sequence. Every first element is stored in the START node. == Inference == Labelling input sequences by SkNN consists of finding the sequence of transitions in the graph, starting from node START. Each transition corresponds to a single element of the input sequence. As a result, the label of each element is determined as the target node label of the transition. The cost of the path is defined as the sum of all transitions, with the cost of transition from node A to node B being the distance from the current input sequence element to the nearest element of class B, stored in node A. Determining an optimal path may be performed using a modified Viterbi algorithm (where the sum of the distances is minimized, unlike the original algorithm which maximizes the product of probabilities).

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