RevoScaleR

RevoScaleR is a machine learning package in R created by Microsoft. It is available as part of Machine Learning Server, Microsoft R Client, and Machine Learning Services in Microsoft SQL Server 2016. The package contains functions for creating linear model, logistic regression, random forest, decision tree and boosted decision tree, and K-means, in addition to some summary functions for inspecting and visualizing data. It has a Python package counterpart called revoscalepy. Another closely related package is MicrosoftML, which contains machine learning algorithms that RevoScaleR does not have, such as neural network and SVM. In June 2021, Microsoft announced to open source the RevoScaleR and revoscalepy packages, making them freely available under the MIT License. == Concepts == Many R packages are designed to analyze data that can fit in the memory of the machine and usually do not make use of parallel processing. RevoScaleR was designed to address these limitations. The functions in RevoScaleR orientate around three main abstraction concepts that users can specify to process large amount of data that might not fit in memory and exploit parallel resources to speed up the analysis. === Compute Contexts === A compute context refers to the location where the computation on the data happens. It could be "local" (on the client machine) or "remote" (on a data platform such as a SQL server, or Spark). Pushing the computation to a remote server allows people to take advantage of the greater compute resources that a remote machine may have. If the data being analyzed reside on the same machine, using a remote compute context also removes the need to pull data across the network onto the client machine. === Data source === Data source defines where the data comes from. There are various data sources available in RevoScaleR, such as text data, Xdf data, in-SQL data, and a spark dataframe. People can wrap their data in a data source object and use that as run analytics in different compute context. Different data sources are available in different compute context. For example, if the compute context is set to SQL server, then the only data source one can use would be an in-SQL data source. === Analytics === Analytic functions in RevoScaleR takes in data source object, a compute context, and the other parameters needed to build the specific model, such as formula for the logistic regression or the number of trees in a decision tree. In addition to those parameters, one can also specify the level of parallelism, such as the size of the data chunk for each process or number of processes to build the model. However, parallelism is only available in non-express edition. == Limitations == The package is mostly meant to be used with a SQL server or other remote machines. To fully leverage the abstractions it uses to process a large dataset, one needs a remote server and non-Express free edition of the package. It cannot be easily installed such as by running "install.packages("RevoScaleR")" like most open source R packages. It's available only through Microsoft R Client, a distribution of R for data science, or Microsoft Machine Learning Server (stand-alone with no SQL server attached), or Microsoft Machine Learning Services (a SQL server services). However, one can still use the analytics functions in an Express, free version of the package.

Moral outsourcing

Moral outsourcing is the placing of responsibility for ethical decision-making onto external entities, often algorithms. The term is often used in discussions of computer science and algorithmic fairness, but it can apply to any situation in which one appeals to outside agents in order to absolve themselves of responsibility for their actions. In this context, moral outsourcing specifically refers to the tendency of society to blame technology, rather than its creators or users, for any harm it may cause. == Definition == The term "moral outsourcing" was first coined by Dr. Rumman Chowdhury, a data scientist concerned with the overlap between artificial intelligence and social issues. Chowdhury used the term to describe looming fears of a so-called “Fourth Industrial Revolution” following the rise of artificial intelligence. Moral outsourcing is often applied by technologists to shrink away from their part in building offensive products. In her TED Talk, Chowdhury gives the example of a creator excusing their work by saying they were simply doing their job. This is a case of moral outsourcing and not taking ownership for the consequences of creation. When it comes to AI, moral outsourcing allows for creators to decide when the machine is human and when it is a computer - shifting the blame and responsibility of moral plights off of the technologists and onto the technology. Conversations around AI and bias and its impacts require accountability to bring change. It is difficult to address these biased systems if their creators use moral outsourcing to avoid taking any responsibility for the issue. One example of moral outsourcing is the anger that is directed at machines for “taking jobs away from humans” rather than companies for employing that technology and jeopardizing jobs in the first place. The term "moral outsourcing" refers to the concept of outsourcing, or enlisting an external operation to complete specific work for another organization. In the case of moral outsourcing, the work of resolving moral dilemmas or making choices according to an ethical code is supposed to be conducted by another entity. == Real-world applications == In the medical field, AI is increasingly involved in decision-making processes about which patients to treat, and how to treat them. The responsibility of the doctor to make informed decisions about what is best for their patients is outsourced to an algorithm. Sympathy is also noted to be an important part of medical practice; an aspect that artificial intelligence, glaringly, is missing. This form of moral outsourcing is a major concern in the medical community. Another field of technology in which moral outsourcing is frequently brought up is autonomous vehicles. California Polytechnic State University professor Keith Abney proposed an example scenario: "Suppose we have some [troublemaking] teenagers, and they see an autonomous vehicle, they drive right at it. They know the autonomous vehicle will swerve off the road and go off a cliff, but should it?" The decision of whether to sacrifice the autonomous vehicle (and any passengers inside) or the vehicle coming at it will be written into the algorithms defining the car's behavior. In the case of moral outsourcing, the responsibility of any damage caused by an accident may be attributed to the autonomous vehicle itself, rather than the creators who wrote the protocol the vehicle will use to "decide" what to do. Moral outsourcing is also used to delegate the consequences of predictive policing algorithms to technology, rather than the creators or the police. There are many ethical concerns with predictive policing due to the fact that it results in the over-policing of low income and minority communities. In the context of moral outsourcing, the positive feedback loop of sending disproportionate police forces into minority communities is attributed to the algorithm and the data being fed into this system--rather than the users and creators of the predictive policing technology. == Outside of technology == === Religion === Moral outsourcing is also commonly seen in appeals to religion to justify discrimination or harm. In his book What It Means to be Moral, sociologist Phil Zuckerman contradicts the popular religious notion that morality comes from God. Religion is oftentimes cited as a foundation for a moral stance without any tangible relation between the religious beliefs and personal stance. In these cases, religious individuals will "outsource" their personal beliefs and opinions by claiming that they are a result of their religious identification. This is seen where religion is cited as a factor for political beliefs, medical beliefs, and in extreme cases an excuse for violence. === Manufacturing === Moral outsourcing can also be seen in the business world in terms of manufacturing goods and avoiding environmental responsibility. Some companies in the United States will move their production process to foreign countries with more relaxed environmental policies to avoid the pollution laws that exist in the US. A study by the Harvard Business Review found that "in countries with tight environmental regulation, companies have 29% lower domestic emissions on average. On the other hand, such a tightening in regulation results in 43% higher emissions abroad." The consequences of higher pollution rates are then attributed to the loose regulations in these countries, rather than on the companies themselves who purposefully moved into these areas to avoid strict pollution policy.

Density-based clustering validation

Density-Based Clustering Validation (DBCV) is a metric designed to assess the quality of clustering solutions, particularly for density-based clustering algorithms like DBSCAN, Mean shift, and OPTICS. This metric is particularly suited for identifying concave and nested clusters, where traditional metrics such as the Silhouette coefficient, Davies–Bouldin index, or Calinski–Harabasz index often struggle to provide meaningful evaluations. Unlike traditional validation measures, which often rely on compact and well-separated clusters, DBCV index evaluates how well clusters are defined in terms of local density variations and structural coherence. This metric was introduced in 2014 by David Moulavi and colleagues in their work. It utilizes density connectivity principles to quantify clustering structures, making it especially effective at detecting arbitrarily shaped clusters in concave datasets, where traditional metrics may be less reliable. The DBCV index has been employed for clustering analysis in bioinformatics, ecology, techno-economy, and health informatics , as well as in numerous other fields. == Definition == DBCV index evaluates clustering structures by analyzing the relationships between data points within and across clusters. Given a dataset X = x 1 , x 2 , . . . , x n {\displaystyle X={x_{1},x_{2},...,x_{n}}} , a density-based algorithm partitions it into K clusters C 1 , C 2 , . . . , C K {\displaystyle {C_{1},C_{2},...,C_{K}}} . Each point x i {\displaystyle x_{i}} belongs to a specific cluster, denoted as C c l u s t e r ( x i ) {\displaystyle C_{cluster(x_{i})}} A key concept in DBCV index is the notion of density-connected paths. Two points within the same cluster are considered density-connected if there exists a sequence of intermediate points linking them, where each consecutive pair meets a predefined density criterion. The density-based distance between two points is determined by identifying the optimal path that minimizes the maximum local reachability distance along its trajectory. DBCV index extends the Silhouette coefficient by redefining cluster cohesion and separation using density-based distances: Within-cluster density distance measures how closely a point is related to other members of its cluster: a i = 1 | C c l u s t e r ( x i ) | − 1 ∑ x j ∈ C c l u s t e r ( x i ) , y ≠ x d d e n s i t y ( x j , x i ) {\displaystyle a_{i}={\frac {1}{|C_{cluster(x_{i})}|-1}}\sum _{x_{j}\in C_{cluster(x_{i})},y\neq x}d_{density}(x_{j},x_{i})} Nearest-cluster density distance quantifies how far a point is from the closest external cluster: b i = min C ≠ C cluster ( x i ) C ∈ { C 1 , … , C K } ( 1 | C | ∑ x j ∈ C d density ( x i , x j ) ) . {\displaystyle b_{i}=\min _{C\neq C_{{\text{cluster}}(x_{i})} \atop C\in \{C_{1},\dots ,C_{K}\}}\left({\frac {1}{|C|}}\sum _{x_{j}\in C}d_{\text{density}}(x_{i},x_{j})\right).} Using these measures, the DBCV index is computed as: D B C V = 1 n ∑ i = 1 n b i − a i max ( a i , b i ) {\displaystyle DBCV={\frac {1}{n}}\sum _{i=1}^{n}{\frac {b_{i}-a_{i}}{\max(a_{i},b_{i})}}} == Explanation == DBCV index values range between −1 and +1: +1: Strongly cohesive and well-separated clusters. 0: Ambiguous clustering structure. −1: Poorly formed clusters or incorrect assignments. By leveraging density-based distances instead of traditional Euclidean measures, DBCV index provides a more robust evaluation of clustering performance in datasets with irregular or non-spherical distributions.

Radial basis function network

In the field of mathematical modeling, a radial basis function network is an artificial neural network that uses radial basis functions as activation functions. The output of the network is a linear combination of radial basis functions of the inputs and neuron parameters. Radial basis function networks have many uses, including function approximation, time series prediction, classification, and system control. They were first formulated in a 1988 paper by Broomhead and Lowe, both researchers at the Royal Signals and Radar Establishment. == Network architecture == Radial basis function (RBF) networks typically have three layers: an input layer, a hidden layer with a non-linear RBF activation function and a linear output layer. The input can be modeled as a vector of real numbers x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} . The output of the network is then a scalar function of the input vector, φ : R n → R {\displaystyle \varphi :\mathbb {R} ^{n}\to \mathbb {R} } , and is given by φ ( x ) = ∑ i = 1 N a i ρ ( | | x − c i | | ) {\displaystyle \varphi (\mathbf {x} )=\sum _{i=1}^{N}a_{i}\rho (||\mathbf {x} -\mathbf {c} _{i}||)} where N {\displaystyle N} is the number of neurons in the hidden layer, c i {\displaystyle \mathbf {c} _{i}} is the center vector for neuron i {\displaystyle i} , and a i {\displaystyle a_{i}} is the weight of neuron i {\displaystyle i} in the linear output neuron. Functions that depend only on the distance from a center vector are radially symmetric about that vector, hence the name radial basis function. In the basic form, all inputs are connected to each hidden neuron. The norm is typically taken to be the Euclidean distance (although the Mahalanobis distance appears to perform better with pattern recognition) and the radial basis function is commonly taken to be Gaussian ρ ( ‖ x − c i ‖ ) = exp ⁡ [ − β i ‖ x − c i ‖ 2 ] {\displaystyle \rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}=\exp \left[-\beta _{i}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert ^{2}\right]} . The Gaussian basis functions are local to the center vector in the sense that lim | | x | | → ∞ ρ ( ‖ x − c i ‖ ) = 0 {\displaystyle \lim _{||x||\to \infty }\rho (\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert )=0} i.e. changing parameters of one neuron has only a small effect for input values that are far away from the center of that neuron. Given certain mild conditions on the shape of the activation function, RBF networks are universal approximators on a compact subset of R n {\displaystyle \mathbb {R} ^{n}} . This means that an RBF network with enough hidden neurons can approximate any continuous function on a closed, bounded set with arbitrary precision. The parameters a i {\displaystyle a_{i}} , c i {\displaystyle \mathbf {c} _{i}} , and β i {\displaystyle \beta _{i}} are determined in a manner that optimizes the fit between φ {\displaystyle \varphi } and the data. === Normalization === ==== Normalized architecture ==== In addition to the above unnormalized architecture, RBF networks can be normalized. In this case the mapping is φ ( x ) = d e f ∑ i = 1 N a i ρ ( ‖ x − c i ‖ ) ∑ i = 1 N ρ ( ‖ x − c i ‖ ) = ∑ i = 1 N a i u ( ‖ x − c i ‖ ) {\displaystyle \varphi (\mathbf {x} )\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\sum _{i=1}^{N}a_{i}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}}=\sum _{i=1}^{N}a_{i}u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} where u ( ‖ x − c i ‖ ) = d e f ρ ( ‖ x − c i ‖ ) ∑ j = 1 N ρ ( ‖ x − c j ‖ ) {\displaystyle u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{j=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{j}\right\Vert {\big )}}}} is known as a normalized radial basis function. ==== Theoretical motivation for normalization ==== There is theoretical justification for this architecture in the case of stochastic data flow. Assume a stochastic kernel approximation for the joint probability density P ( x ∧ y ) = 1 N ∑ i = 1 N ρ ( ‖ x − c i ‖ ) σ ( | y − e i | ) {\displaystyle P\left(\mathbf {x} \land y\right)={1 \over N}\sum _{i=1}^{N}\,\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\,\sigma {\big (}\left\vert y-e_{i}\right\vert {\big )}} where the weights c i {\displaystyle \mathbf {c} _{i}} and e i {\displaystyle e_{i}} are exemplars from the data and we require the kernels to be normalized ∫ ρ ( ‖ x − c i ‖ ) d n x = 1 {\displaystyle \int \rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}\,d^{n}\mathbf {x} =1} and ∫ σ ( | y − e i | ) d y = 1 {\displaystyle \int \sigma {\big (}\left\vert y-e_{i}\right\vert {\big )}\,dy=1} . The probability densities in the input and output spaces are P ( x ) = ∫ P ( x ∧ y ) d y = 1 N ∑ i = 1 N ρ ( ‖ x − c i ‖ ) {\displaystyle P\left(\mathbf {x} \right)=\int P\left(\mathbf {x} \land y\right)\,dy={1 \over N}\sum _{i=1}^{N}\,\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} and The expectation of y given an input x {\displaystyle \mathbf {x} } is φ ( x ) = d e f E ( y ∣ x ) = ∫ y P ( y ∣ x ) d y {\displaystyle \varphi \left(\mathbf {x} \right)\ {\stackrel {\mathrm {def} }{=}}\ E\left(y\mid \mathbf {x} \right)=\int y\,P\left(y\mid \mathbf {x} \right)dy} where P ( y ∣ x ) {\displaystyle P\left(y\mid \mathbf {x} \right)} is the conditional probability of y given x {\displaystyle \mathbf {x} } . The conditional probability is related to the joint probability through Bayes' theorem P ( y ∣ x ) = P ( x ∧ y ) P ( x ) {\displaystyle P\left(y\mid \mathbf {x} \right)={\frac {P\left(\mathbf {x} \land y\right)}{P\left(\mathbf {x} \right)}}} which yields φ ( x ) = ∫ y P ( x ∧ y ) P ( x ) d y {\displaystyle \varphi \left(\mathbf {x} \right)=\int y\,{\frac {P\left(\mathbf {x} \land y\right)}{P\left(\mathbf {x} \right)}}\,dy} . This becomes φ ( x ) = ∑ i = 1 N e i ρ ( ‖ x − c i ‖ ) ∑ i = 1 N ρ ( ‖ x − c i ‖ ) = ∑ i = 1 N e i u ( ‖ x − c i ‖ ) {\displaystyle \varphi \left(\mathbf {x} \right)={\frac {\sum _{i=1}^{N}e_{i}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}{\sum _{i=1}^{N}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}}}=\sum _{i=1}^{N}e_{i}u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} when the integrations are performed. === Local linear models === It is sometimes convenient to expand the architecture to include local linear models. In that case the architectures become, to first order, φ ( x ) = ∑ i = 1 N ( a i + b i ⋅ ( x − c i ) ) ρ ( ‖ x − c i ‖ ) {\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{N}\left(a_{i}+\mathbf {b} _{i}\cdot \left(\mathbf {x} -\mathbf {c} _{i}\right)\right)\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} and φ ( x ) = ∑ i = 1 N ( a i + b i ⋅ ( x − c i ) ) u ( ‖ x − c i ‖ ) {\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{N}\left(a_{i}+\mathbf {b} _{i}\cdot \left(\mathbf {x} -\mathbf {c} _{i}\right)\right)u{\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )}} in the unnormalized and normalized cases, respectively. Here b i {\displaystyle \mathbf {b} _{i}} are weights to be determined. Higher order linear terms are also possible. This result can be written φ ( x ) = ∑ i = 1 2 N ∑ j = 1 n e i j v i j ( x − c i ) {\displaystyle \varphi \left(\mathbf {x} \right)=\sum _{i=1}^{2N}\sum _{j=1}^{n}e_{ij}v_{ij}{\big (}\mathbf {x} -\mathbf {c} _{i}{\big )}} where e i j = { a i , if i ∈ [ 1 , N ] b i j , if i ∈ [ N + 1 , 2 N ] {\displaystyle e_{ij}={\begin{cases}a_{i},&{\mbox{if }}i\in [1,N]\\b_{ij},&{\mbox{if }}i\in [N+1,2N]\end{cases}}} and v i j ( x − c i ) = d e f { δ i j ρ ( ‖ x − c i ‖ ) , if i ∈ [ 1 , N ] ( x i j − c i j ) ρ ( ‖ x − c i ‖ ) , if i ∈ [ N + 1 , 2 N ] {\displaystyle v_{ij}{\big (}\mathbf {x} -\mathbf {c} _{i}{\big )}\ {\stackrel {\mathrm {def} }{=}}\ {\begin{cases}\delta _{ij}\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )},&{\mbox{if }}i\in [1,N]\\\left(x_{ij}-c_{ij}\right)\rho {\big (}\left\Vert \mathbf {x} -\mathbf {c} _{i}\right\Vert {\big )},&{\mbox{if }}i\in [N+1,2N]\end{cases}}} in the unnormalized case and in the normalized case. Here δ i j {\displaystyle \delta _{ij}} is a Kronecker delta function defined as δ i j = { 1 , if i = j 0 , if i ≠ j {\displaystyle \delta _{ij}={\begin{cases}1,&{\mbox{if }}i=j\\0,&{\mbox{if }}i\neq j\end{cases}}} . == Training == RBF networks are typically trained from pairs of input and target values x ( t ) , y ( t ) {\displaystyle \mathbf {x} (t),y(t)} , t = 1 , … , T {\displaystyle t=1,\dots ,T} by a two-step algorithm. In the first step, the center vectors c i {\displaystyle \mathbf {c} _{i}} of the RBF functions in the hidden layer

Error-driven learning

In reinforcement learning, error-driven learning is a method for adjusting a model's (intelligent agent's) parameters based on the difference between its output results and the ground truth. These models stand out as they depend on environmental feedback, rather than explicit labels or categories. They are based on the idea that language acquisition involves the minimization of the prediction error (MPSE). By leveraging these prediction errors, the models consistently refine expectations and decrease computational complexity. Typically, these algorithms are operated by the GeneRec algorithm. Error-driven learning has widespread applications in cognitive sciences and computer vision. These methods have also found successful application in natural language processing (NLP), including areas like part-of-speech tagging, parsing, named entity recognition (NER), machine translation (MT), speech recognition (SR), and dialogue systems. == Formal Definition == Error-driven learning models are ones that rely on the feedback of prediction errors to adjust the expectations or parameters of a model. The key components of error-driven learning include the following: A set S {\displaystyle S} of states representing the different situations that the learner can encounter. A set A {\displaystyle A} of actions that the learner can take in each state. A prediction function P ( s , a ) {\displaystyle P(s,a)} that gives the learner's current prediction of the outcome of taking action a {\displaystyle a} in state s {\displaystyle s} . An error function E ( o , p ) {\displaystyle E(o,p)} that compares the actual outcome o {\displaystyle o} with the prediction p {\displaystyle p} and produces an error value. An update rule U ( p , e ) {\displaystyle U(p,e)} that adjusts the prediction p {\displaystyle p} in light of the error e {\displaystyle e} . == Algorithms == Error-driven learning algorithms refer to a category of reinforcement learning algorithms that leverage the disparity between the real output and the expected output of a system to regulate the system's parameters. Typically applied in supervised learning, these algorithms are provided with a collection of input-output pairs to facilitate the process of generalization. The widely utilized error backpropagation learning algorithm is known as GeneRec, a generalized recirculation algorithm primarily employed for gene prediction in DNA sequences. Many other error-driven learning algorithms are derived from alternative versions of GeneRec. == Applications == === Cognitive science === Simpler error-driven learning models effectively capture complex human cognitive phenomena and anticipate elusive behaviors. They provide a flexible mechanism for modeling the brain's learning process, encompassing perception, attention, memory, and decision-making. By using errors as guiding signals, these algorithms adeptly adapt to changing environmental demands and objectives, capturing statistical regularities and structure. Furthermore, cognitive science has led to the creation of new error-driven learning algorithms that are both biologically acceptable and computationally efficient. These algorithms, including deep belief networks, spiking neural networks, and reservoir computing, follow the principles and constraints of the brain and nervous system. Their primary aim is to capture the emergent properties and dynamics of neural circuits and systems. === Computer vision === Computer vision is a complex task that involves understanding and interpreting visual data, such as images or videos. In the context of error-driven learning, the computer vision model learns from the mistakes it makes during the interpretation process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This repeated process of learning from errors helps improve the model's performance over time. For NLP to do well at computer vision, it employs deep learning techniques. This form of computer vision is sometimes called neural computer vision (NCV), since it makes use of neural networks. NCV therefore interprets visual data based on a statistical, trial and error approach and can deal with context and other subtleties of visual data. === Natural Language Processing === ==== Part-of-speech tagging ==== Part-of-speech (POS) tagging is a crucial component in Natural Language Processing (NLP). It helps resolve human language ambiguity at different analysis levels. In addition, its output (tagged data) can be used in various applications of NLP such as information extraction, information retrieval, question Answering, speech eecognition, text-to-speech conversion, partial parsing, and grammar correction. ==== Parsing ==== Parsing in NLP involves breaking down a text into smaller pieces (phrases) based on grammar rules. If a sentence cannot be parsed, it may contain grammatical errors. In the context of error-driven learning, the parser learns from the mistakes it makes during the parsing process. When an error is encountered, the parser updates its internal model to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the parser's performance over time. In conclusion, error-driven learning plays a crucial role in improving the accuracy and efficiency of NLP parsers by allowing them to learn from their mistakes and adapt their internal models accordingly. ==== Named entity recognition (NER) ==== NER is the task of identifying and classifying entities (such as persons, locations, organizations, etc.) in a text. Error-driven learning can help the model learn from its false positives and false negatives and improve its recall and precision on (NER). In the context of error-driven learning, the significance of NER is quite profound. Traditional sequence labeling methods identify nested entities layer by layer. If an error occurs in the recognition of an inner entity, it can lead to incorrect identification of the outer entity, leading to a problem known as error propagation of nested entities. This is where the role of NER becomes crucial in error-driven learning. By accurately recognizing and classifying entities, it can help minimize these errors and improve the overall accuracy of the learning process. Furthermore, deep learning-based NER methods have shown to be more accurate as they are capable of assembling words, enabling them to understand the semantic and syntactic relationship between various words better. ==== Machine translation ==== Machine translation is a complex task that involves converting text from one language to another. In the context of error-driven learning, the machine translation model learns from the mistakes it makes during the translation process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. ==== Speech recognition ==== Speech recognition is a complex task that involves converting spoken language into written text. In the context of error-driven learning, the speech recognition model learns from the mistakes it makes during the recognition process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. ==== Dialogue systems ==== Dialogue systems are a popular NLP task as they have promising real-life applications. They are also complicated tasks since many NLP tasks deserving study are involved. In the context of error-driven learning, the dialogue system learns from the mistakes it makes during the dialogue process. When an error is encountered, the model updates its internal parameters to avoid making the same mistake in the future. This iterative process of learning from errors helps improve the model's performance over time. == Advantages == Error-driven learning has several advantages over other types of machine learning algorithms: They can learn from feedback and correct their mistakes, which makes them adaptive and robust to noise and changes in the data. They can handle large and high-dimensional data sets, as they do not require explicit feature engineering or prior knowledge of the data distribution. They can achieve high accuracy and performance, as they can learn complex and nonlinear relationships between the input and the output. == Limitations == Although error driven learning has its advantages, their algorithms also have the following limitations: They can suffer from overfitting, which means that they memorize the training data and fail to generalize to new and unseen data. This can be mitigated by using regularization techniques, such as adding a penalty term to the loss function, or reducing the complexity of the model. They can be sensitive to the choice of

Ideonomy

Ideonomy is a combinatorial "science of ideas" developed by American independent scholar Patrick M. Gunkel (1947–2017). Specifically, Ideonomy is concerned with the systematic organization of ideas and the discovery of the rules behind how ideas combine, diverge, and transform. Gunkel defined ideonomy as "the science of the laws of ideas and of the application of such laws to the generation of all possible ideas in connection with any subject, idea, or thing." In his 1992 book A History of Knowledge, Charles Van Doren compared ideonomy to a "mining operation" that excavates meanings and thought to discover treasures hidden deep within language. Sources from the 1980s and 1990s demonstrate that ideonomy was useful to academic researchers in fields including biology, toxicology, and nursing/patient care. Beginning in the 2010s, academics in a wide range of fields including machine learning, marketing, computational modeling, and cybersecurity have relied on materials generated for ideonomy to provide methodological support for their research. == Etymology and definition == The word "ideonomy" combines the Greek roots ideo- (from idea, meaning pattern or form) and -nomy (from nomos, meaning law or custom). The suffix -nomy suggests the laws concerning or the totality of knowledge about a given subject, as in astronomy or taxonomy. In a note posted on the MIT ideonomy website, Gunkel states that the word was supposedly first coined by the French Encyclopedists to refer to a science of ideas. No evidence is provided for this statement, however. The concept bears some relationship to Antoine Destutt de Tracy's "ideology" (1796), which originally meant a systematic science of ideas before acquiring its modern political connotations. Gunkel provided several metaphorical descriptions of ideonomy: An "idea bank": a computer network enabling systematic exploration of infinite possible ideas A "kaleidoscope" that can exhibit all possible combinations and transformations of ideas A "prism" capable of diffracting any idea into its cognitive components A "gigantic microscope for magnifying the ideocosm" == History and development == In 1984, Gunkel received a five-year unsolicited grant from the Richard Lounsbery Foundation of New York to develop ideonomy. A June 1, 1987 article on the front page of The Wall Street Journal brought Gunkel and ideonomy to wider public attention. Some academics were interested in using ideonomy's techniques, including biologist Betsey Dyer, who published several contemporaneous peer-reviewed studies citing ideonomy. Academic researchers in the field of toxicology and nursing/patient care also used ideonomy. However, ideonomy's broadest contribution to date came beginning in the 2010s, as a list of personality traits generated for combinatorial matching was used by researchers in artificial intelligence to code human emotions for machine-learning tasks, develop computational models related to personality, develop a measurement framework for influencer-brand recommender systems, and aid information awareness/cybersecurity assessment. == Methodology == The foundational empirical method of ideonomy involves the systematic creation of extensive lists. Gunkel's apartment reportedly contained thousands of lists on every conceivable topic. Gunkel termed each list an "organon," which he described as expanding through "combination, permutation, transformation, generalization, specialization, intersection, interaction, reapplication, recursive use, etc. of existing organons." The ideonomic process follows a progressive structure. The ideonomist begins with a simple list of examples of a particular idea, concept, or thing. The list need not be exhaustive. By studying this list, the ideonomist isolates and identifies types. This categorical analysis then reveals missing items, allowing the primary list to be improved and refined. Gunkel emphasized that list items must not only cover genuine categories of nature but also be formulated in ways that yield the largest possible number of syntactically coherent possibilities when combined. The core technique of ideonomy is "ideocombinatorics"—the systematic intersection and combination of items from different lists to generate novel composite concepts. Gunkel developed computer programs to automate this process. For example, combining a list of 230 Universal Elementary Shapes (pits, pyramids, trenches, hemispheres, needles) with a list of 74 Types of Order (recurrence, identity, likeness of parts) yields 17,020 possible "shapes of order." These combinations, when phrased as questions ("Can there be pits of recurrence?"), could suggest new categories of phenomena worthy of investigation. The computer-generated output is typically repetitive and often meaningless. However, with sufficient frequency, the combinations yield results that are unexpectedly interesting and fruitful. In one documented case, Gunkel's programs generated 45,540 questions about toxins for microbiologist David Bermudes. One question—"Can hierarchies of cell process be used as a basis for classifying toxic action?"—prompted Bermudes to develop a novel approach to classifying biological toxins by the type of molecule they attack, rather than by chemical structure or physiological system affected. According to one contemporaneous account of ideonomy, "Gunkel takes for his field all fields and all ideas about anything. He uses a computer to generate lists of words and phrases and by juxtaposition reviews the resultant patterns for novel ideas. The computer is ideal for this task because the mind would rebel at the formidable processing task ideonomy involves. What we have here is computer generated originality." == Applications == Gunkel and his supporters identified several practical applications for ideonomic methods: Scientific research: Biologist Betsey Dyer of Wheaton College published research crediting ideonomy for helping to generate ideas. Medical science: When Austin pathologist Michael T. O'Brien was presented with the ideonomically-generated question "Can arteries have rashes?", he initially dismissed it as nonsense. Upon reflection, he realized that large arteries are supplied with blood by tiny vessels that might become inflamed and dilated, analogous to skin vessels in a rash—a phenomenon potentially worth researching. Analogical thinking: Harvard law professor Robert Clark used ideonomic analogies to write a research paper comparing plant structure with human hierarchies. Artificial intelligence: Douglas Lenat, a researcher at Microelectronics and Computer Technology Corporation (MCC) in Austin, suggested that Gunkel's lists enumerating types of human mistakes could help design AI systems capable of recognizing and correcting their own errors. == Reception and criticism == Ideonomy received mixed reactions from the academic and scientific communities. Prominent supporters included: Edward Fredkin, former director of MIT's computer science laboratory, who praised Gunkel's "provocative ideas on artificial intelligence." Marvin Minsky, AI scientist and MIT professor, who described ideonomy as "perhaps the most extensive study of ways to generate ideas." Frederick Seitz, president emeritus of Rockefeller University, who noted Gunkel's "encyclopedic scope" Robert C. Clark, Harvard law professor, who called Gunkel "the most intelligent person I ever met" However, skeptics questioned whether ideonomy constituted a genuine science. Fredkin himself noted that Gunkel "pours out about 60 ideas a minute, and 59 of them are bad," though he added that "even with one good idea out of 60, it's still an amazing accomplishment." Douglas Lenat observed that brainstorming with Gunkel was "a bit like being hit over the head by the muse with a sledgehammer" and that "he puts people off." Gunkel himself acknowledged that ideonomy was in its infancy and might seem "absurdly utopian." His planned magnum opus on ideonomy remained incomplete, and was posted on an MIT website thanks to faculty advisor Whitman Richards. Gunkel wrote: "Pioneering in a completely new field, yes in a new science, is almost unreal. It is heartbreaking, it is pitiable, it is almost inhuman. Honestly, it is a hell. There is nothing heroic about it." == Related concepts == Gunkel identified several historical precedents for ideonomic thinking: Gottfried Wilhelm Leibniz (1646–1716): The philosopher's work on a universal characteristic (characteristica universalis) and calculus of reasoning Peter Mark Roget (1779–1869): Creator of Roget's Thesaurus, which organized concepts into a systematic taxonomy Dmitri Mendeleev (1834–1907): Developer of the periodic table, demonstrating how combining lists of element families could reveal previously unseen connections Fritz Zwicky (1898–1974): The Caltech astrophysicist whom Gunkel called the "grandfather of ideonomy" for his development of "morphological research"—systematic exploration of all possible solutions t

LPBoost

Linear Programming Boosting (LPBoost) is a supervised classifier from the boosting family of classifiers. LPBoost maximizes a margin between training samples of different classes, and thus also belongs to the class of margin classifier algorithms. Consider a classification function f : X → { − 1 , 1 } , {\displaystyle f:{\mathcal {X}}\to \{-1,1\},} which classifies samples from a space X {\displaystyle {\mathcal {X}}} into one of two classes, labelled 1 and -1, respectively. LPBoost is an algorithm for learning such a classification function, given a set of training examples with known class labels. LPBoost is a machine learning technique especially suited for joint classification and feature selection in structured domains. == LPBoost overview == As in all boosting classifiers, the final classification function is of the form f ( x ) = ∑ j = 1 J α j h j ( x ) , {\displaystyle f({\boldsymbol {x}})=\sum _{j=1}^{J}\alpha _{j}h_{j}({\boldsymbol {x}}),} where α j {\displaystyle \alpha _{j}} are non-negative weightings for weak classifiers h j : X → { − 1 , 1 } {\displaystyle h_{j}:{\mathcal {X}}\to \{-1,1\}} . Each individual weak classifier h j {\displaystyle h_{j}} may be just a little bit better than random, but the resulting linear combination of many weak classifiers can perform very well. LPBoost constructs f {\displaystyle f} by starting with an empty set of weak classifiers. Iteratively, a single weak classifier to add to the set of considered weak classifiers is selected, added and all the weights α {\displaystyle {\boldsymbol {\alpha }}} for the current set of weak classifiers are adjusted. This is repeated until no weak classifiers to add remain. The property that all classifier weights are adjusted in each iteration is known as totally-corrective property. Early boosting methods, such as AdaBoost do not have this property and converge slower. == Linear program == More generally, let H = { h ( ⋅ ; ω ) | ω ∈ Ω } {\displaystyle {\mathcal {H}}=\{h(\cdot ;\omega )|\omega \in \Omega \}} be the possibly infinite set of weak classifiers, also termed hypotheses. One way to write down the problem LPBoost solves is as a linear program with infinitely many variables. The primal linear program of LPBoost, optimizing over the non-negative weight vector α {\displaystyle {\boldsymbol {\alpha }}} , the non-negative vector ξ {\displaystyle {\boldsymbol {\xi }}} of slack variables and the margin ρ {\displaystyle \rho } is the following. min α , ξ , ρ − ρ + D ∑ n = 1 ℓ ξ n sb.t. ∑ ω ∈ Ω y n α ω h ( x n ; ω ) + ξ n ≥ ρ , n = 1 , … , ℓ , ∑ ω ∈ Ω α ω = 1 , ξ n ≥ 0 , n = 1 , … , ℓ , α ω ≥ 0 , ω ∈ Ω , ρ ∈ R . {\displaystyle {\begin{array}{cl}{\underset {{\boldsymbol {\alpha }},{\boldsymbol {\xi }},\rho }{\min }}&-\rho +D\sum _{n=1}^{\ell }\xi _{n}\\{\textrm {sb.t.}}&\sum _{\omega \in \Omega }y_{n}\alpha _{\omega }h({\boldsymbol {x}}_{n};\omega )+\xi _{n}\geq \rho ,\qquad n=1,\dots ,\ell ,\\&\sum _{\omega \in \Omega }\alpha _{\omega }=1,\\&\xi _{n}\geq 0,\qquad n=1,\dots ,\ell ,\\&\alpha _{\omega }\geq 0,\qquad \omega \in \Omega ,\\&\rho \in {\mathbb {R} }.\end{array}}} Note the effects of slack variables ξ ≥ 0 {\displaystyle {\boldsymbol {\xi }}\geq 0} : their one-norm is penalized in the objective function by a constant factor D {\displaystyle D} , which—if small enough—always leads to a primal feasible linear program. Here we adopted the notation of a parameter space Ω {\displaystyle \Omega } , such that for a choice ω ∈ Ω {\displaystyle \omega \in \Omega } the weak classifier h ( ⋅ ; ω ) : X → { − 1 , 1 } {\displaystyle h(\cdot ;\omega ):{\mathcal {X}}\to \{-1,1\}} is uniquely defined. When the above linear program was first written down in early publications about boosting methods it was disregarded as intractable due to the large number of variables α {\displaystyle {\boldsymbol {\alpha }}} . Only later it was discovered that such linear programs can indeed be solved efficiently using the classic technique of column generation. === Column generation for LPBoost === In a linear program a column corresponds to a primal variable. Column generation is a technique to solve large linear programs. It typically works in a restricted problem, dealing only with a subset of variables. By generating primal variables iteratively and on-demand, eventually the original unrestricted problem with all variables is recovered. By cleverly choosing the columns to generate the problem can be solved such that while still guaranteeing the obtained solution to be optimal for the original full problem, only a small fraction of columns has to be created. ==== LPBoost dual problem ==== Columns in the primal linear program corresponds to rows in the dual linear program. The equivalent dual linear program of LPBoost is the following linear program. max λ , γ γ sb.t. ∑ n = 1 ℓ y n h ( x n ; ω ) λ n + γ ≤ 0 , ω ∈ Ω , 0 ≤ λ n ≤ D , n = 1 , … , ℓ , ∑ n = 1 ℓ λ n = 1 , γ ∈ R . {\displaystyle {\begin{array}{cl}{\underset {{\boldsymbol {\lambda }},\gamma }{\max }}&\gamma \\{\textrm {sb.t.}}&\sum _{n=1}^{\ell }y_{n}h({\boldsymbol {x}}_{n};\omega )\lambda _{n}+\gamma \leq 0,\qquad \omega \in \Omega ,\\&0\leq \lambda _{n}\leq D,\qquad n=1,\dots ,\ell ,\\&\sum _{n=1}^{\ell }\lambda _{n}=1,\\&\gamma \in \mathbb {R} .\end{array}}} For linear programs the optimal value of the primal and dual problem are equal. For the above primal and dual problems, the optimal value is equal to the negative 'soft margin'. The soft margin is the size of the margin separating positive from negative training instances minus positive slack variables that carry penalties for margin-violating samples. Thus, the soft margin may be positive although not all samples are linearly separated by the classification function. The latter is called the 'hard margin' or 'realized margin'. ==== Convergence criterion ==== Consider a subset of the satisfied constraints in the dual problem. For any finite subset we can solve the linear program and thus satisfy all constraints. If we could prove that of all the constraints which we did not add to the dual problem no single constraint is violated, we would have proven that solving our restricted problem is equivalent to solving the original problem. More formally, let γ ∗ {\displaystyle \gamma ^{}} be the optimal objective function value for any restricted instance. Then, we can formulate a search problem for the 'most violated constraint' in the original problem space, namely finding ω ∗ ∈ Ω {\displaystyle \omega ^{}\in \Omega } as ω ∗ = argmax ω ∈ Ω ∑ n = 1 ℓ y n h ( x n ; ω ) λ n . {\displaystyle \omega ^{}={\underset {\omega \in \Omega }{\textrm {argmax}}}\sum _{n=1}^{\ell }y_{n}h({\boldsymbol {x}}_{n};\omega )\lambda _{n}.} That is, we search the space H {\displaystyle {\mathcal {H}}} for a single decision stump h ( ⋅ ; ω ∗ ) {\displaystyle h(\cdot ;\omega ^{})} maximizing the left hand side of the dual constraint. If the constraint cannot be violated by any choice of decision stump, none of the corresponding constraint can be active in the original problem and the restricted problem is equivalent. ==== Penalization constant ==== D {\displaystyle D} The positive value of penalization constant D {\displaystyle D} has to be found using model selection techniques. However, if we choose D = 1 ℓ ν {\displaystyle D={\frac {1}{\ell \nu }}} , where ℓ {\displaystyle \ell } is the number of training samples and 0 < ν < 1 {\displaystyle 0<\nu <1} , then the new parameter ν {\displaystyle \nu } has the following properties. ν {\displaystyle \nu } is an upper bound on the fraction of training errors; that is, if k {\displaystyle k} denotes the number of misclassified training samples, then k ℓ ≤ ν {\displaystyle {\frac {k}{\ell }}\leq \nu } . ν {\displaystyle \nu } is a lower bound on the fraction of training samples outside or on the margin. == Algorithm == Input: Training set X = { x 1 , … , x ℓ } {\displaystyle X=\{{\boldsymbol {x}}_{1},\dots ,{\boldsymbol {x}}_{\ell }\}} , x i ∈ X {\displaystyle {\boldsymbol {x}}_{i}\in {\mathcal {X}}} Training labels Y = { y 1 , … , y ℓ } {\displaystyle Y=\{y_{1},\dots ,y_{\ell }\}} , y i ∈ { − 1 , 1 } {\displaystyle y_{i}\in \{-1,1\}} Convergence threshold θ ≥ 0 {\displaystyle \theta \geq 0} Output: Classification function f : X → { − 1 , 1 } {\displaystyle f:{\mathcal {X}}\to \{-1,1\}} Initialization Weights, uniform λ n ← 1 ℓ , n = 1 , … , ℓ {\displaystyle \lambda _{n}\leftarrow {\frac {1}{\ell }},\quad n=1,\dots ,\ell } Edge γ ← 0 {\displaystyle \gamma \leftarrow 0} Hypothesis count J ← 1 {\displaystyle J\leftarrow 1} Iterate h ^ ← argmax ω ∈ Ω ∑ n = 1 ℓ y n h ( x n ; ω ) λ n {\displaystyle {\hat {h}}\leftarrow {\underset {\omega \in \Omega }{\textrm {argmax}}}\sum _{n=1}^{\ell }y_{n}h({\boldsymbol {x}}_{n};\omega )\lambda _{n}} if ∑ n = 1 ℓ y n h ^ ( x n ) λ n + γ ≤ θ {\displaystyle \sum _{n=1}^{\ell }y_{n}{\hat {h}}({\boldsymbol {x}}_{n})\lambda _{n}+\gamma \leq \theta } then break h J ← h ^ {\displaystyle h_{J}\leftarrow {\hat {h}}} J