Natural Language Web or NLWeb was introduced by Microsoft in 2025. It is an open Python project designed to simplify the creation of natural language interfaces for websites. It enables users to query website contents using natural language, similar to interacting with an AI assistant. Every instance functions as a Model Context Protocol (MCP) server allowing websites to make their content discoverable and accessible to AI agents and other participants. NLWeb leverages existing web standards like Schema.org and RSS to build conversational capabilities of processing user queries through language models, performing semantic searches against website content and generating natural responses. It is platform-agnostic, running on all major systems and connecting to any vector database. Content to be indexed by NLWeb works best when it is organized in an AI friendly way. This means short, interlinked and semantically annotated articles work best. Initial adopters of NLWeb include TripAdvisor, Shopify, Eventbrite, and Hearst.
Weak artificial intelligence
Weak artificial intelligence (weak AI) is artificial intelligence that implements a limited part of the mind, or, as narrow AI, artificial narrow intelligence (ANI), is focused on one narrow task. Weak AI is contrasted with strong AI, which can be interpreted in various ways: Artificial general intelligence (AGI): a machine with the ability to apply intelligence to any problem, rather than just one specific problem. Artificial superintelligence (ASI): a machine with a vastly superior intelligence to the average human being. Artificial consciousness: a machine that has consciousness, sentience and mind (John Searle uses "strong AI" in this sense). Narrow AI can be classified as being "limited to a single, narrowly defined task. Most modern AI systems would be classified in this category." Artificial general intelligence is conversely the opposite. == Applications and risks == Some examples of narrow AI are AlphaGo, self-driving cars, robot systems used in the medical field, and diagnostic doctors. Narrow AI systems are sometimes dangerous if unreliable. And the behavior that it follows can become inconsistent. It could be difficult for the AI to grasp complex patterns and get to a solution that works reliably in various environments. This "brittleness" can cause it to fail in unpredictable ways. Narrow AI failures can sometimes have significant consequences. It could for example cause disruptions in the electric grid, damage nuclear power plants, cause global economic problems, and misdirect autonomous vehicles. Medicines could be incorrectly sorted and distributed. Also, medical diagnoses can ultimately have serious and sometimes deadly consequences if the AI is faulty or biased. Simple AI programs have already worked their way into society, oftentimes unnoticed by the public. Autocorrection for typing, speech recognition for speech-to-text programs, and vast expansions in the data science fields are examples. Narrow AI has also been the subject of some controversy, including resulting in unfair prison sentences, discrimination against women in the workplace for hiring, resulting in death via autonomous driving, among other cases. Despite being "narrow" AI, recommender systems are efficient at predicting user reactions based on their posts, patterns, or trends. For instance, TikTok's "For You" algorithm can determine a user's interests or preferences in less than an hour. Some other social media AI systems are used to detect bots that may be involved in propaganda or other potentially malicious activities. == Weak AI versus strong AI == John Searle contests the possibility of strong AI (by which he means conscious AI). He further believes that the Turing test (created by Alan Turing and originally called the "imitation game", used to assess whether a machine can converse indistinguishably from a human) is not accurate or appropriate for testing whether an AI is "strong". Scholars such as Antonio Lieto have argued that the current research on both AI and cognitive modelling are perfectly aligned with the weak-AI hypothesis (that should not be confused with the "general" vs "narrow" AI distinction) and that the popular assumption that cognitively inspired AI systems espouse the strong AI hypothesis is ill-posed and problematic since "artificial models of brain and mind can be used to understand mental phenomena without pretending that that they are the real phenomena that they are modelling" (as, on the other hand, implied by the strong AI assumption).
Statistical learning theory
Statistical learning theory is a framework for machine learning drawing from the fields of statistics and functional analysis. Statistical learning theory deals with the statistical inference problem of finding a predictive function based on data. Statistical learning theory has led to successful applications in fields such as computer vision, speech recognition, and bioinformatics. == Introduction == The goals of learning are understanding and prediction. Learning falls into many categories, including supervised learning, unsupervised learning, online learning, and reinforcement learning. From the perspective of statistical learning theory, supervised learning is best understood. Supervised learning involves learning from a training set of data. Every point in the training is an input–output pair, where the input maps to an output. The learning problem consists of inferring the function that maps between the input and the output, such that the learned function can be used to predict the output from future input. Depending on the type of output, supervised learning problems are either problems of regression or problems of classification. If the output takes a continuous range of values, it is a regression problem. Using Ohm's law as an example, a regression could be performed with voltage as input and current as an output. The regression would find the functional relationship between voltage and current to be R {\displaystyle R} , such that V = I R {\displaystyle V=IR} Classification problems are those for which the output will be an element from a discrete set of labels. Classification is very common for machine learning applications. In facial recognition, for instance, a picture of a person's face would be the input, and the output label would be that person's name. The input would be represented by a large multidimensional vector whose elements represent pixels in the picture. After learning a function based on the training set data, that function is validated on a test set of data, data that did not appear in the training set. == Formal description == Take X {\displaystyle X} to be the vector space of all possible inputs, and Y {\displaystyle Y} to be the vector space of all possible outputs. Statistical learning theory takes the perspective that there is some unknown probability distribution over the product space Z = X × Y {\displaystyle Z=X\times Y} , i.e. there exists some unknown p ( z ) = p ( x , y ) {\displaystyle p(z)=p(\mathbf {x} ,y)} . The training set is made up of n {\displaystyle n} samples from this probability distribution, and is notated S = { ( x 1 , y 1 ) , … , ( x n , y n ) } = { z 1 , … , z n } {\displaystyle S=\{(\mathbf {x} _{1},y_{1}),\dots ,(\mathbf {x} _{n},y_{n})\}=\{\mathbf {z} _{1},\dots ,\mathbf {z} _{n}\}} Every x i {\displaystyle \mathbf {x} _{i}} is an input vector from the training data, and y i {\displaystyle y_{i}} is the output that corresponds to it. In this formalism, the inference problem consists of finding a function f : X → Y {\displaystyle f:X\to Y} such that f ( x ) ∼ y {\displaystyle f(\mathbf {x} )\sim y} . Let H {\displaystyle {\mathcal {H}}} be a space of functions f : X → Y {\displaystyle f:X\to Y} called the hypothesis space. The hypothesis space is the space of functions the algorithm will search through. Let V ( f ( x ) , y ) {\displaystyle V(f(\mathbf {x} ),y)} be the loss function, a metric for the difference between the predicted value f ( x ) {\displaystyle f(\mathbf {x} )} and the actual value y {\displaystyle y} . The expected risk is defined to be I [ f ] = ∫ X × Y V ( f ( x ) , y ) p ( x , y ) d x d y {\displaystyle I[f]=\int _{X\times Y}V(f(\mathbf {x} ),y)\,p(\mathbf {x} ,y)\,d\mathbf {x} \,dy} The target function, the best possible function f {\displaystyle f} that can be chosen, is given by the f {\displaystyle f} that satisfies f = argmin h ∈ H I [ h ] {\displaystyle f=\mathop {\operatorname {argmin} } _{h\in {\mathcal {H}}}I[h]} Because the probability distribution p ( x , y ) {\displaystyle p(\mathbf {x} ,y)} is unknown, a proxy measure for the expected risk must be used. This measure is based on the training set, a sample from this unknown probability distribution. It is called the empirical risk I S [ f ] = 1 n ∑ i = 1 n V ( f ( x i ) , y i ) {\displaystyle I_{S}[f]={\frac {1}{n}}\sum _{i=1}^{n}V(f(\mathbf {x} _{i}),y_{i})} A learning algorithm that chooses the function f S {\displaystyle f_{S}} that minimizes the empirical risk is called empirical risk minimization. == Loss functions == The choice of loss function is a determining factor on the function f S {\displaystyle f_{S}} that will be chosen by the learning algorithm. The loss function also affects the convergence rate for an algorithm. It is important for the loss function to be convex. Different loss functions are used depending on whether the problem is one of regression or one of classification. === Regression === The most common loss function for regression is the square loss function (also known as the L2-norm). This familiar loss function is used in Ordinary Least Squares regression. The form is: V ( f ( x ) , y ) = ( y − f ( x ) ) 2 {\displaystyle V(f(\mathbf {x} ),y)=(y-f(\mathbf {x} ))^{2}} The absolute value loss (also known as the L1-norm) is also sometimes used: V ( f ( x ) , y ) = | y − f ( x ) | {\displaystyle V(f(\mathbf {x} ),y)=|y-f(\mathbf {x} )|} === Classification === In some sense the 0-1 indicator function is the most natural loss function for classification. It takes the value 0 if the predicted output is the same as the actual output, and it takes the value 1 if the predicted output is different from the actual output. For binary classification with Y = { − 1 , 1 } {\displaystyle Y=\{-1,1\}} , this is: V ( f ( x ) , y ) = θ ( − y f ( x ) ) {\displaystyle V(f(\mathbf {x} ),y)=\theta (-yf(\mathbf {x} ))} where θ {\displaystyle \theta } is the Heaviside step function. == Regularization == In machine learning problems, a major problem that arises is that of overfitting. Because learning is a prediction problem, the goal is not to find a function that most closely fits the (previously observed) data, but to find one that will most accurately predict output from future input. Empirical risk minimization runs this risk of overfitting: finding a function that matches the data exactly but does not predict future output well. Overfitting is symptomatic of unstable solutions; a small perturbation in the training set data would cause a large variation in the learned function. It can be shown that if the stability for the solution can be guaranteed, generalization and consistency are guaranteed as well. Regularization can solve the overfitting problem and give the problem stability. Regularization can be accomplished by restricting the hypothesis space H {\displaystyle {\mathcal {H}}} . A common example would be restricting H {\displaystyle {\mathcal {H}}} to linear functions: this can be seen as a reduction to the standard problem of linear regression. H {\displaystyle {\mathcal {H}}} could also be restricted to polynomial of degree p {\displaystyle p} , exponentials, or bounded functions on L1. Restriction of the hypothesis space avoids overfitting because the form of the potential functions are limited, and so does not allow for the choice of a function that gives empirical risk arbitrarily close to zero. One example of regularization is Tikhonov regularization. This consists of minimizing 1 n ∑ i = 1 n V ( f ( x i ) , y i ) + γ ‖ f ‖ H 2 {\displaystyle {\frac {1}{n}}\sum _{i=1}^{n}V(f(\mathbf {x} _{i}),y_{i})+\gamma \left\|f\right\|_{\mathcal {H}}^{2}} where γ {\displaystyle \gamma } is a fixed and positive parameter, the regularization parameter. Tikhonov regularization ensures existence, uniqueness, and stability of the solution. == Bounding empirical risk == Consider a binary classifier f : X → { 0 , 1 } {\displaystyle f:{\mathcal {X}}\to \{0,1\}} . We can apply Hoeffding's inequality to bound the probability that the empirical risk deviates from the true risk to be a Sub-Gaussian distribution. P ( | R ^ ( f ) − R ( f ) | ≥ ϵ ) ≤ 2 e − 2 n ϵ 2 {\displaystyle \mathbb {P} (|{\hat {R}}(f)-R(f)|\geq \epsilon )\leq 2e^{-2n\epsilon ^{2}}} But generally, when we do empirical risk minimization, we are not given a classifier; we must choose it. Therefore, a more useful result is to bound the probability of the supremum of the difference over the whole class. P ( sup f ∈ F | R ^ ( f ) − R ( f ) | ≥ ϵ ) ≤ 2 S ( F , n ) e − n ϵ 2 / 8 ≈ n d e − n ϵ 2 / 8 {\displaystyle \mathbb {P} {\bigg (}\sup _{f\in {\mathcal {F}}}|{\hat {R}}(f)-R(f)|\geq \epsilon {\bigg )}\leq 2S({\mathcal {F}},n)e^{-n\epsilon ^{2}/8}\approx n^{d}e^{-n\epsilon ^{2}/8}} where S ( F , n ) {\displaystyle S({\mathcal {F}},n)} is the shattering number and n {\displaystyle n} is the number of samples in your dataset. The exponential term comes from Hoeffding but there is an extra cost of taking the supremum over the whole cla
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.
Hierarchical Risk Parity
Hierarchical Risk Parity (HRP) is an advanced investment portfolio optimization framework developed in 2016 by Marcos López de Prado at Guggenheim Partners and Cornell University. HRP is a probabilistic graph-based alternative to the prevailing mean-variance optimization (MVO) framework developed by Harry Markowitz in 1952, and for which he received the Nobel Prize in economic sciences. HRP algorithms apply discrete mathematics and machine learning techniques to create diversified and robust investment portfolios that outperform MVO methods out-of-sample. HRP aims to address the limitations of traditional portfolio construction methods, particularly when dealing with highly correlated assets. Following its publication, HRP has been implemented in numerous open-source libraries, and received multiple extensions. == Key features == HRP portfolios have been proposed as a robust alternative to traditional quadratic optimization methods, including the Critical Line Algorithm (CLA) of Markowitz. HRP addresses three central issues commonly associated with quadratic optimizers: numerical instability, excessive concentration in a small number of assets, and poor out-of-sample performance. HRP leverages techniques from graph theory and machine learning to construct diversified portfolios using only the information embedded in the covariance matrix. Unlike quadratic programming methods, HRP does not require the covariance matrix to be invertible. Consequently, HRP remains applicable even in cases where the covariance matrix is ill-conditioned or singular—conditions under which standard optimizers fail. Monte Carlo simulations indicate that HRP achieves lower out-of-sample variance than CLA, despite the fact that minimizing variance is the explicit optimization objective of CLA. Furthermore, HRP portfolios exhibit lower realized risk compared to those generated by traditional risk parity methodologies. Empirical backtests have demonstrated that HRP would have historically outperformed conventional portfolio construction techniques. Algorithms within the HRP framework are characterized by the following features: Machine Learning Approach: HRP employs hierarchical clustering, a machine learning technique, to group similar assets based on their correlations. This allows the algorithm to identify the underlying hierarchical structure of the portfolio, and avoid that errors spread through the entire network. Risk-Based Allocation: The algorithm allocates capital based on risk, ensuring that assets only compete with similar assets for representation in the portfolio. This approach leads to better diversification across different risk sources, while avoiding the instability associated with noisy returns estimates. Covariance Matrix Handling: Unlike traditional methods like Mean-Variance Optimization, HRP does not require inverting the covariance matrix. This makes it more stable and applicable to portfolios with a large number of assets, particularly when the covariance matrix's condition number is high. == The problem: Markowitz's Curse == Portfolio construction is perhaps the most recurrent financial problem. On a daily basis, investment managers must build portfolios that incorporate their views and forecasts on risks and returns. Despite the theoretical elegance of Markowitz's mean-variance framework, its practical implementation is hindered by several limitations that undermine the reliability of solutions derived from the Critical Line Algorithm (CLA). A principal concern is the high sensitivity of optimal portfolios to small perturbations in expected returns: even minor forecasting errors can result in significantly different allocations (Michaud, 1998). Given the inherent difficulty of producing accurate return forecasts, numerous researchers have advocated for approaches that forgo expected returns entirely and instead rely solely on the covariance structure of asset returns. This has given rise to risk-based allocation methods, among which risk parity is a widely cited example (Jurczenko, 2015). While eliminating return forecasts mitigates some instability, it does not eliminate it. Quadratic programming techniques employed in portfolio optimization require the inversion of a positive-definite covariance matrix, meaning all eigenvalues must be strictly positive. When the matrix is numerically ill-conditioned—that is, when the ratio of its largest to smallest eigenvalue (its condition number) is large—matrix inversion becomes unreliable and prone to significant numerical errors (Bailey and López de Prado, 2012). The condition number of a covariance, correlation, or any symmetric (and thus diagonalizable) matrix is defined as the absolute value of the ratio between its largest and smallest eigenvalues in modulus. The figure on the right presents the sorted eigenvalues of several correlation matrices; the condition number is represented by the ratio of the first to last eigenvalues in each sequence. A diagonal correlation matrix, which is equal to its own inverse, exhibits the minimum possible condition number. As the number of correlated (or multicollinear) assets in a portfolio increases, the condition number rises. At high levels, this leads to severe numerical instability, whereby slight modifications in any matrix entry may result in drastically different inverses. This phenomenon, often referred to as Markowitz’s curse, encapsulates the paradox wherein increased correlation among assets heightens the theoretical need for diversification, yet simultaneously increases the likelihood of unstable optimization outcomes. Consequently, the potential benefits of diversification are frequently overshadowed by estimation errors. These problems are exacerbated as the dimensionality of the covariance matrix increases. The estimation of each covariance term consumes degrees of freedom, and in general, a minimum of 1 2 N ( N + 1 ) {\displaystyle {\frac {1}{2}}N(N+1)} independent and identically distributed (IID) observations is required to estimate a non-singular covariance matrix of dimension N {\displaystyle N} . For example, constructing an invertible covariance matrix of dimension 50 necessitates at least five years of daily IID observations. However, empirical evidence suggests that the correlation structure of financial assets is highly unstable over such extended periods. These difficulties are highlighted by the observation that even naïve allocation strategies—such as equally weighted portfolios—have frequently outperformed both mean-variance and risk-based optimizations in out-of-sample tests (De Miguel et al., 2009). == The solution: Hierarchical Risk Parity == The HRP algorithm addresses Markowitz's curse in three steps: Hierarchical Clustering: Assets are grouped into clusters based on their correlations, forming a hierarchical tree structure. Quasi-Diagonalization: The correlation matrix is reordered based on the clustering results, revealing a block diagonal structure. Recursive Bisection: Weights are assigned to assets through a top-down approach, splitting the portfolio into smaller sub-portfolios and allocating capital based on inverse variance. === Step 1: Hierarchical clustering === Given a T × N {\displaystyle T\times N} matrix of asset returns X {\displaystyle X} , where each column represents a time series of returns for one of N {\displaystyle N} assets over T {\displaystyle T} time periods, a hierarchical clustering process can be used to construct a tree-based representation of asset relationships. First, we compute the N × N {\displaystyle N\times N} correlation matrix ρ = ρ i , j i , j = 1 . . . N {\displaystyle \rho ={\rho _{i,j}}\;{i,j=1\;...\;N}} , where ρ i , j = c o r r ( X i , X j ) {\displaystyle \rho _{i,j}=\mathrm {corr} (X_{i},X_{j})} . From this, a pairwise distance matrix D = d i , j {\displaystyle D={d_{i,j}}} is defined using the transformation: d i , j = 1 2 ( 1 − ρ i , j ) {\displaystyle d_{i,j}={\sqrt {{\frac {1}{2}}(1-\rho _{i,j})}}} This distance function defines a proper metric space, satisfying non-negativity, identity of indiscernibles, symmetry, and the triangle inequality. Next, a secondary distance matrix D ~ = d ~ i , j {\displaystyle {\tilde {D}}={{\tilde {d}}_{i,j}}} is computed, where each entry measures the Euclidean distance between the distance profiles of two assets: d ~ i , j = ∑ n = 1 N ( d n , i − d n , j ) 2 {\displaystyle {\tilde {d}}_{i,j}={\sqrt {\sum _{n=1}^{N}(d_{n,i}-d_{n,j})^{2}}}} While d i , j {\displaystyle d_{i,j}} reflects correlation-based proximity between two assets, d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} quantifies dissimilarity across the entire system, as it depends on all pairwise distances. Hierarchical clustering proceeds by identifying the pair ( i , j ) {\displaystyle (i,j)} with the smallest value of d ~ i , j {\displaystyle {\tilde {d}}_{i,j}} (for i ≠ j {\displaystyle i\neq j} ), and forming a new cluster u [ 1 ] = ( i , j ) {\displaystyle u[1]=(i,j)} .
Labeled data
Labeled data is a group of samples that have been tagged with one or more labels. Labeling typically takes a set of unlabeled data and augments each piece of it with informative tags called judgments. For example, a data label might indicate whether a photo contains a horse or a cow, which words were uttered in an audio recording, what type of action is being performed in a video, what the topic of a news article is, what the overall sentiment of a tweet is, or whether a dot in an X-ray is a tumor. Labels can be obtained by having humans make judgments about a given piece of unlabeled data. Labeled data is significantly more expensive to obtain than the raw unlabeled data. The quality of labeled data directly influences the performance of supervised machine learning models in operation, as these models learn from the provided labels. == Crowdsourced labeled data == In 2006, Fei-Fei Li, the co-director of the Stanford Human-Centered AI Institute, initiated research to improve the artificial intelligence models and algorithms for image recognition by significantly enlarging the training data. The researchers downloaded millions of images from the World Wide Web and a team of undergraduates started to apply labels for objects to each image. In 2007, Li outsourced the data labeling work on Amazon Mechanical Turk, an online marketplace for digital piece work. The 3.2 million images that were labeled by more than 49,000 workers formed the basis for ImageNet, one of the largest hand-labeled database for outline of object recognition. == Automated data labelling == After obtaining a labeled dataset, machine learning models can be applied to the data so that new unlabeled data can be presented to the model and a likely label can be guessed or predicted for that piece of unlabeled data. == Challenges == === Data-driven bias === Algorithmic decision-making is subject to programmer-driven bias as well as data-driven bias. Training data that relies on bias labeled data will result in prejudices and omissions in a predictive model, despite the machine learning algorithm being legitimate. The labeled data used to train a specific machine learning algorithm needs to be a statistically representative sample to not bias the results. For example, in facial recognition systems underrepresented groups are subsequently often misclassified if the labeled data available to train has not been representative of the population,. In 2018, a study by Joy Buolamwini and Timnit Gebru demonstrated that two facial analysis datasets that have been used to train facial recognition algorithms, IJB-A and Adience, are composed of 79.6% and 86.2% lighter skinned humans respectively. === Human error and inconsistency === Human annotators are prone to errors and biases when labeling data. This can lead to inconsistent labels and affect the quality of the data set. The inconsistency can affect the machine learning model's ability to generalize well. === Domain expertise === Certain fields, such as legal document analysis or medical imaging, require annotators with specialized domain knowledge. Without the expertise, the annotations or labeled data may be inaccurate, negatively impacting the machine learning model's performance in a real-world scenario.
Tensor (machine learning)
In machine learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor"), may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition factors data tensors into smaller tensors. Operations on data tensors can be expressed in terms of matrix multiplication and the Kronecker product. The computation of gradients, a crucial aspect of backpropagation, can be performed using software libraries such as PyTorch and TensorFlow. Computations are often performed on graphics processing units (GPUs) using CUDA, and on dedicated hardware such as Google's Tensor Processing Unit or Nvidia's Tensor core. These developments have greatly accelerated neural network architectures, and increased the size and complexity of models that can be trained. == History == A tensor is by definition a multilinear map. In mathematics, this may express a multilinear relationship between sets of algebraic objects. In physics, tensor fields, considered as tensors at each point in space, are useful in expressing mechanics such as stress or elasticity. In machine learning, the exact use of tensors depends on the statistical approach being used. In 2001, the field of signal processing and statistics were making use of tensor methods. Pierre Comon surveys the early adoption of tensor methods in the fields of telecommunications, radio surveillance, chemometrics and sensor processing. Linear tensor rank methods (such as, Parafac/CANDECOMP) analyzed M-way arrays ("data tensors") composed of higher order statistics that were employed in blind source separation problems to compute a linear model of the data. He noted several early limitations in determining the tensor rank and efficient tensor rank decomposition. In the early 2000s, multilinear tensor methods crossed over into computer vision, computer graphics and machine learning with papers by Vasilescu or in collaboration with Terzopoulos, such as Human Motion Signatures, TensorFaces TensorTextures and Multilinear Projection. Multilinear algebra, the algebra of higher-order tensors, is a suitable and transparent framework for analyzing the multifactor structure of an ensemble of observations and for addressing the difficult problem of disentangling the causal factors based on second order or higher order statistics associated with each causal factor. Tensor (multilinear) factor analysis disentangles and reduces the influence of different causal factors with multilinear subspace learning. When treating an image or a video as a 2- or 3-way array, i.e., "data matrix/tensor", tensor methods reduce spatial or time redundancies as demonstrated by Wang and Ahuja. Yoshua Bengio, Geoff Hinton and their collaborators briefly discuss the relationship between deep neural networks and tensor factor analysis beyond the use of M-way arrays ("data tensors") as inputs. One of the early uses of tensors for neural networks appeared in natural language processing. A single word can be expressed as a vector via Word2vec. Thus a relationship between two words can be encoded in a matrix. However, for more complex relationships such as subject-object-verb, it is necessary to build higher-dimensional networks. In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From 2014 to 2015, tensor methods become more common in convolutional neural networks (CNNs). Tensor methods organize neural network weights in a "data tensor", analyze and reduce the number of neural network weights. Lebedev et al. accelerated CNN networks for character classification (the recognition of letters and digits in images) by using 4D kernel tensors. == Definition == Let F {\displaystyle \mathbb {F} } be a field (such as the real numbers R {\displaystyle \mathbb {R} } or the complex numbers C {\displaystyle \mathbb {C} } ). A tensor T ∈ F I 1 × I 2 × … × I C {\displaystyle {\mathcal {T}}\in {\mathbb {F} }^{I_{1}\times I_{2}\times \ldots \times I_{C}}} is a multilinear transformation from a set of domain vector spaces to a range vector space: T : { F I 1 × F I 2 × … F I C } ↦ F I 0 {\displaystyle {\mathcal {T}}:\{{\mathbb {F} }^{I_{1}}\times {\mathbb {F} }^{I_{2}}\times \ldots {\mathbb {F} }^{I_{C}}\}\mapsto {\mathbb {F} }^{I_{0}}} Here, C {\displaystyle C} and I 0 , I 1 , … , I C {\displaystyle I_{0},I_{1},\ldots ,I_{C}} are positive integers, and ( C + 1 ) {\displaystyle (C+1)} is the number of modes of a tensor (also known as the number of ways of a multi-way array). The dimensionality of mode c {\displaystyle c} is I c {\displaystyle I_{c}} , for 0 ≤ c ≤ C {\displaystyle 0\leq c\leq C} . In statistics and machine learning, an image is vectorized when viewed as a single observation, and a collection of vectorized images is organized as a "data tensor". For example, a set of facial images { d i p , i e , i l , i v ∈ R I X } {\displaystyle \{{\mathbb {d} }_{i_{p},i_{e},i_{l},i_{v}}\in {\mathbb {R} }^{I_{X}}\}} with I X {\displaystyle I_{X}} pixels that are the consequences of multiple causal factors, such as a facial geometry i p ( 1 ≤ i p ≤ I P ) {\displaystyle i_{p}(1\leq i_{p}\leq I_{P})} , an expression i e ( 1 ≤ i e ≤ I E ) {\displaystyle i_{e}(1\leq i_{e}\leq I_{E})} , an illumination condition i l ( 1 ≤ i l ≤ I L ) {\displaystyle i_{l}(1\leq i_{l}\leq I_{L})} , and a viewing condition i v ( 1 ≤ i v ≤ I V ) {\displaystyle i_{v}(1\leq i_{v}\leq I_{V})} may be organized into a data tensor (ie. multiway array) D ∈ R I X × I P × I E × I L × V {\displaystyle {\mathcal {D}}\in {\mathbb {R} }^{I_{X}\times I_{P}\times I_{E}\times I_{L}\times V}} where I P {\displaystyle I_{P}} are the total number of facial geometries, I E {\displaystyle I_{E}} are the total number of expressions, I L {\displaystyle I_{L}} are the total number of illumination conditions, and I V {\displaystyle I_{V}} are the total number of viewing conditions. Tensor factorizations methods such as TensorFaces and multilinear (tensor) independent component analysis factorizes the data tensor into a set of vector spaces that span the causal factor representations, where an image is the result of tensor transformation T {\displaystyle {\mathcal {T}}} that maps a set of causal factor representations to the pixel space. Another approach to using tensors in machine learning is to embed various data types directly. For example, a grayscale image, commonly represented as a discrete 2-way array D ∈ R I R X × I C X {\displaystyle {\mathbf {D} }\in {\mathbb {R} }^{I_{RX}\times I_{CX}}} with dimensionality I R X × I C X {\displaystyle I_{RX}\times I_{CX}} where I R X {\displaystyle I_{RX}} are the number of rows and I C X {\displaystyle I_{CX}} are the number of columns. When an image is treated as 2-way array or 2nd order tensor (i.e. as a collection of column/row observations), tensor factorization methods compute the image column space, the image row space and the normalized PCA coefficients or the ICA coefficients. Similarly, a color image with RGB channels, D ∈ R N × M × 3 . {\displaystyle {\mathcal {D}}\in \mathbb {R} ^{N\times M\times 3}.} may be viewed as a 3rd order data tensor or 3-way array.-------- In natural language processing, a word might be expressed as a vector v {\displaystyle v} via the Word2vec algorithm. Thus v {\displaystyle v} becomes a mode-1 tensor v ↦ A ∈ R N . {\displaystyle v\mapsto {\mathcal {A}}\in \mathbb {R} ^{N}.} The embedding of subject-object-verb semantics requires embedding relationships among three words. Because a word is itself a vector, subject-object-verb semantics could be expressed using mode-3 tensors v a × v b × v c ↦ A ∈ R N × N × N . {\displaystyle v_{a}\times v_{b}\times v_{c}\mapsto {\mathcal {A}}\in \mathbb {R} ^{N\times N\times N}.} In practice the neural network designer is primarily concerned with the specification of embeddings, the connection of tensor layers, and the operations performed on them in a network. Modern machine learning frameworks manage the optimization, tensor factorization and backpropagation automatically. === As unit values === Tensors may be used as the unit values of neural networks which extend the concept of scalar, vector and matrix values to multiple dimensions. The output value of single layer unit y m {\displaystyle y_{m}} is the sum-product of its input units and the connection weights filtered through the activation function f {\displaystyle f} : y m = f ( ∑ n x n u m , n ) , {\displaystyle y_{m}=f\left(\sum _{n}x_{n}u_{m,n}\right),} where y m ∈ R .