Supervised learning (SL) is a paradigm in machine learning where input objects and a desired output value train a model. The training data is processed, building a function that maps new data to expected output values. An optimal scenario will allow for the algorithm to correctly determine output values for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way. This statistical quality of an algorithm is measured through the so-called generalization error.
In machine learning, a linear classifier makes a classification decision for each object based on a linear combination of its features. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-linear classifiers while taking less time to train and use.
Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess (PR) capabilities but their primary function is to distinguish and create emergent patterns. PR has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power.
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. In machine learning, specifically empirical risk minimization, MSE may refer to the empirical risk, as an estimate of the true MSE.
In machine learning, early stopping is a form of regularization used to avoid overfitting when training a model with an iterative method, such as gradient descent. Such methods update the model to make it better fit the training data with each iteration. Up to a point, this improves the model's performance on data outside of the training set. Past that point, however, improving the model's fit to the training data comes at the expense of increased generalization error. Early stopping rules provide guidance as to how many iterations can be run before the learner begins to over-fit. Early stopping rules have been employed in many different machine learning methods, with varying amounts of theoretical foundation.
In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the size of a class of sets. The notion can be extended to classes of binary functions. It is defined as the cardinality of the largest set of points that the algorithm can shatter, which means the algorithm can always learn a perfect classifier for any labeling of at least one configuration of those data points. It was originally defined by Vladimir Vapnik and Alexey Chervonenkis.
In mathematical statistics, the Fisher information is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information.
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.
Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that works by creating a multitude of decision trees during training. For classification tasks, the output of the random forest is the class selected by most trees. For regression tasks, the output is the average of the predictions of the trees. Random forests correct for decision trees' habit of overfitting to their training set.
In mathematics, statistics, finance, and computer science, particularly in machine learning and inverse problems, regularization is a process that converts the answer of a problem to a simpler one. It is often used in solving ill-posed problems or to prevent overfitting.
For supervised learning applications in machine learning and statistical learning theory, generalization error is a measure of how accurately an algorithm is able to predict outcomes for previously unseen data. As learning algorithms are evaluated on finite samples, the evaluation of a learning algorithm may be sensitive to sampling error. As a result, measurements of prediction error on the current data may not provide much information about the algorithm's predictive ability on new, unseen data. The generalization error can be minimized by avoiding overfitting in the learning algorithm. The performance of machine learning algorithms is commonly visualized by learning curve plots that show estimates of the generalization error throughout the learning process.
Robust statistics are statistics that maintain their properties even if the underlying distributional assumptions are incorrect. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution. For example, robust methods work well for mixtures of two normal distributions with different standard deviations; under this model, non-robust methods like a t-test work poorly.
An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data. An autoencoder learns two functions: an encoding function that transforms the input data, and a decoding function that recreates the input data from the encoded representation. The autoencoder learns an efficient representation (encoding) for a set of data, typically for dimensionality reduction, to generate lower-dimensional embeddings for subsequent use by other machine learning algorithms.
Structural risk minimization (SRM) is an inductive principle of use in machine learning. Commonly in machine learning, a generalized model must be selected from a finite data set, with the consequent problem of overfitting – the model becoming too strongly tailored to the particularities of the training set and generalizing poorly to new data. The SRM principle addresses this problem by balancing the model's complexity against its success at fitting the training data. This principle was first set out in a 1974 book by Vladimir Vapnik and Alexey Chervonenkis and uses the VC dimension.
In statistics and machine learning, the bias–variance tradeoff describes the relationship between a model's complexity, the accuracy of its predictions, and how well it can make predictions on previously unseen data that were not used to train the model. In general, as we increase the number of tunable parameters in a model, it becomes more flexible, and can better fit a training data set. It is said to have lower error, or bias. However, for more flexible models, there will tend to be greater variance to the model fit each time we take a set of samples to create a new training data set. It is said that there is greater variance in the model's estimated parameters.
In machine learning, the vanishing gradient problem is encountered when training neural networks with gradient-based learning methods and backpropagation. In such methods, during each training iteration, each neural network weight receives an update proportional to the partial derivative of the loss function with respect to the current weight. The problem is that as the network depth or sequence length increases, the gradient magnitude typically is expected to decrease, slowing the training process. In the worst case, this may completely stop the neural network from further learning. As one example of the problem cause, traditional activation functions such as the hyperbolic tangent function have gradients in the range [-1,1], and backpropagation computes gradients using the chain rule. This has the effect of multiplying n of these small numbers to compute gradients of the early layers in an n-layer network, meaning that the gradient decreases exponentially with n while the early layers train very slowly.
Weak supervision is a paradigm in machine learning, the relevance and notability of which increased with the advent of large language models due to large amount of data required to train them. It is characterized by using a combination of a small amount of human-labeled data, followed by a large amount of unlabeled data. In other words, the desired output values are provided only for a subset of the training data. The remaining data is unlabeled or imprecisely labeled. Intuitively, it can be seen as an exam and labeled data as sample problems that the teacher solves for the class as an aid in solving another set of problems. In the transductive setting, these unsolved problems act as exam questions. In the inductive setting, they become practice problems of the sort that will make up the exam. Technically, it could be viewed as performing clustering and then labeling the clusters with the labeled data, pushing the decision boundary away from high-density regions, or learning an underlying one-dimensional manifold where the data reside.
In machine learning, a variational autoencoder (VAE) is an artificial neural network architecture introduced by Diederik P. Kingma and Max Welling. It is part of the families of probabilistic graphical models and variational Bayesian methods.
In the study of artificial neural networks (ANNs), the neural tangent kernel (NTK) is a kernel that describes the evolution of deep artificial neural networks during their training by gradient descent. It allows ANNs to be studied using theoretical tools from kernel methods.
An energy-based model (EBM) is an application of canonical ensemble formulation from statistical physics for learning from data. The approach prominently appears in generative artificial intelligence.
