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What you will learn in Machine Learning Algorithms in Depth

by Vadim Smolyakov

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Chapter by chapter

Concepts explained in this book

• classifierA classification algorithm learns a mapping from inputs to discrete class outputs.
• variational inferenceAccurate variational inference uses richer variational models than fully factorized approximations to improve posterior approximation quality.
• objective functionTraining loss is the value of a model's loss function evaluated on examples in its training dataset.
• linear regressionLinear regression is a regression model that represents a response as a linear combination of input features.
• stochastic gradient descentStochastic gradient descent is an iterative optimization method that updates parameters using gradients estimated from random data subsets.
• evidence lower boundThe evidence lower bound is a lower bound on the log marginal likelihood that serves as an optimization objective in variational inference.
• active learningActive learning is a supervised learning technique in which a learner selects unlabeled instances for labeling to improve performance with fewer labeled examples.
• decision boundaryA decision boundary is a surface in feature space that separates regions assigned to different predicted classes.
• Kullback–Leibler divergenceKullback-Leibler divergence is a nonnegative measure of the discrepancy between two probability distributions.
• thresholdA threshold is a cutoff value for a feature that determines how data points are divided during a tree split.
• machine learningAn algorithm that learns rules or predictive relationships from data rather than receiving all task instructions explicitly.
• latent Dirichlet allocationLatent Dirichlet allocation is a generative probabilistic model that represents documents as mixtures of topics and topics as distributions over words.
• markov chain monte carloMarkov chain Monte Carlo is a Monte Carlo methodology that samples a Markov chain to approximate a target probability distribution, typically a posterior distribution.
• unsupervised learningUnsupervised learning is a machine learning paradigm that learns structure or representations from data without labeled target outputs.
• conjugacyA conjugate prior is a prior distribution whose posterior belongs to the same distributional family after updating with data.
• backpropagationBackpropagation computes gradients of an objective with respect to parameters by propagating derivatives backward through a computational composition.
• radial basis function kernelA kernel function whose value typically decreases exponentially with the squared Euclidean distance between its input vectors.
• expectation maximizationThe expectation-maximization algorithm iteratively estimates latent variables and maximizes expected complete-data likelihood to fit models with unobserved variables.
• kernel functionA positive-definite function that measures similarity between pairs of inputs and defines an associated feature-space inner product.
• transformer architectureA transformer model is a neural network architecture that uses attention-based mechanisms to model contextual relationships in structured sequences or other data.
• stationary distributionA stationary distribution is a probability distribution that remains unchanged under the transition dynamics of a stochastic process.
• uncertainty samplingUncertainty sampling is an active learning strategy that selects instances for which the current model is most uncertain about the predicted label.
• simulated annealingSimulated annealing is a heuristic optimization method that probabilistically accepts higher-energy states according to a temperature-controlled schedule to escape local optima.
• supervised learningA machine learning algorithm that learns from examples pairing inputs with desired outputs.
• amortized inferenceAmortized variational inference learns a shared inference function that predicts variational posterior parameters from observations instead of optimizing separate variational parameters for each observation.
• proposal distributionA proposal distribution is a conditional or unconditional probability distribution used to generate candidate states for a sampling method.
• Gaussian processA Gaussian process is a collection of random variables such that every finite subset has a jointly Gaussian distribution, defining a probability distribution over functions.
• Markov chainA Markov model is a stochastic model in which the conditional distribution of future states depends on the present state rather than the full history.
• indicator functionAn indicator function returns one when a stated condition is true and zero otherwise.
• feedforward networkA feed-forward network is a neural network whose computation flows directly from inputs to outputs without recurrent state.
• genetic algorithmA genetic algorithm is an evolutionary optimization technique that iteratively evaluates a population of candidate solutions and generates new candidates through selection, crossover, and mutation.
• approximate distributionAn approximate posterior distribution is a tractable distribution used to approximate the conditional distribution of latent variables given observed data.
• transition matrixA transition matrix is a matrix whose entries specify the probabilities of moving between states of a stochastic process.
• posterior probabilityA posterior distribution is the probability distribution of unknown quantities after incorporating observed data into prior beliefs.
• attentionAttention is a technique that computes context-dependent weighted combinations of input representations according to their relevance to a query.
• entropyEntropy is a measure of uncertainty in a probability distribution, computed as the expected negative log probability.
• Fisher information matrixFisher information measures the expected curvature of a model's log likelihood with respect to its parameters.
• softmaxA function that converts a vector of scores into nonnegative values summing to one, typically interpreted as class probabilities.
• parameterA weight matrix is a matrix of learned coefficients that parameterizes connections between neural-network units.
• mean-field approximationA variational inference technique that approximates a joint posterior with a product of independent marginal distributions.
• variational autoencoderA variational autoencoder is a generative neural network that learns an approximate latent-variable posterior and reconstructs observations from sampled latent representations.
• CARTCART is a decision-tree learning algorithm that recursively partitions data using optimized split criteria.
• evaluation datasetA validation dataset is a dataset used to evaluate candidate model configurations during model development and selection.
• PageRankPageRank is an algorithm that assigns importance scores to linked webpages based on the stationary behavior of a random-surfer process.
• query by committeeQuery by committee selects examples on which a committee of models disagrees most strongly for annotation.
• early stoppingEarly stopping is a training procedure that terminates optimization when performance on a validation criterion stops improving.
• ReLUReLU is the rectified-linear-unit activation function that outputs the greater of zero and its input.
• target distributionA target distribution is the probability distribution from which a sampling method aims to generate samples.
• perceptronA linear binary classifier that predicts a class from the sign of a weighted sum of input features.
• importance weightAn importance weight is a numerical factor that adjusts the contribution of a sample or outcome in a weighted estimate.
• binary random variableA binary random variable is a random variable restricted to two possible values, here −1 and +1.
• graphA graph is a mathematical or computational structure of vertices connected by edges that can represent dependencies or relationships.
• log probabilityA log likelihood is the logarithm of a model likelihood for observed data, commonly optimized instead of the likelihood itself.
• principal component analysisPrincipal component analysis is a dimensionality-reduction technique that projects data onto orthogonal directions of greatest variance.
• graph neural networkA graph neural network is a neural-network architecture that computes representations by propagating information over graph-structured data.
• expressive powerModel capacity is the range and complexity of functions that a model architecture can represent.
• latent spaceA latent space is the representational space of unobserved variables or encoded representations associated with observed data.
• graph convolutional networkA graph convolutional network is a graph neural network that computes node representations by aggregating information from graph neighborhoods.
• regularizationA modeling technique that adds a penalty or constraint to discourage undesirable parameter values, such as excessive magnitude.
• ensembleAn ensemble method combines predictions or decisions from multiple models to obtain a joint predictive result.
• Monte Carlo simulationMonte Carlo sampling is a stochastic technique that uses random samples or simulated paths to estimate properties of uncertain quantities.
• kernel density estimateA nonparametric technique that estimates a probability density by combining localized kernel functions centered on observations.
• mixture density networkA mixture density network is a neural network that predicts the parameters of a conditional mixture probability distribution.
• dp-means algorithmDP-means is a Bayesian nonparametric clustering algorithm that creates a new cluster when a data point is sufficiently distant from existing cluster centroids and penalizes the number of clusters in its objective.
• learning rate scheduleA learning rate schedule is a rule that specifies how an optimization learning rate changes across iterations.
• support vector machineA supervised learning model that separates classes by selecting a decision boundary with a large margin, optionally using a kernel for nonlinear separation.
• metropolis-hastings samplingMetropolis-Hastings sampling is a Markov chain Monte Carlo technique that proposes state changes and accepts or rejects them using a probability designed to preserve the target distribution.
• hyperparameterA hyperparameter is a configuration value set outside the ordinary parameter-learning process that controls a model or learning procedure.
• data structureA data structure is a scheme for storing and organizing data to support particular access and update operations.
• dynamic programmingDynamic programming solves problems with overlapping subproblems by storing and reusing solutions to smaller subproblems.
• structure learning algorithmStructure learning is the process of inferring the structure of a graph or probabilistic model from observed data.
• labelThe correct target value against which a model prediction is compared.
• mean squared errorMean squared error is a regression loss equal to the average squared difference between predictions and target values.
• hyperplaneA hyperplane is a flat affine subspace whose dimension is one less than that of its ambient space.
• gibbs samplingGibbs sampling is a Markov chain Monte Carlo technique that samples each variable from its conditional distribution given the other variables.
• convolutional layerA convolutional layer is a neural-network layer that applies learned convolution kernels to an input representation.
• greedy algorithmA greedy algorithm repeatedly selects a locally optimal option in the hope of obtaining a globally optimal solution.
• density estimatorA density estimate is an estimated probability density function inferred from observed data or a statistical model.
• Vision TransformerA vision transformer is a transformer-based image model that processes an image as a sequence of embedded patches.
• Cramer-Rao lower boundThe Cramer-Rao lower bound is a lower bound on the variance of an unbiased estimator under regularity conditions.
• query strategyA query strategy is a criterion for selecting unlabeled training examples to be labeled in active learning.
• message passingMessage passing is a graph-computation technique in which nodes exchange information with neighboring nodes to update their representations.
• decision treeA decision tree is a hierarchical predictive model that makes decisions by applying feature-based tests at internal nodes.
• Bayesian optimizationBayesian optimization is a sequential optimization technique that uses a probabilistic surrogate model and an acquisition rule to optimize an expensive black-box function.
• hidden Markov modelA hidden Markov model is a probabilistic model with latent discrete states that form a Markov chain and generate observed data through state-dependent emission distributions.
• positional embeddingA positional encoding is a representation added to token embeddings to convey a token's position in a sequence.
• cross-attentionCross-attention computes attention with queries from one sequence or representation source and keys and values from another.
• masked attentionMasked attention restricts attention connections so that a position cannot use information from disallowed positions, such as future tokens.
• multi-head attentionMultihead attention runs multiple attention mechanisms in parallel and combines their output representations.
• importance samplingImportance sampling is a Monte Carlo technique that estimates expectations or integrals under a target distribution by weighting samples drawn from a proposal distribution.
• prior probabilityA prior distribution represents probability beliefs about model parameters or latent variables before observing the current data.
• area under the curveArea under the curve is a scalar summary of the area beneath a performance curve, with larger values indicating better ranking performance in the ROC sense.
• confusion matrixA confusion matrix is a table counting predictions by combinations of predicted and actual classes.
• f-scoreThe F1 score is the harmonic mean of precision and recall.
• false-positive rateThe proportion of actual negative examples incorrectly predicted as positive.
• hinge lossA hinge loss function penalizes classification examples whose signed margin falls below a specified threshold.
• linearly separableLinearly separable data is data whose classes can be separated by a linear decision boundary.
• precisionThe proportion of positive predictions that are correct.
• precision-recall curveA precision-recall curve plots precision against recall across classification thresholds.
• recallThe proportion of actual positive examples correctly predicted as positive.
• receiver operating characteristicA receiver operating characteristic curve plots the true positive rate against the false positive rate across classification thresholds.
• sign functionA sign function returns the sign of a numeric input, commonly mapping positive and negative values to +1 and −1.
• adjacency matrixAn adjacency matrix is a matrix that records which pairs of graph vertices are connected by edges.
• dropoutDropout is a regularization technique that randomly removes or zeroes neural-network connections or activations during training.
• weight decayA regularization method that adds a penalty proportional to the squared magnitude of model parameters to discourage large weights.
• performanceTime complexity is a measure of how an algorithm's execution time grows with input size.
• anomaly detectionA technique for identifying observations that differ substantially from established data patterns.
• emission matrixAn emission matrix contains the probabilities of observed symbols conditional on each latent state in a hidden Markov model.
• support vectorA support vector is a training data point lying on a margin boundary that determines the parameters of a support vector machine.
• divide-and-conquer approachDivide and conquer is a problem-solving paradigm that recursively decomposes a problem into smaller subproblems and combines their solutions.
• sigmoidA sigmoid function is a continuous S-shaped function that maps real-valued inputs to values between zero and one.
• negative log-likelihoodA negative log likelihood is a loss equal to the negative logarithm of the likelihood assigned to observed outcomes by a probabilistic model.
• normal distributionA Gaussian distribution is a continuous probability distribution characterized by a bell-shaped density determined by location and scale parameters.
• max poolingMax pooling is a downsampling operation that retains the largest value within each local window of a feature sequence.
• monte carlo integrationMonte Carlo integration is a numerical integration technique that estimates an integral using random samples.
• adamAdam is an adaptive optimization method that combines momentum-like first-moment estimates with RMSProp-like second-moment scaling and bias correction.
• Gini impurityThe Gini index is an impurity measure for evaluating the heterogeneity of class labels in a set or node.
• leaf nodeA leaf node is a terminal node of a decision tree representing an input region and its prediction.
• node impurityImpurity is a measure of how mixed the class labels are within a data region or tree node.
• tree-based methodA tree-based model makes predictions by recursively partitioning an input space into regions represented by nodes and leaves.
• CVXOPTCVXOPT is a Python software package for convex optimization, including quadratic programming.
• marginA margin is the distance between a classifier's decision boundary and the nearest training examples or class-separating boundaries.
• quadratic programA quadratic program is an optimization problem with a quadratic objective function and linear constraints on its variables.
• computation graphA graph representation in which nodes and edges describe the composition and flow of computations.
• error rateThe proportion of examples whose predicted class differs from the true class.
• generalizationThe ability of a learned model to perform accurately on previously unseen examples.
• brute-force searchComplete search is a problem-solving technique that traverses an entire search space to find a solution, optionally pruning parts known not to contain one.
• base learnerA base learner is an individual predictive model that serves as a component of an ensemble.
• feature mapA feature map is a function that represents input objects as vectors in a feature space, possibly an infinite-dimensional one.
• LeNetLeNet is a convolutional neural network architecture designed for visual recognition tasks.
• BERTBERT is a pretrained bidirectional transformer language model designed to learn contextual representations of text.
• diffusion modelA diffusion model is a generative model that learns to reverse a gradual noise-adding process to generate samples from a data distribution.
• fine-tuningFine-tuning is adapting a pretrained model to a target task by continuing training, typically with task-specific output parameters.
• GPT modelGPT-3 is a large autoregressive transformer language model that generates text from preceding context.
• Inception moduleAn inception module is a neural-network block that applies convolutions with multiple kernel sizes to obtain features at different receptive-field scales.
• likelihood-based generative modelA likelihood-based generative model represents a data distribution with a likelihood function and learns by fitting that likelihood.
• meanA mean is a numerical location parameter representing the average or central value of a probability distribution.
• Bernoulli naive BayesA probabilistic classification model that uses Bernoulli likelihoods for binary features and assumes conditional independence given the class.
• forward-backward algorithmThe forward-backward algorithm combines forward and backward recursions to compute latent-state marginal probabilities using observations from an entire sequence.
• AdaGradAdaGrad is an adaptive optimization method that scales each parameter's learning rate using the accumulated squared gradients for that parameter.
• momentumMomentum is an optimization technique that incorporates an exponentially weighted moving average of past gradients into parameter updates.
• Nesterov momentumNesterov momentum is an optimization technique that evaluates the gradient after applying the current velocity to obtain an anticipatory correction.
• RMSpropRMSProp is an adaptive gradient optimization algorithm that normalizes updates using an exponentially decaying average of squared gradients.
• variational free energyAn optimization objective in variational inference whose minimization is equivalent to maximizing a variational lower bound on model evidence.
• baggingBagging is an ensemble technique that trains models on bootstrap-resampled data and aggregates their predictions to reduce variance.
• Viterbi algorithmA Viterbi decoder finds the most likely sequence of hidden states in a sequential probabilistic model.
• maximum weight spanning treeA maximum weight spanning tree is a spanning tree whose total edge weight is maximal among all spanning trees of a weighted graph.
• hierarchical modelA hierarchical regression model represents regression relationships across groups while sharing information through higher-level parameters.
• interceptA bias parameter is a learned additive parameter that shifts a neural-network layer's preactivation values.
• bias-variance tradeoffThe bias-variance tradeoff describes the balance between systematic prediction error from restrictive assumptions and error from sensitivity to training data.
• effective sample sizeEffective sample size is a measure of the amount of independent information represented by a possibly weighted or correlated sample.
• estimatorAn estimator is a rule that computes an approximation to an unknown statistical quantity from observed data or samples.
• unnormalized distributionAn unnormalized distribution assigns probability weights proportional to a distribution density but lacks the factor required for its total mass to equal one.
• activation functionAn activation function is a nonlinear function applied to a neural-network layer output to increase the model's expressive capacity.
• coupling strengthA coupling strength is a parameter controlling the influence of one variable's state on a neighboring variable's state in an interaction model.
• interaction potentialAn interaction potential is a positive function assigning a compatibility weight to the joint states of variables connected by an edge.
• Ising modelThe Ising model is a probabilistic model of binary states on a graph with pairwise interactions favoring aligned neighboring states.
• Markov random fieldA Markov random field is a joint distribution over variables represented by an undirected graph whose edges encode conditional independence relationships.
• image denoisingImage denoising is the computational restoration of an image by reducing noise while preserving meaningful visual structure.
• topic modelA topic model is a probabilistic latent-variable model that represents discrete observations such as documents through unobserved thematic components.
• logistic regressionA probabilistic classification model that maps inputs to class probabilities using a logistic or softmax transformation of a linear score.
• gradientA gradient is a vector of partial derivatives that indicates how a scalar function changes with respect to its variables.
• embeddingA vector is an ordered mathematical object representing magnitude and direction or coordinates in a vector space.
• dynamic programming tableA dynamic programming table is a stored tabular arrangement of solutions to subproblems for reuse in constructing a larger solution.
• Robbins-Monro conditionsThe Robbins-Monro conditions are convergence requirements on a sequence of stochastic-approximation step sizes, typically involving divergent sums of step sizes and convergent sums of their squares.
• mixture weightA mixture proportion is a nonnegative weight assigned to a component distribution, with all component proportions summing to one.
• temperatureA temperature parameter is a positive scaling value that controls the probability of accepting unfavorable transitions in simulated annealing.
• topic distributionA topic distribution is a probability distribution over words that characterizes the word usage of a topic in a topic model.
• convolutional neural networkA convolutional neural network is a neural-network architecture that uses convolution and pooling operations to process structured spatial or grid-like data.
• naive bayes classifierA probabilistic classifier that assumes features are conditionally independent given the class label.
• boostingBoosting is an ensemble learning technique that combines weak learners trained sequentially with greater emphasis on previously misclassified examples.
• uniform distributionA uniform random variable has a constant probability density over a specified interval and zero density outside it.
• latent variableA latent variable is an unobserved variable inferred through its probabilistic relationship with observed data.
• term frequency-inverse document frequencyTF-IDF is a term-weighting technique that combines a term's frequency in a document with the inverse frequency of documents containing that term.

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