Search results for “линейный классификатор”

The general scheme of supervised learning for regression, binary and multiclass classification; the margin and continuous approximations of the threshold loss; the linear classifier as a model of a neuron; the stochastic gradient method, momentum, Nesterov's accelerated gradient and heuristics; multicollinearity and L2 regularization; the maximum likelihood principle, its link to empirical risk minimization and the probabilistic meaning of regularization.

The continuity and compactness hypotheses; the Minkowski metric and feature-free distances; the generalized metric classifier, the k nearest neighbours method, the Parzen window and the method of potential functions as a linear classifier; complete cross-validation, the compactness profile and the exact CCV formula for the nearest neighbour method; prototype selection; Nadaraya–Watson kernel smoothing, the choice of kernel and bandwidth.

The neuron as a linear model; implementing Boolean functions and the exclusive-OR problem; two-layer networks as universal approximators, Cybenko's theorem; the multilayer network and the backpropagation method; the adaptive gradient methods RMSProp, AdaDelta, Adam, Nadam; gradient explosion and gradient clipping; Dropout, ReLU activation functions, batch normalization, initialization and network pruning (Optimal Brain Damage).

The optimal separating hyperplane and the width of the separating strip; the hinge loss and L2 regularization; the Karush–Kuhn–Tucker conditions, the dual problem and the types of objects; kernels, rectifying spaces and the constructive building of kernels; SVM as a two-layer neural network; choosing the constant C; SVM regression; L1 regularization, Elastic Net SVM, SFM and RVM.

The probabilistic formulation of classification: prior and posterior class probabilities, class likelihood functions, the maximum a posteriori principle; the optimal Bayes classifier and losses from errors; empirical estimation of prior probabilities and class densities; the naive Bayes classifier, features with exponential-family densities and the linear naive Bayes classifier; a survey of Bayesian classifiers: the Parzen window method, the quadratic discriminant, Fisher's linear discriminant, Gaussian mixtures with diagonal covariance matrices, and the radial basis function network.

Estimating a probability density from a sample: the maximum likelihood principle, the multivariate Gaussian density and its geometric meaning, multicollinearity and regularisation of the covariance matrix; separating a mixture of distributions, the EM algorithm as a method of simple iterations, the Gaussian mixture (GMM); the nonparametric Parzen–Rosenblatt estimate, the choice of kernel and window width; Bayesian classification theory: the generative and discriminative approaches, the optimal Bayes classifier, the Parzen window method, the quadratic discriminant, Fisher's linear discriminant, the radial basis function network and its training by the EM algorithm.

Ensembles of models: base algorithms, the space of estimates, the decision rule and correcting functions; the problem of diversity of base algorithms; bagging, the random subspace method and a common pseudocode of stochastic ensembling; the unbiased out-of-bag estimate and estimating feature importance; converting simple voting into weighted voting; the random forest; boosting for binary classification with abstentions, the exponential approximation of the threshold loss function, the main theorem of AdaBoost with proof, convergence, classical AdaBoost and heuristics; why boosting does not overfit: experiments, bounding the probability of error through margins, the distribution of margins, comparison with bagging; the ComBoost algorithm.

Interpretability and explainability of machine learning models: goals, tasks and basic notions, who needs explanations and why; interpretable models; feature importance in linear regression: the t-statistic, net effects, contributions and situational importance; partial dependence plots (PDP) and individual conditional expectation plots (ICE); permutation feature importance; the Shapley value from cooperative game theory, its axioms and Monte Carlo estimation, its use in linear regression; surrogate modelling in the neighbourhood of an object, the LIME, Anchors, SHAP, Shapley Kernel and SAGE methods; the Shapley value for training objects, Data Shapley and Gradient Shapley; counterfactual explanations.

The combinatorial theory of overfitting: the probability of overfitting and why the Vapnik–Chervonenkis bounds are loose; experiments with overfitting — a monotone chain of algorithms, the effect of splitting and connectivity of the family on the probability of overfitting and on the complete cross-validation estimate, overfitting of chains, the exact formula for the probability of overfitting when choosing between two algorithms; the splitting–connectivity graph of a family of algorithms, examples for linear classifiers, a monotone chain and a two-dimensional net; generating and forbidden sets, upper connectivity and inferiority of an algorithm; the splitting–connectivity upper bound, the idea of its proof and its properties.

The problem of estimating generalization ability; the error matrix and the probability of overfitting; the case of a single algorithm and the hypergeometric distribution; the principle of uniform convergence of frequencies and Boole's inequality; the Vapnik–Chervonenkis bound, the growth function and the capacity of a family of algorithms; inverting the bound and the complexity penalty; structural risk minimization; the splitting and similarity effects; the Occam's razor bound and its link to regularization.

A closing review of the first semester: empirical risk minimisation and gradient methods; underfitting, overfitting, multicollinearity and regularisation; optimisation formulations of supervised learning (regression, classification, ranking) and unsupervised learning (density, mixtures, clustering, one-class classification, semi-supervised learning, PU-learning, principal component analysis, autoencoders); the six scientific schools of machine learning — symbolism, evolutionism, analogism, Bayesianism, connectionism, compositionism — and their Soviet roots; estimate-calculating algorithms; practice: CRISP-DM, data preprocessing, model evaluation and selection, loss analysis, A/B testing, meta-learning and AutoML.

A linear operator and its matrix, the action x' = Ax, similar matrices, and the formula B = C⁻¹AC.

Kohonen networks: clustering as a two-layer neural network, the hard (WTA) and soft (WTM) competition rules, self-organising Kohonen maps and their interpretation; autoencoders: the formulation of the problem, the linear autoencoder and the principal component method, sparse, denoising, contractive, relational and variational autoencoders, reparametrisation, autoencoders for supervised learning, multilayer autoencoders; joint training of several models: pre-training and transfer learning, multi-task learning and few-shot learning, self-supervised learning, distillation and surrogate modelling, learning using privileged information (LUPI), generative adversarial networks (GAN).

Collaborative filtering problems: transaction data, the clients–items matrix, filling in missing values and ranking recommendations, the Netflix Prize competition; user-based and item-based correlation methods, the Pearson, cosine and Jaccard similarity measures, Fisher's exact test; the sparse linear model SLIM; latent models and matrix factorisations: SVD, the alternating least squares method ALS, the latent factor model LFM and stochastic gradient, nonnegative matrix factorisations NNMF, PLSA; taking implicit preferences into account (implicit feedback); matrix factorisation as a linear autoencoder, neural network and denoising autoencoders; taking features of clients and items into account, factorisation machines libFM, a hypergraph topic model; the quality of recommendations: RMSE, precision@k, recall@k, diversity, novelty, coverage, serendipity, bias, offline and online evaluation.

Nonlinear regression: the Newton–Raphson and Gauss–Newton methods as a series of linear regressions; logistic regression and iteratively reweighted least squares (IRLS); the generalized additive model and backfitting; the probabilistic meaning of least squares; the generalized linear model (GLM), the exponential family of distributions and the link function; logistic regression as a special case of GLM; the median, quantile regression and robust loss functions.

Reminder: the neuron model, the multilayer network, stochastic gradient, momentum, vanishing and exploding gradients, ReLU, dropout, batch normalisation; depth matters more than width; feature generation and end-to-end learning; convolutional neural networks: convolution and pooling layers, the standard CNN scheme, AlexNet and ImageNet, residual networks ResNet and Highway Networks; convolutional networks for speech, texts and games; recurrent neural networks, training by BPTT, long short-term memory networks LSTM, the peephole variant, GRU.

Sequence-to-sequence problems: the recurrent network, the encoder–decoder architecture and its limitations; the recurrent network with an attention model, interpreting the attention matrix in machine translation and image captioning; similarity functions, the query–key–value attention model, the attention formula, self-attention; multi-head attention and its regularisation, hierarchical attention for document classification, the graph attention model GAT; the transformer for machine translation: the encoder, positional encoding, layer normalisation and skip connections, the decoder with masking, the training criterion, BLEU and WER; the transformer encoder BERT, the MLM and NSP criteria, fine-tuning, BPE and WordPiece tokenisation, model sizes.

Probabilistic topic modelling of text document collections: the bag-of-words and conditional independence hypotheses, the maximum likelihood criterion, three interpretations of the problem (soft clustering, stochastic matrix factorisation, autoencoder); the lemma on maximising a function on unit simplices; the ill-posedness of the problem and the additive regularisation of topic models ARTM, the EM algorithm and its interpretation; PLSA and LDA, the Dirichlet distribution, the maximum a posteriori probability and giving up Bayesian inference; smoothing, sparsing, background topics, decorrelation; multimodal and multilingual models, unigrams and bigrams; regularisers for classification and regression on texts, for word co-occurrence in short texts, for links between documents and for topic hierarchies.