Search results for “нейронные сети”

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).

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).

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.

Vector representations (embeddings) of texts and graphs: the distributional semantics hypothesis, syntagmatic and paradigmatic similarity of words, the CBOW and Skip-gram models of the word2vec program, hierarchical SoftMax on a Huffman tree, negative sampling (SGNS) and the connection of word2vec with the matrix factorisation of the PMI matrix, semantic analogies of words, the FastText model on character n-grams; texts as graphs; multidimensional scaling and the stress criterion, stochastic neighbour embedding SNE, perplexity, t-SNE; matrix factorisations of graphs, the random-walk models DeepWalk and node2vec; graph embedding methods as autoencoders, the generalised GraphEDM model, graph neural networks and message passing.

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.

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.

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 interpretability of models; decision trees and the greedy ID3 algorithm; the axioms of impurity, the entropy and Gini criteria; handling missing values; the merits and drawbacks of the greedy strategy; tree pruning (post-pruning); CART regression trees and Minimal Cost-Complexity Pruning; rule induction: logical regularities, families of rules (conjunctions, syndromes, half-planes, balls), search metaheuristics, a tree as a covering set of conjunctions; the Pareto front in (p,n) space, logical and statistical regularities, Fisher's exact test, informativeness criteria; building a classifier from regularities.

Learning on a data stream: the formulation of the online learning problem, the learning curve, the issues: efficient model updates, making the model more complex as the sample grows, the equivalence of online and offline, storing the sample and catastrophic forgetting; how online learning differs from incremental learning, continual learning, anytime algorithms; lazy learning and online prototype selection; the online naive Bayes classifier with exponential distributions of features; the perceptron, Passive-Aggressive and online gradient descent; the recursive least squares method and the Sherman–Morrison formula; incremental training of decision trees ID5R; online training of an ensemble by the Hedge(β) algorithm and its financial interpretation; online deep learning and Hedge BackProp; incremental learning of new classes, iCaRL.

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.

Objects, features and answers; the types of supervised learning problems; parametric models and the learning method; loss functions and empirical risk minimization; the Runge example and overfitting; hold-out, leave-one-out and cross-validation; applied problems from medical diagnosis to sales forecasting; the CRISP-DM standard.

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.

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.

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.