Search results for “регуляризация”

17 results

Machine Learning 1. Lecture 5. The Support Vector Machine

2026LectureКонстантин Вячеславович Воронцов

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.

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Machine Learning 1. Lecture 2. Stochastic Gradient and the Linear Classifier

2026LectureКонстантин Вячеславович Воронцов

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.

130

Machine Learning 1. Lecture 12. Density Estimation and Bayesian Classification

2026LectureКонстантин Вячеславович Воронцов

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.

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Machine Learning 1. Lecture 15. A Short Review of the Semester

2026LectureКонстантин Вячеславович Воронцов

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.

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Machine Learning 2. Lecture 5. Topic Modelling

2026LectureКонстантин Вячеславович Воронцов

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.

130

Machine Learning 1. Lecture 8. Feature Selection, Model Evaluation and Model Selection

2026LectureКонстантин Вячеславович Воронцов

Measures of classification quality: type I and type II errors, the ROC curve and AUC, gradient maximization of AUC, log-loss, precision and recall, micro- and macro-averaging, the F-measure; internal and external criteria of generalization ability; hold-out, leave-one-out, q-fold and t×q-fold cross-validation, stratification; model consistency; regularization, AIC, BIC and the Vapnik–Chervonenkis bound; multi-criteria model selection; feature selection: full search, Add, Add-Del, depth-first search, beam search (GMDH), the genetic algorithm and random search with adaptation.

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Machine Learning 1. Lecture 11. Advanced Ensemble Methods

2026LectureКонстантин Вячеславович Воронцов

Bias–variance analysis: the decomposition of the error into noise, bias and variance, the bias and variance of simple voting, why complex ensembles do not overfit; gradient boosting for an arbitrary loss function as a parametric approximation of a gradient step; stochastic gradient boosting; special cases: regression, AdaBoost, AnyBoost, variants of loss functions; XGBoost: the tree as a linear model, L0 and L2 regularisation, analytical leaf values and the splitting criterion; CatBoost: leakage in the gradients, ordered boosting on subsamples of doubling length, unbiased target statistics for categorical features.

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Machine Learning 1. Lecture 13. Clustering and Semi-Supervised Learning

2026LectureКонстантин Вячеславович Воронцов

The clustering problem and its ill-posedness, the aims of clustering, types of cluster structure, sensitivity to the choice of metric; the problem of semi-supervised learning and transductive learning, why it reduces neither to classification nor to clustering; criteria of clustering quality, the silhouette coefficient, the BCubed measures of precision and recall; the k-means method (Lloyd's algorithm) as a simplification of the EM algorithm for a mixture of Gaussians; the DBSCAN algorithm; agglomerative hierarchical clustering, the Lance–Williams formula and its special cases, the dendrogram, monotonicity, contracting and dilating distances, Ward's distance; semi-supervised learning based on classification: self-training, co-training, co-learning, the transductive SVM, expectation regularisation (XR).

280

Machine Learning 2. Lecture 4. Attention Models and Transformers

2026LectureКонстантин Вячеславович Воронцов

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.

450

Machine Learning. Additional Lecture 2. A Survey of Optimisation Problems in Machine Learning

2026LectureКонстантин Вячеславович Воронцов

A survey lecture: machine learning as formulations of optimisation problems, a model, a loss function, a regulariser. Regression and classification, continuous approximations of the threshold loss function, SVM and logistic regression, quantile, robust and SVM regression; the L0, L1, L2, Elastic Net, SFM, RFM regularisers and feature selection; learning to rank: ordinal regression, the pairwise approach and AUC, LambdaRank; estimating a density and a mixture of distributions, clustering as a special case of a mixture, the one-class SVM; semi-supervised learning, the transductive SVM, PU-learning; matrix factorisations, autoencoders, multidimensional scaling, graph factorisations, GraphEDM; transfer learning, multi-task and self-supervised learning, distillation, learning using privileged information, generative adversarial networks; a typology of machine learning problems.

210

Machine Learning 1. Lecture 3. Neural Networks: Gradient Optimization Methods

2026LectureКонстантин Вячеславович Воронцов

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).

130

Machine Learning 1. Lecture 7. Generalizations of Linear Models

2026LectureКонстантин Вячеславович Воронцов

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.

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Machine Learning 2. Lecture 1. Deep Neural Networks

2026LectureКонстантин Вячеславович Воронцов

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.

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Machine Learning 1. Lecture 6. Linear Regression Models

2026LectureКонстантин Вячеславович Воронцов

Multiple linear regression and least squares, the pseudoinverse and the geometric meaning of least squares; the solution through the singular value decomposition; multicollinearity and the condition number; ridge regression, choosing the regularization parameter and the effective dimension; LASSO and non-smooth regularizers for feature selection; principal component analysis as a low-rank matrix decomposition; the spectral method of least squares.

130

Machine Learning 1. Generalization Theory

2026LectureКонстантин Вячеславович Воронцов

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.

140

Machine Learning 2. Adaptive Forecasting Methods

2026LectureКонстантин Вячеславович Воронцов

Time series forecasting problems: the time series model, the forecasting horizon, the least squares method; econometrics as the main source of problems — trends, seasonalities, change points; examples of forecasting sales volumes and electricity prices; the linear autoregression model; a brief survey of forecasting methods; adaptive short-term forecasting methods: the exponential moving average and the smoothing parameter, the models of Holt, Theil–Wage, Winters with linear and exponential trend, adaptive autoregression; the tracking signal and a statistical test of model adequacy, the Trigg–Leach model; adaptive selection and adaptive composition of models, the LAVR method — local adaptation of weights with regularisation, the monotonicity constraint as a regulariser; experiments on the sales forecasting problem.

140

Константин Вячеславович Воронцов

@konstantin_vorontsov

Константин Вячеславович Воронцов — профессор РАН, доктор физико-математических наук. Заведующий кафедрой «Математические методы прогнозирования» ВМК МГУ, где с 2021 года — профессор; заведующий лабораторией «Машинное обучение и семантический анализ» Института искусственного интеллекта МГУ (с 2022 года); заведующий кафедрой «Машинное обучение и цифровая гуманитаристика» МФТИ (с 2021 года); заведующий кафедрой «Интеллектуальные системы» МФТИ (с 2022 года), на которой работает с 2004 года; главный научный сотрудник отдела «Интеллектуальные системы» ВЦ ФИЦ ИУ РАН, где работает с 2001 года. Окончил МФТИ (1994) и аспирантуру ВЦ РАН (1997). Кандидатская диссертация «Локальные базисы в алгебраическом подходе к проблеме распознавания» (1999, специальность 01.01.09); докторская диссертация «Комбинаторная теория надёжности обучения по прецедентам» (2010, специальность 05.13.17). Автор комбинаторной теории надёжности обучения по прецедентам, оценивающей вероятность переобучения с учётом эффектов расслоения и сходства в семействах алгоритмов; основное направление его исследований — теория и методы аддитивной регуляризации тематических моделей (ARTM). С 2014 года — научный руководитель разработки библиотеки тематического моделирования с открытым кодом BigARTM, с 2019 года — поисково-рекомендательной системы SciSearch. Один из идеологов и администраторов ресурса MachineLearning.ru (с 2008 года). Медаль РАН с премией для молодых учёных (1999, совместно с Е. В. Нарыжным); почётное звание профессора РАН (2015); юбилейная медаль РАН «300 лет Российской академии наук» (2024); премия Yandex ML Prize в номинации «Зал славы» (2025). Автор курсов «Вероятностные тематические модели», «Математические методы анализа текстов», «Прикладной статистический анализ данных» и спецкурса по теории надёжности обучения по прецедентам; в 2008–2020 годах преподавал в Школе анализа данных Яндекса. С 2004 года читает годовой курс «Машинное обучение» в МФТИ и ВМК МГУ.