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43 results

Machine Learning 2. Lecture 8. Association Rule Mining

2026LectureКонстантин Вячеславович Воронцов

Association rule mining as unsupervised learning: binary features, support and frequent itemsets, the association rule, minimum support MinSupp and minimum confidence MinConf; market basket analysis; the link between association rules and logical regularities; the anti-monotonicity of support; the APriori algorithm: breadth-first search for frequent itemsets and recursive extraction of rules; modifications: search on a random subsample, item hierarchies, incremental and decremental algorithms; the FP-growth algorithm: the prefix FP-tree, building it in one pass over the transaction database, computing the support of any itemset from the tree, the conditional FP-tree and recursive search for frequent itemsets; the speed of FP-growth compared with APriori.
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160

Probability Theory. Lecture 1

2026LectureСтанислав Шапошников

The finite probability space and five properties of probability, a description of all probability measures on a finite set, equally likely outcomes and the choice of a model, classical paradoxes (two dice, the division of the stakes, Bertrand's paradox), conditional probability and the product rule, the law of total probability as a way to define a measure, Bayes' formula, independence of events.
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170

Algebra 1. Lecture 1

2026LectureАртём Авилов

What algebra studies — algebraic structures. Groups (definition, examples, additive notation, uniqueness of the identity and of inverses), rings (variants of the axioms, rings with and without identity), fields and division rings, vector spaces and modules, algebras over a field. The symmetric group SnS_n — permutations, non-commutativity, two-row notation, cycles and transpositions, decomposition into transpositions, disjoint permutations commute, decomposition into disjoint cycles and its uniqueness, powers, inversions, parity and the sign of a permutation, multiplying by a transposition changes the sign.

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310

Machine Learning 1. Lecture 9. Logical Classification Methods

2026LectureКонстантин Вячеславович Воронцов

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.
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160

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).
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280

Аффинные пространства

2026LectureTaras Panov

Аффинные пространства и подпространства, аффинные системы координат и формулы их замены, прямые и плоскости в аффинных пространствах.
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460

Machine Learning 1. Lecture 14. Anomaly Detection and Robust Methods

2026LectureКонстантин Вячеславович Воронцов

Anomaly and novelty detection; heuristic anomaly scores: local density, isolation forest, a mixture with a background component, robust principal component analysis; outlier removal in nonparametric regression, the LOWESS algorithm; anomaly as the value of the loss function; the theory of robust learning: slowly growing functions, iterative reweighting of objects with IRS and IRLS, robust loss functions, the median, the quantile and the censored mean, robust aggregation functions and their smoothing, the IR-ERM algorithm; one-class SVM, learning from positive and unlabeled objects (PU-learning), problems with new and unknown classes.
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480

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.
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140

Mathematical Analysis 1. Lecture 1

2026LectureСтанислав Шапошников

Naive set theory and Russell's paradox, Kuratowski's ordered pair and the Cartesian product, a function as a subset of a product, composition, injections, surjections and bijections, the group of bijections and the embedding of any group into it, equinumerosity and indicator functions, the Cantor–Bernstein and Cantor theorems.
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290

Евклидовы пространства

2026LectureTaras Panov

Евклидовы и эрмитовы пространства, скалярное произведение, неравенство Коши–Буняковского и неравенство треугольника, ортогональные системы векторов.
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190

Machine Learning 1. Bayesian Classification Theory

2026LectureКонстантин Вячеславович Воронцов

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.
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180

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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190

Machine Learning 2. Lecture 2. Neural Networks for Unsupervised Learning

2026LectureКонстантин Вячеславович Воронцов

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).
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210

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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390

Geometry. Lecture 1

2026LectureФёдор Попеленский

What geometries there are and what they have in common — Klein's Erlangen programme; the school 3–4–5 triangle and the ellipsoid; the cube and the brick as finite geometries; metric spaces; groups, quantifiers in the axioms; the group of bijections and the order of composition; left and right actions of a group on a set; the metrics d1d_1, d2d_2, d∞d_\infty on Rn\mathbb{R}^n; isometries, subgroups; the order of an element; orbits, stabilisers, transitive actions; the list of geometries in the course — the Euclidean plane, the regular triangle and S3S_3, the cube and its 48 symmetries, the Poincaré model of the Lobachevsky plane; fundamental domains; subgeometries — the square in the cube.

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330