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Search results for “вектор Шепли”

43 results

Machine Learning 2. Lecture 12. Interpretability and Explainability

2026LectureКонстантин Вячеславович Воронцов

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.
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230

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.
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210

Machine Learning 2. Lecture 3. Vector Representations of Texts and Graphs

2026LectureКонстантин Вячеславович Воронцов

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.
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250

Geometry. Lecture 2

2026LectureФёдор Попеленский

Finite geometries — the Platonic solids. A reminder — right actions, orbits, stabilisers, fundamental domains (corrected definition) and the example of Z+Z\mathbb{Z} + \mathbb{Z} on the plane; the formula ∣G∣=∣Orb⁡(x)∣⋅∣Stab⁡(x)∣|G| = |\operatorname{Orb}(x)| \cdot |\operatorname{Stab}(x)| and the 48 symmetries of the cube; regular polyhedra — Sosinsky's definition and the definition via flags, a stellated counterexample; the five Platonic solids; regular polytopes in R4\mathbb{R}^4 (six) and in Rn\mathbb{R}^n for n≥5n \ge 5 (the cube, the simplex, the hyperoctahedron) with the coordinates of their vertices; why there are no more than five — face angles and the Schläfli symbol; uniqueness of the gluing and the rigidity theorem; Euler's formula; the finite subgroups of SO(3)SO(3) — Zn\mathbb{Z}_n, DnD_n and the rotation groups of the tetrahedron, cube and icosahedron; the duality cube–octahedron, icosahedron–dodecahedron; which figures on the sphere realise Zn\mathbb{Z}_n, DnD_n and Z2\mathbb{Z}_2.

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380

Machine Learning 1. Lecture 4. Metric Methods of Classification and Regression

2026LectureКонстантин Вячеславович Воронцов

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.
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150

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

Machine Learning 2. Lecture 6. Learning to Rank

2026LectureКонстантин Вячеславович Воронцов

The learning-to-rank problem: recovering a partial order relation, the pointwise, pairwise and listwise approaches, the linear ranking model, applications; ordinal regression and the ordinal SVM (SVOR); the pairwise criterion, Ranking SVM, RankNet, the transition to the listwise method LambdaRank; ranking search results: query–document objects, assessor ratings, text, link and click features, TF-IDF and its probabilistic meaning, Okapi BM25, PageRank; quality criteria: precision and recall, MAP, the share of defective pairs and its link with AUC, DCG and NDCG, the pFound user behaviour model; the DSSM neural model: a siamese network, word hashing by letter trigrams, training on clicks with negative sampling.
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130

Базис, координаты и проекция вектора

2026TheorySergey

Разложение вектора по базису на плоскости и в пространстве, ортонормированный базис и декартова система координат, координаты вектора и линейные операции над ними, проекция вектора на ось, её линейность и проекция на вектор.
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60

Векторы

2026OtherSergey

Геометрические векторы: определение, длина, равенство, коллинеарность и компланарность; линейные операции над векторами и их свойства; разложение вектора по коллинеарному.
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70

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 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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170

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.
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450

Векторное произведение

2026OtherSergey

Ориентация тройки векторов, определение векторного произведения через длину, перпендикулярность и правую тройку, геометрический смысл (площадь параллелограмма), свойства с доказательствами и полный вывод формулы через определитель.
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90

Machine Learning 1. Lecture 1. Basic Concepts and Examples of Applied Problems

2026LectureКонстантин Вячеславович Воронцов

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.
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210

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.
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130

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).
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130