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Search results for “функции потерь”

63 results

Machine Learning 2. Lecture 9. Incremental and Online Learning

2026LectureКонстантин Вячеславович Воронцов

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.
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200

Machine Learning. Additional Lecture 1. The Theory of Overfitting

2026LectureКонстантин Вячеславович Воронцов

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.
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220

Vector calculus. Line integrals of the first kind

2026Problem sheetSergey

Integration with respect to arc length: parametrising a curve, the length element ds=∣r′(t)∣ dtds = |\mathbf{r}'(t)|\,dt, arc length, curves in polar coordinates, the mass and centre of mass of a wire, symmetry instead of computation.

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530

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

Vector calculus. Green's theorem

2026Problem sheetSergey

A contour integral as a double integral: the hypotheses of Green's theorem, orientation of the contour, area as a contour integral, closing an open arc, an annulus, a singular point inside the contour.
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260

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

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

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

Vector calculus. Stokes' theorem. Circulation

2026Problem sheetSergey

Circulation of a field as the flux of its curl: computing the curl, matching the orientation of the contour and the normal, circulation computed two ways.
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310

Machine Learning 2. Lecture 11. Active Learning

2026LectureКонстантин Вячеславович Воронцов

Active learning: the model itself chooses which objects to give the teacher for labelling. The problem setting, why active learning is faster than passive learning, learning curves; pool-based sampling, query synthesis and stream-based selective sampling, cost-sensitive methods; uncertainty sampling (least confidence, minimum margin, maximum entropy), query by committee, version space reduction, expected model change, expected error reduction; query synthesis by the Nelder–Mead method and by the variance reduction criterion; density weighting; exploratory actions, the ε-active and EG-active algorithms with the exponentiated gradient; active learning in crowdsourcing: reconciling annotators' labels, models of their reliability and of object difficulty, assigning tasks to annotators.
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450

Алгебра 1. Лекция 4. Формальные степенные ряды и производящие функции

2026LectureAlexey Ilyin

В этой лекции рассматриваются формальные степенные ряды как алгебраический объект. Вводятся операции сложения, умножения, а также аналоги производной и интеграла. Ключевая идея лекции — применение этого аппарата для решения линейно-рекуррентных соотношений с помощью производящих функций, что демонстрируется на классическом примере чисел Фибоначчи.
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240

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.
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130