Search results for “уравнение Беллмана”

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.

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.

Задачные листки к курсу линейной алгебры. Институт и учебное заведение в исходных публикациях не указаны, поэтому здесь не названы.

Линейные пространства над произвольным полем, подпространства, линейная зависимость, базис и размерность, сумма и пересечение подпространств, замена базиса.

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.

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.

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.

Integrating a vector field along a directed curve: parametrising a segment and a graph, the work of a force, path dependence, a potential field and its potential, a curl-free field in a domain that is not simply connected.