Search results for “нелинейная регрессия”

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.

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.

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.

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.