Search results for “EM-алгоритм”

Estimating a probability density from a sample: the maximum likelihood principle, the multivariate Gaussian density and its geometric meaning, multicollinearity and regularisation of the covariance matrix; separating a mixture of distributions, the EM algorithm as a method of simple iterations, the Gaussian mixture (GMM); the nonparametric Parzen–Rosenblatt estimate, the choice of kernel and window width; Bayesian classification theory: the generative and discriminative approaches, the optimal Bayes classifier, the Parzen window method, the quadratic discriminant, Fisher's linear discriminant, the radial basis function network and its training by the EM algorithm.

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.

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).

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.

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.