Search results for “t-SNE”

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.

Modern psycholinguistic research and fact-checking actively explore the space of media discourse. However, the representation of the judicial space in the mass media has not been sufficiently studied due to the peculiarities of communicative behavior in the judicial and legal space of the ethno-socius and the attitude to the judiciary. The authors hypothesize that the differences in public behavior in court and the coverage of the work of courts in the American, Kazakh and Russian media are due to the socio-cultural features of the phenomena of judicial and legal communication in public space under the influence of established traditions in such coordinate systems as “person – judicial system”, “openness – closeness of society”, “unity – disunity of society”, “accessibility – stigmatization”, “court – journalistic investigation”, etc. The results confirm the hypothesis of the authors' team, revealing the difference in the perception of the judicial system in the USA, Kazakhstan and Russia, illustrating the "rejection" of the Soviet and post-Soviet stigmatization of the judicial and legal space by the Kazakh society towards democratic norms. The prospects of the study are related to the subsequent development of an automatic system for evaluating speech behavior strategies in court and their coverage in the media as a category of fact-checking.

Opinion mining is a popular task, that is applied, for example, to determine news polarisation and identify product review classes. Our task is unsupervised clusterization of opinionated texts, in particular news on political events. Many papers that tackle this issue use generative models based on lexical features. Our goal is to determine the entities defying an opinion amongst lexical, syntactic and semantic features as well as their compositions. More specifically, we test the hypothesis that an opinion is determined by the composition of the mentioned facts (SPO triples), the semantic roles of the words and the sentiment lexicon used in it. In this paper we formalise this task and prove that using a composition of the above features provides the best quality when clusterising opinionated texts. To test this hypothesis we have gathered and labelled two corpuses of news on political events and proposed a set of unsupervised algorithms for extracting the features.

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.

Measures of classification quality: type I and type II errors, the ROC curve and AUC, gradient maximization of AUC, log-loss, precision and recall, micro- and macro-averaging, the F-measure; internal and external criteria of generalization ability; hold-out, leave-one-out, q-fold and t×q-fold cross-validation, stratification; model consistency; regularization, AIC, BIC and the Vapnik–Chervonenkis bound; multi-criteria model selection; feature selection: full search, Add, Add-Del, depth-first search, beam search (GMDH), the genetic algorithm and random search with adaptation.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.

Reference table of indefinite integrals of the exponential function and its products with powers of x.

An example, due to Serre, of a smooth projective surface in positive characteristic whose Picard scheme fails to be reduced, worked out via the two governing dimension inequalities.

Bias–variance analysis: the decomposition of the error into noise, bias and variance, the bias and variance of simple voting, why complex ensembles do not overfit; gradient boosting for an arbitrary loss function as a parametric approximation of a gradient step; stochastic gradient boosting; special cases: regression, AdaBoost, AnyBoost, variants of loss functions; XGBoost: the tree as a linear model, L0 and L2 regularisation, analytical leaf values and the splitting criterion; CatBoost: leakage in the gradients, ordered boosting on subsamples of doubling length, unbiased target statistics for categorical features.

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.

Collaborative filtering problems: transaction data, the clients–items matrix, filling in missing values and ranking recommendations, the Netflix Prize competition; user-based and item-based correlation methods, the Pearson, cosine and Jaccard similarity measures, Fisher's exact test; the sparse linear model SLIM; latent models and matrix factorisations: SVD, the alternating least squares method ALS, the latent factor model LFM and stochastic gradient, nonnegative matrix factorisations NNMF, PLSA; taking implicit preferences into account (implicit feedback); matrix factorisation as a linear autoencoder, neural network and denoising autoencoders; taking features of clients and items into account, factorisation machines libFM, a hypergraph topic model; the quality of recommendations: RMSE, precision@k, recall@k, diversity, novelty, coverage, serendipity, bias, offline and online evaluation.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.

The Millennium Meeting, Paris, 24 May 2000, at which the seven problems were announced.

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.