Search results for “байесовский классификатор”

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.

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.

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.

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.

Objects, features and answers; the types of supervised learning problems; parametric models and the learning method; loss functions and empirical risk minimization; the Runge example and overfitting; hold-out, leave-one-out and cross-validation; applied problems from medical diagnosis to sales forecasting; the CRISP-DM standard.