Search results for “LIME”

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.

Linear dependence and independence of the rows of a matrix, the criterion via a linear combination, and the connection to rank.

Linear systems in matrix form, the Kronecker–Capelli theorem, homogeneous systems, and the fundamental system of solutions.

The axioms of a linear (vector) space, examples and counterexamples.

A linear operator and its matrix, the action x' = Ax, similar matrices, and the formula B = C⁻¹AC.

Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.

Vectors in coordinates: dividing a segment, midpoints of sides, the angle between vectors, the cross product and the scalar triple product.

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.

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.

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.

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.

Ensembles of models: base algorithms, the space of estimates, the decision rule and correcting functions; the problem of diversity of base algorithms; bagging, the random subspace method and a common pseudocode of stochastic ensembling; the unbiased out-of-bag estimate and estimating feature importance; converting simple voting into weighted voting; the random forest; boosting for binary classification with abstentions, the exponential approximation of the threshold loss function, the main theorem of AdaBoost with proof, convergence, classical AdaBoost and heuristics; why boosting does not overfit: experiments, bounding the probability of error through margins, the distribution of margins, comparison with bagging; the ComBoost algorithm.

Linear dependence of vectors, basis and coordinates, dimension, subspaces, and linear span.

Addition, scalar multiplication, transposition and multiplication of matrices, along with subtraction, powers, and trace.

The basic properties of addition, scalar multiplication, transposition, and multiplication of matrices, with justifications.

The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.

The basic properties of determinants with brief proofs, and their use in simplifying computations.