Related papers: Dual feature-based and example-based explanation m…

The problem to compute the vertices of a polytope given by affine inequalities is called vertex enumeration. The inverse problem, which is equivalent by polarity, is called the convex hull problem. We introduce `approximate vertex…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

Although prototype-based explanations provide a human-understandable way of representing model predictions they often fail to direct user attention to the most relevant features. We propose a novel approach to identify the most informative…

Numerous algorithms have been proposed for detecting anomalies (outliers, novelties) in an unsupervised manner. Unfortunately, it is not trivial, in general, to understand why a given sample (record) is labelled as an anomaly and thus…

The recent criticisms of the robustness of post hoc model approximation explanation methods (like LIME and SHAP) have led to the rise of model-precise abductive explanations. For each data point, abductive explanations provide a minimal…

As black box explanations are increasingly being employed to establish model credibility in high-stakes settings, it is important to ensure that these explanations are accurate and reliable. However, prior work demonstrates that…

It is well known that every closure system can be represented by an implicational base, or by the set of its meet-irreducible elements. In Horn logic, these are respectively known as the Horn expressions and the characteristic models. In…

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

Counterfactual explanations are gaining prominence within technical, legal, and business circles as a way to explain the decisions of a machine learning model. These explanations share a trait with the long-established "principal reason"…

In order to ensure the reliability of the explanations of machine learning models, it is crucial to establish their advantages and limits and in which case each of these methods outperform. However, the current understanding of when and how…

Complex black-box machine learning models are regularly used in critical decision-making domains. This has given rise to several calls for algorithmic explainability. Many explanation algorithms proposed in literature assign importance to…

Contrastive explanations clarify why an event occurred in contrast to another. They are more inherently intuitive to humans to both produce and comprehend. We propose a methodology to produce contrastive explanations for classification…

The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…

It is shown how the Beneath-and-Beyond algorithm can be used to yield another proof of the equivalence of V- and H-representations of convex polytopes. In this sense this paper serves as the sketch of an introduction to polytope theory with…

This paper develops a unified framework for estimating the volume of a set in $\mathbb{R}^d$ based on observations of points uniformly distributed over the set. The framework applies to all classes of sets satisfying one simple axiom: a…

Multicriteria decision analysis aims at supporting a person facing a decision problem involving conflicting criteria. We consider an additive utility model which provides robust conclusions based on preferences elicited from the decision…

The convex hull of N independent random points chosen on the boundary of a simple polytope in R^n is investigated. Asymptotic formulas for the expected number of vertices and facets, and for the expectation of the volume difference are…

Local explainability methods -- those which seek to generate an explanation for each prediction -- are becoming increasingly prevalent due to the need for practitioners to rationalize their model outputs. However, comparing local…

Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed $k$, the method finds a convex polytope with $k$ vertices, called archetype points, such that the polytope is…

Model explanations based on pure observational data cannot compute the effects of features reliably, due to their inability to estimate how each factor alteration could affect the rest. We argue that explanations should be based on the…