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Recent advances in interpretable Machine Learning (iML) and eXplainable AI (XAI) construct explanations based on the importance of features in classification tasks. However, in a high-dimensional feature space this approach may become…
The main objective of eXplainable Artificial Intelligence (XAI) is to provide effective explanations for black-box classifiers. The existing literature lists many desirable properties for explanations to be useful, but there is no consensus…
Explainable Artificial Intelligence (XAI) provides tools to help understanding how the machine learning models work and reach a specific outcome. It helps to increase the interpretability of models and makes the models more trustworthy and…
Let $(X_i,i\geq 1)$ be a sequence of i.i.d. random variables with values in $[0,1]$, and $f$ be a function such that $`E(f(X_1)^2)<+\infty$. We show a functional central limit theorem for the process $t\mapsto \sum_{i=1}^n f(X_i)1_{X_i\leq…
In this paper, we present a novel method to compute decision rules to build a more accurate interpretable machine learning model, denoted as ExMo. The ExMo interpretable machine learning model consists of a list of IF...THEN... statements…
Limit theorems for non-additive probabilities or non-linear expectations are challenging issues which have raised progressive interest recently. The purpose of this paper is to study the strong law of large numbers and the law of the…
The additive genetic effect is arguably the most important quantity inferred in animal and plant breeding analyses. The term effect indicates that it represents causal information, which is different from standard statistical concepts as…
We investigate the randomized decision tree complexity of a specific class of read-once threshold functions. A read-once threshold formula can be defined by a rooted tree, every internal node of which is labeled by a threshold function…
Chang's lemma (Duke Mathematical Journal, 2002) is a classical result with applications across several areas in mathematics and computer science. For a Boolean function $f$ that takes values in {-1,1} let $r(f)$ denote its Fourier rank. For…
We give a new bound on the sum of the linear Fourier coefficients of a Boolean function in terms of its parity decision tree complexity. This result generalizes an inequality of O'Donnell and Servedio for regular decision trees. We use this…
Explainable artificial intelligence (XAI) is one of the most intensively developed area of AI in recent years. It is also one of the most fragmented with multiple methods that focus on different aspects of explanations. This makes difficult…
Suppose $\XX{N}$ is a uniformly distributed $N$-dimensional binary vector and $\YY{N}$ is obtained by passing $\XX{N}$ through a binary symmetric channel with crossover probability $\alpha$. Recently, Courtade and Kumar postulates that…
Here we argue that the notion of falsifiability, a key concept in defining a valid scientific theory, can be quantified using Bayesian Model Selection, which is a standard tool in modern statistics. This relates falsifiability to the…
Evaluating explanation techniques using human subjects is costly, time-consuming and can lead to subjectivity in the assessments. To evaluate the accuracy of local explanations, we require access to the true feature importance scores for a…
Uncertainty estimation (UE) of generative large language models (LLMs) is crucial for evaluating the reliability of generated sequences. A significant subset of UE methods utilize token probabilities to assess uncertainty, aggregating…
The problem of counting the number of models of a given Boolean formula has numerous applications, including computing the leakage of deterministic programs in Quantitative Information Flow. Model counting is a hard, #P-complete problem.…
We consider univariate regression estimation from an individual (non-random) sequence $(x_1,y_1),(x_2,y_2), ... \in \real \times \real$, which is stable in the sense that for each interval $A \subseteq \real$, (i) the limiting relative…
Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…
We prove a Chernoff-like large deviation bound on the sum of non-independent random variables that have the following dependence structure. The variables $Y_1,...,Y_r$ are arbitrary Boolean functions of independent random variables…
This paper proposes an alternative approach to the basic taxonomy of explanations produced by explainable artificial intelligence techniques. Methods of Explainable Artificial Intelligence (XAI) were developed to answer the question why a…