Related papers: Dense-choice Counter Machines revisited
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
As machine learning systems become ubiquitous, there has been a surge of interest in interpretable machine learning: systems that provide explanation for their outputs. These explanations are often used to qualitatively assess other…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
AI-driven outcomes can be challenging for end-users to understand. Explanations can address two key questions: "Why this outcome?" (factual) and "Why not another?" (counterfactual). While substantial efforts have been made to formalize…
Explainability of deep convolutional neural networks (DCNNs) is an important research topic that tries to uncover the reasons behind a DCNN model's decisions and improve their understanding and reliability in high-risk environments. In this…
A $k$-Counter Net ($k$-CN) is a finite-state automaton equipped with $k$ integer counters that are not allowed to become negative, but do not have explicit zero tests. This language-recognition model can be thought of as labelled vector…
Recently, decision trees (DT) have been used as an explainable representation of controllers (a.k.a. strategies, policies, schedulers). Although they are often very efficient and produce small and understandable controllers for discrete…
The aim of this paper is twofold. First, we extend the results of [33] concerning the existence and uniqueness of second-order reflected 2BSDEs to the case of two obstacles. Under some regularity assumptions on one of the barriers, similar…
Counterfactual explanations (CEs) are advocated as being ideally suited to providing algorithmic recourse for subjects affected by the predictions of machine learning models. While CEs can be beneficial to affected individuals, recent work…
Counterfactual explanations focus on "actionable knowledge" to help end-users understand how a machine learning outcome could be changed to a more desirable outcome. For this purpose a counterfactual explainer needs to discover input…
In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
A fundamental challenge in approximating an unknown density using finite Gaussian mixture models is selecting the number of mixture components, also known as order. Traditional approaches choose a single best model using information…
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…
Selective rationalization has become a common mechanism to ensure that predictive models reveal how they use any available features. The selection may be soft or hard, and identifies a subset of input features relevant for prediction. The…
We consider arbitrary bounded discrete time series originating from dynamical system with recursivity. More precisely, we provide an explicit construction of recurrent neural networks which effectively approximate the corresponding discrete…
Some types of statistical convergence such as statistical order and deferred statistical convergences have been studied and investigated in Riesz spaces, recently. In this paper, we introduce the concept of deferred statistical convergence…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
Evaluating the performance of clustering models is a challenging task where the outcome depends on the definition of what constitutes a cluster. Due to this design, current existing metrics rarely handle multiple clustering models with…