Related papers: Yay for Determinants!
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
We provide a novel tool which may be used to construct new examples of positive maps in matrix algebras (or, equivalently, entanglement witnesses). It turns out that this can be used to prove positivity of several well known maps (such as…
Explainable AI (XAI) methods have mostly been built to investigate and shed light on single machine learning models and are not designed to capture and explain differences between multiple models effectively. This paper addresses the…
The problem of parameter estimation from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a…
Some applications of a result, which is proved recently, is considered. We first prove three determinantal identities concerning the binomial coefficient and Stirling numbers of the first and the second kind. We also easily obtain the…
Explainable recommendation through counterfactual reasoning seeks to identify the influential aspects of items in recommendations, which can then be used as explanations. However, state-of-the-art approaches, which aim to minimize changes…
We look into the problems of comparing nondeterministic discounted-sum automata on finite and infinite words. That is, the problems of checking for automata $A$ and $B$ whether or not it holds that for all words $w$, $A(w)=B(w), A(w) \leq…
Recommender systems are ubiquitous in on-line services to drive businesses. And many sequential recommender models were deployed in these systems to enhance personalization. The approach of using the transformer decoder as the sequential…
Given data over variables $(X_1,...,X_m, Y)$ we consider the problem of finding out whether $X$ jointly causes $Y$ or whether they are all confounded by an unobserved latent variable $Z$. To do so, we take an information-theoretic approach…
Regular expressions and automata models with capture variables are core tools in rule-based information extraction. These formalisms, also called regular document spanners, use regular languages in order to locate the data that a user wants…
Active learning (AL), which aims to construct an effective training set by iteratively curating the most formative unlabeled data for annotation, has been widely used in low-resource tasks. Most active learning techniques in classification…
The purpose of the present work is to provide short and supple teaching notes for a $30$ hours introductory course on elementary \textit{Enumerative Algebraic Combinatorics}. We fully adopt the \textit{Rota way}. The themes are organized…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
Creating test collections for offline retrieval evaluation requires human effort to judge documents' relevance. This expensive activity motivated much work in developing methods for constructing benchmarks with fewer assessment costs. In…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.
By automatically recognize argument component, essay writers can do some inspections to texts that they have written. It will assist essay scoring process objectively and precisely because essay grader is able to see how well the argument…
Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction…
We consider a method for conformalizing a stacked ensemble of predictive models, showing that the potentially simple form of the meta-learner at the top of the stack enables a procedure with manageable computational cost that achieves…