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Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…
We study the recursion-theoretic complexity of Positive Almost-Sure Termination ($\mathsf{PAST}$) in an imperative programming language with rational variables, bounded nondeterministic choice, and discrete probabilistic choice. A program…
We improve lower bounds on the $k$th-order nonlinear complexity of pseudorandom sequences over finite fields and we establish a probabilistic result on the behavior of the $k$th-order nonlinear complexity of random sequences over finite…
We consider the problem of binary classification with abstention in the relatively less studied \emph{bounded-rate} setting. We begin by obtaining a characterization of the Bayes optimal classifier for an arbitrary input-label distribution…
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
This paper formalizes a latent variable inference problem we call {\em supervised pattern discovery}, the goal of which is to find sets of observations that belong to a single ``pattern.'' We discuss two versions of the problem and prove…
We consider the problem of learning the causal MAG of a system from observational data in the presence of latent variables and selection bias. Constraint-based methods are one of the main approaches for solving this problem, but the…
We introduce a formal notion of defendability against backdoors using a game between an attacker and a defender. In this game, the attacker modifies a function to behave differently on a particular input known as the "trigger", while…
This study examines whether unobserved factors substantially bias education evaluations that rely on the Conditional Independence Assumption. We add 14 new within-study comparisons to the literature, all from primary schools in England.…
We give an explicit upper bound for the number of equivalence classes of binary forms with rational integral coefficients of given degree and given discriminant, and with given splitting field. Further, we give an explicit upper bound for…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
Modeling a sequence of design steps, or a sequence of parameter settings, yields a sequence of dynamical systems. In many cases, such a sequence is intended to approximate a certain limit case. However, formally defining that limit turns…
Existing survival analysis techniques heavily rely on strong modelling assumptions and are, therefore, prone to model misspecification errors. In this paper, we develop an inferential method based on ideas from conformal prediction, which…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
We introduce the first complete formal solution to corrigibility in the off-switch game, with provable guarantees in multi-step, partially observed environments. Our framework consists of five *structurally separate* utility heads --…
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
Decidability of the problems of unboundedness and simultaneous unboundedness (aka. the diagonal problem) for higher-order recursion schemes was established by Clemente, Parys, Salvati, and Walukiewicz (2016). Then a procedure of optimal…
In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling.…
In this paper we consider stopping problems with partial observation under a general risk-sensitive optimization criterion for problems with finite and infinite time horizon. Our aim is to maximize the certainty equivalent of the stopping…