Related papers: Predicativity and parametric polymorphism of Brouw…

In this paper, we consider the complexity of propositional proofs of classical and intuitionistic tautologies. In fact, we describe a nondeterministic polynomial-time decision procedure for intuitionistic implicational tautologies. For this…

In causal estimation problems, the parameter of interest is often only partially identified, implying that the parameter cannot be recovered exactly, even with infinite data. Here, we study Bayesian inference for partially identified…

Geometric theories based on classical logic are conservative over their intuitionistic counterparts for geometric implications. The latter result (sometimes referred to as Barr's theorem) is squarely a consequence of Gentzen's Hauptsatz.…

We study how to infer new choices from previous choices in a conservative manner. To make such inferences, we use the theory of choice functions: a unifying mathematical framework for conservative decision making that allows one to impose…

Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…

The concepts of Bayesian prediction, model comparison, and model selection have developed significantly over the last decade. As a result, the Bayesian community has witnessed a rapid growth in theoretical and applied contributions to…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

Inspired from a joint work by A. Beckmann, S. Buss and S. Friedman, we propose a class of set-theoretic functions, predicatively computable functions. Each function in this class is polynomial time computable when we restrict to finite…

Predictive Bayesian inference (PBI) represents a model-and prior-agnostic approach to standard Bayesian inference which allows users to quantify uncertainty for a functional of interest only by specifying a forward predictive model for…

The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…

There are three principle paradigms of statistical inference: (i) Bayesian, (ii) information-based and (iii) frequentist inference. We describe an objective prior (the weighting or $w$-prior) which unifies objective Bayes and…

We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.

In this paper, we will give a natural definition for morphisms between multiplicative unitaries. We will then discuss some equivalences of this definition and some interesting properties of them. Moreover, we will define normal…

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…

Inside a product of projective spaces, we try to understand which Chow classes come from irreducible subvarieties. The answer is closely related to the theory of integer polymatroids. The support of a representable class can be (partially)…

Unobserved confounding is a central barrier to drawing causal inferences from observational data. Several authors have recently proposed that this barrier can be overcome in the case where one attempts to infer the effects of several…

The task of distribution generalization concerns making reliable prediction of a response in unseen environments. The structural causal models are shown to be useful to model distribution changes through intervention. Motivated by the…

Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…

There exist initial segments of both the Dyment lattice and the Dyment-Muchnik lattice that yield Brouwer algebras modeling exactly the intuitionistic propositional calculus. For the Dyment-Muchnik lattice, this result is obtained by…

We present an interpretable companion model for any pre-trained black-box classifiers. The idea is that for any input, a user can decide to either receive a prediction from the black-box model, with high accuracy but no explanations, or…