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Despite their enormous predictive power, machine learning models are often unsuitable for applications in regulated industries such as finance, due to their limited capacity to provide explanations. While model-agnostic frameworks such as…
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on the set of these structures. This article presents a…
We investigate the problem of type isomorphisms in the presence of higher-order references. We first introduce a finitary programming language with sum types and higher-order references, for which we build a fully abstract games model…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
Predicative analysis of recursion schema is a method to characterize complexity classes like the class FPTIME of polynomial time computable functions. This analysis comes from the works of Bellantoni and Cook, and Leivant by data tiering.…
The fine-tuning of deep pre-trained models has revealed compositional properties, with multiple specialized modules that can be arbitrarily composed into a single, multi-task model. However, identifying the conditions that promote…
In hierarchical text classification, we perform a sequence of inference steps to predict the category of a document from top to bottom of a given class taxonomy. Most of the studies have focused on developing novels neural network…
It is proposed that to the usual probability theory, three definitions and a new theorem are added, the resulting theory allows one to displace the central role usually given to the notion of conditional probability. When a mapping $\phi$…
When does a machine learning model predict the future of individuals and when does it recite patterns that predate the individuals? In this work, we propose a distinction between these two pathways of prediction, supported by theoretical,…
In this article, we introduce the idempotentization process, which bears some philosophical and mathematical similarities with modern analytification and tropicalization. Idempotentization associates to any affine scheme an idempotent…
We introduce a refinement of the usual Ehrenfeucht-Fra\"{\i}ss\'e game. The new game will help us make finer distinctions than the traditional one. In particular, it can be used to measure the size formulas needed for expressing a given…
Our aim is to give some insights about how to approach the formal description of situations where one has to conciliate several contradictory statements, rules, laws or ideas. We show that such a conciliation structure can be naturally…
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…
This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…
Baseball is a game of strategic decisions including bullpen usage, pinch-hitting and intentional walks. Managers must adjust their strategies based on the changing state of the game in order to give their team the best chance of winning. In…
Considering the flexibility and applicability of Bayesian modeling, in this work we revise the main characteristics of two hierarchical models in a regression setting. We study the full probabilistic structure of the models along with the…
Behavioral experiments on the trust game have shown that trust and trustworthiness are universal among human beings, contradicting the prediction by assuming \emph{Homo economicus} in orthodox Economics. This means some mechanism must be at…
This paper is concerned with the theoretical understanding of $\alpha$-stable sheets $U$ on $\mathbb{R}^d$. Our motivation for this is in the context of Bayesian inverse problems, where we consider these processes as prior distributions,…
Our aim is to model a game for power as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods…
Evolutionary game theory has been a successful tool to combine classical game theory with learning-dynamical descriptions in multiagent systems. Provided some symmetric structures of interacting players, many studies have been focused on…