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The lossless data compression algorithm based on Bayesian Attention Networks is derived from first principles. Bayesian Attention Networks are defined by introducing an attention factor per a training sample loss as a function of two sample…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
A central problem in business concerns the optimal allocation of limited resources to a set of available tasks, where the payoff of these tasks is inherently uncertain. In credit card fraud detection, for instance, a bank can only assign a…
The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A…
The sequence of $\alpha$-trimmings of empirical probabilities is shown to converge, in the Painlev\'{e}--Kuratowski sense, on the class of probability measures endowed with the weak topology, to the $\alpha$-trimming of the population…
The focal-loss has become a widely used alternative to cross-entropy in class-imbalanced classification problems, particularly in computer vision. Despite its empirical success, a systematic information-theoretic study of the focal-loss…
This paper proposes a linear categorical random coefficient model, in which the random coefficients follow parametric categorical distributions. The distributional parameters are identified based on a linear recurrence structure of moments…
In this article, we prove the cutoff phenomenon for a general class of the discrete-time nonlinear recombination models. This system models the evolution of a probability measure on a finite product space $S^n$ representing the state of…
The task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions. Using the techniques of low-temperature expansions, we arrive at a systematic series for the Bayesian posterior…
The problem of model selection is inevitable in an increasingly large number of applications involving partial theoretical knowledge and vast amounts of information, like in medicine, biology or economics. The associated techniques are…
Models based on preferential attachment have had much success in reproducing the power law degree distributions which seem ubiquitous in both natural and engineered systems. Here, rather than assuming preferential attachment, we give an…
For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose…
Cyclic systems of dichotomous random variables have played a prominent role in contextuality research, describing such experimental paradigms as the Klyachko-Can-Binicoglu-Shumovky, Einstein-Podolsky-Rosen-Bell, and Leggett-Garg ones in…
Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed…
The inequality of wealth distribution is a universal phenomenon in the civilized nations, and it is often imputed to the Matthew effect, that is, the rich get richer and the poor get poorer. Some philosophers unjustified this phenomenon and…
This paper addresses the sample selection model within the context of the gender gap problem, where even random treatment assignment is affected by selection bias. By offering a robust alternative free from distributional or specification…
Machine learning systems are increasingly being used to make impactful decisions such as loan applications and criminal justice risk assessments, and as such, ensuring fairness of these systems is critical. This is often challenging as the…
Beginning in the 1970s, statistician-cum-logician Per Martin-L\"of wrote a series of papers developing what became Martin-L\"of type theory, realizing a system where the distinction between mathematics and programming disappears. Inspired…
Exponential families are widely used in machine learning; they include many distributions in continuous and discrete domains (e.g., Gaussian, Dirichlet, Poisson, and categorical distributions via the softmax transformation). Distributions…
In this paper, we take a statistical decision-theoretic viewpoint on social choice, putting a focus on the decision to be made on behalf of a system of agents. In our framework, we are given a statistical ranking model, a decision space,…