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We construct a classifier which attains the rate of convergence $\log n/n$ under sparsity and margin assumptions. An approach close to the one met in approximation theory for the estimation of function is used to obtain this result. The…

While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…

This paper proposes probabilistic conformal prediction (PCP), a predictive inference algorithm that estimates a target variable by a discontinuous predictive set. Given inputs, PCP construct the predictive set based on random samples from…

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…

Microbiological systems evolve to fulfill their tasks with maximal efficiency. The immune system is a remarkable example, where self-non self distinction is accomplished by means of molecular interaction between self proteins and antigens,…

A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…

We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…

We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed…

An overview is given about the statistical physics of neural networks generating and analysing time series. Storage capacity, bit and sequence generation, prediction error, antipredictable sequences, interacting perceptrons and the…

Structured prediction can be considered as a generalization of many standard supervised learning tasks, and is usually thought as a simultaneous prediction of multiple labels. One standard approach is to maximize a score function on the…

Program synthesis is the task of automatically generating a program consistent with a given specification. A natural way to specify programs is to provide examples of desired input-output behavior, and many current program synthesis…

An algorithm for automated construction of a sparse Bayesian network given an unstructured probabilistic model and causal domain information from an expert has been developed and implemented. The goal is to obtain a network that explicitly…

Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…

We define the complexity of a continuous-time linear system to be the minimum number of bits required to describe its forward increments to a desired level of fidelity, and compute this quantity using the rate distortion function of a…

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research…

We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection…

In this paper is proved the limit theorem for randomly indexed sequence of random processes in the case where sequences of random index and random processes are independent, also the estimation of convergence rate is obtained.

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…

In this paper we obtain significant bounds for the number of maximal subgroups of a given index of a finite group. These results allow us to give new bounds for the number of random generators needed to generate a finite $d$-generated group…

We introduce a novel model called GAMMT (Generative Ambiguity Models using Multiple Transformers) for sequential data that is based on sets of probabilities. Unlike conventional models, our approach acknowledges that the data generation…