Related papers: Fundamental Limitations in Sequential Prediction a…
In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…
In this work, we address the following question: What minimal structural assumptions are needed to prevent the degradation of statistical learning bounds with increasing dimensionality? We investigate this question in the classical…
Maximization of an expensive, unimodal function under random observations has been an important problem in hyperparameter tuning. It features expensive function evaluations (which means small budgets) and a high level of noise. We develop…
We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The bounds provide an information-theoretic understanding of generalization in learning problems,…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
The reliability of deep learning algorithms is fundamentally challenged by the existence of adversarial examples, which are incorrectly classified inputs that are extremely close to a correctly classified input. We explore the properties of…
Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at…
We study Rademacher processes where the coefficients are functions evaluated at fixed, but arbitrary covariables. Specifically, we assume the function class under consideration to be parametrized by the standard cocube in l dimensions and…
A one-step analysis of Anderson acceleration with general algorithmic depths is presented. The resulting residual bounds within both contractive and noncontractive settings reveal the balance between the contributions from the higher and…
Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
This work studies certain notions of entropy that can be associated to (i) a representation of a separable, unital C*-algebra $\mathfrak{A}$ and (ii) an auxiliary random sequence $(\pi_n)_{n\ge 1}$ of finite-dimensional representations of…
This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…
The objective of this paper is to present general, mechanically verified, refinement rules for reasoning about recursive programs and while loops in the context of concurrency. Unlike many approaches to concurrency, we do not assume that…
Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed…
A run of all failures, a run of all successes, or complete separation in a logistic regression each tempts the analyst to declare a probability of exactly zero or one. The central message of this paper is that all three phenomena share a…
This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear…
Learning continuously during all model lifetime is fundamental to deploy machine learning solutions robust to drifts in the data distribution. Advances in Continual Learning (CL) with recurrent neural networks could pave the way to a large…