Related papers: An elementary proof of linear programming optimali…
The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…
Recently, sufficient conditions of stability or instability for time-delay systems have been proven to be necessary. In this way, a remarkable necessary and sufficient condition has then been developed by Gomez et al. It is presented as a…
In this paper we begin by discussing the simple bilevel programming problem (SBP) and its extension the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their…
In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the…
Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different conditions and concepts relate…
Recent large language models (LLMs) perform strongly on mathematical benchmarks yet often misapply lemmas, importing conclusions without validating assumptions. We formalize lemma$-$judging as a structured prediction task: given a statement…
This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Optimal use of computing resources requires extensive coding, tuning and benchmarking. To boost developer productivity in these time consuming tasks, we introduce the Experimental Linear Algebra Performance Studies framework (ELAPS), a…
We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the Clarke tangent cone of the state constraint set is non-empty (this is the constraint…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
Many sparse linear discriminant analysis (LDA) methods have been proposed to overcome the major problems of the classic LDA in high-dimensional settings. However, the asymptotic optimality results are limited to the case that there are only…
Optimality conditions are central to analysis of optimization problems, characterizing necessary criteria for local minima. Formalizing the optimality conditions within the type-theory-based proof assistant Lean4 provides a precise, robust,…
This paper presents a method which is identical to simplex method phase 1, but do not need any artificial variable (or artificial constraints). So, the new method works in original variable space but visits the same sequence of pivots as…
In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
This paper investigates whether recent advances in Large Language Models (LLMs) can assist in translating human explanations into a format that can robustly support learning Linear Temporal Logic (LTL) from demonstrations. Both LLMs and…
Under some mild Markov assumptions it is shown that the problem of designing optimal sequential tests for two simple hypotheses can be formulated as a linear program. The result is derived by investigating the Lagrangian dual of the…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…