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This paper presents a lower bound for optimizing a finite sum of $n$ functions, where each function is $L$-smooth and the sum is $\mu$-strongly convex. We show that no algorithm can reach an error $\epsilon$ in minimizing all functions from…
Acceleration in symbolic verification consists in computing the exact effect of some control-flow loops in order to speed up the iterative fix-point computation of reachable states. Even if no termination guarantee is provided in theory,…
A software analysis is a computer program that takes some representation of a software product as input and produces some useful information about that product as output. A software product line encompasses \emph{many} software product…
Electronic exams (e-exams) have the potential to substantially reduce the effort required for conducting an exam through automation. Yet, care must be taken to sacrifice neither task complexity nor constructive alignment nor grading…
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…
We present an approach for implementing a formally certified loop-invariant code motion optimization by composing an unrolling pass and a formally certified yet efficient global subexpression elimination.This approach is lightweight: each…
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input are available. Technically, our methods catch the bias…
Rollout algorithms have demonstrated excellent performance on a variety of dynamic and discrete optimization problems. Interpreted as an approximate dynamic programming algorithm, a rollout algorithm estimates the value-to-go at each…
Increased demands in the field of scientific computation require that algorithms be more efficiently implemented. Maintaining correctness in addition to efficiency is a challenge that software engineers in the field have to face. In this…
Algorithms for the numerical evaluation of the incomplete gamma function ratios $P(a,x)=\gamma(a,x)/\Gamma(a)$ and $Q(a,x)=\Gamma(a,x)/\Gamma(a)$ are described for positive values of $a$ and $x$. Also, inversion methods are given for…
This paper proposes a novel method, Explicit Flow Matching (ExFM), for training and analyzing flow-based generative models. ExFM leverages a theoretically grounded loss function, ExFM loss (a tractable form of Flow Matching (FM) loss), to…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function via the inexact accelerated proximal gradient (APG) method. A key limitation of existing inexact APG methods is their reliance on…
Soft sets, as a mathematical tool for dealing with uncertainty, have recently gained considerable attention, including some successful applications in information processing, decision, demand analysis, and forecasting. To construct new soft…
Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repeated passes over the full dataset. This has motivated…
Performative learning addresses the increasingly pervasive situations in which algorithmic decisions may induce changes in the data distribution as a consequence of their public deployment. We propose a novel view in which these…
Data refinement is the standard extension of a refinement relation from programs to datatypes (i.e. a behavioural subtyping relation). Forward/backward simulations provide a tractable method for establishing data refinement, and have been…
Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
We consider functional data where an underlying smooth curve is composed not just with errors, but also with irregular spikes. We propose an approach that, combining regularized spline smoothing and an Expectation-Maximization algorithm,…
A matrix algorithm is said to be superfast (that is, runs at sublinear cost) if it involves much fewer scalars and flops than the input matrix has entries. Such algorithms have been extensively studied and widely applied in modern…