Related papers: A Solution for the Greedy Approximation of a Step …
We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…
This paper introduces a new numerical method for approximating the Lambert W function in the real domain. The method transforms the function into a simpler form that allows iterative refinement of an initial guess. Two iterative strategies…
We derive new explicit expressions for the components of Moore-Penrose inverses of symmetric difference matrices. These generalized inverses are applied in a new regularization approach for scattered data interpolation based on partial…
The paper proposes a new algorithm for solving global univariate optimization problems. The algorithm does not require convexity of the target function. For a broad variety of target functions after performing (if necessary) several…
In this paper, we consider approximations of principal component projection (PCP) without explicitly computing principal components. This problem has been studied in several recent works. The main feature of existing approaches is viewing…
Connecting multiple machine learning models into a pipeline is effective for handling complex problems. By breaking down the problem into steps, each tackled by a specific component model of the pipeline, the overall solution can be made…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
We show how any dataset of any modality (time-series, images, sound...) can be approximated by a well-behaved (continuous, differentiable...) scalar function with a single real-valued parameter. Building upon elementary concepts from chaos…
We study private matrix analysis in the sliding window model where only the last $W$ updates to matrices are considered useful for analysis. We give first efficient $o(W)$ space differentially private algorithms for spectral approximation,…
We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with…
This article introduces a functional method for lower-dimensional smooth representations in terms of time-varying dissimilarities. The method incorporates dissimilarity representation in multidimensional scaling and smoothness approach of…
Direct approaches to the quantum many-body problem suffer from the so-called "curse of dimensionality": the number of parameters needed to fully specify the exact wavefunction grows exponentially with increasing system size. This motivates…
We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes introduce the adaptivity and admit an extensive permitted range of the…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
We study the problem of fine-tuning a language model (LM) for a target task by optimally using the information from $n$ auxiliary tasks. This problem has broad applications in NLP, such as targeted instruction tuning and data selection in…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…