Related papers: Efficient Boys function evaluation using minimax a…
Approximate computing is an emerging paradigm where design accuracy can be traded for improvements in design metrics such as design area and power consumption. In this work, we overview our open-source tool, BLASYS, for synthesis of…
A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on approximate least squares fitting, vector fitting, and a method…
Motivated by portfolio allocation and linear discriminant analysis, we consider estimating a functional $\mathbf{\mu}^T \mathbf{\Sigma}^{-1} \mathbf{\mu}$ involving both the mean vector $\mathbf{\mu}$ and covariance matrix…
Subset selection tasks, arise in recommendation systems and search engines and ask to select a subset of items that maximize the value for the user. The values of subsets often display diminishing returns, and hence, submodular functions…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
This paper presents a tractable algorithm for estimating an unknown Lipschitz function from noisy observations and establishes an upper bound on its convergence rate. The approach extends max-affine methods from convex shape-restricted…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…
Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to the arguments of nonlinear functions. Instead of only optimizing linear parameters,…
We provide a minimax optimal estimation procedure for F and W in matrix valued linear models Y = F W + Z where the parameter matrix W and the design matrix F are unknown but the latter takes values in a known finite set. The proposed finite…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
We consider a recently introduced framework in which fairness is measured by worst-case outcomes across groups, rather than by the more standard differences between group outcomes. In this framework we provide provably convergent…
Submodular optimization is a fundamental problem with many applications in machine learning, often involving decision-making over datasets with sensitive attributes such as gender or age. In such settings, it is often desirable to produce a…
Value functions are central to Dynamic Programming and Reinforcement Learning but their exact estimation suffers from the curse of dimensionality, challenging the development of practical value-function (VF) estimation algorithms. Several…
Vector operators based on robust order statistics have proved successful in digital multichannel imaging applications, particularly color image filtering and enhancement, in dealing with impulsive noise while preserving edges and fine image…
We quantify the minimax rate for a nonparametric regression model over a star-shaped function class $\mathcal{F}$ with bounded diameter. We obtain a minimax rate of ${\varepsilon^{\ast}}^2\wedge\mathrm{diam}(\mathcal{F})^2$ where…
Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…
The use of machine learning models in consequential decision making often exacerbates societal inequity, in particular yielding disparate impact on members of marginalized groups defined by race and gender. The area under the ROC curve…
In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function $f$. Traditional settings for this problem assume just the availability of this single function. However, in…