Related papers: Approximate Span Programs
Gaussian process (GP) predictors are an important component of many Bayesian approaches to machine learning. However, even a straightforward implementation of Gaussian process regression (GPR) requires O(n^2) space and O(n^3) time for a…
Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…
The ultimate goal of any sparse coding method is to accurately recover from a few noisy linear measurements, an unknown sparse vector. Unfortunately, this estimation problem is NP-hard in general, and it is therefore always approached with…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
We study quantum algorithms that are given access to trusted and untrusted quantum witnesses. We establish strong limitations of such algorithms, via new techniques based on Laurent polynomials (i.e., polynomials with positive and negative…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
Factored stochastic constraint programming (FSCP) is a formalism to represent multi-stage decision making problems under uncertainty. FSCP models support factorized probabilistic models and involve constraints over decision and random…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the SDPs generated by this procedure are…
Chance constrained program where one seeks to minimize an objective over decisions which satisfy randomly disturbed constraints with a given probability is computationally intractable. This paper proposes an approximate approach to address…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Minimizing sum of two functions under a linear constraint is what we called splitting problem. This convex optimization has wide applications in machine learning problems, such as Lasso, Group Lasso and Sparse logistic regression. A recent…
The weight decision problem, which requires to determine the Hamming weight of a given binary string, is a natural and important problem, with applications in cryptanalysis, coding theory, fault-tolerant circuit design and so on. In…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
The computation of exact barycenters for a set of discrete measures is of interest in applications where sparse solutions are desired, and to assess the quality of solutions returned by approximate algorithms and heuristics. The task is…
The sequential minimal optimization (SMO) algorithm and variants thereof are the de facto standard method for solving large quadratic programs for support vector machine (SVM) training. In this paper we propose a simple yet powerful…
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…