Related papers: Project and Forget: Solving Large-Scale Metric Con…
Computing exact Optimal Transport (OT) distances for large-scale datasets is computationally prohibitive. While entropy-regularized alternatives offer speed, they sacrifice precision and frequently suffer from numerical instability in…
Recovering a function or high-dimensional parameter vector from indirect measurements is a central task in various scientific areas. Several methods for solving such inverse problems are well developed and well understood. Recently, novel…
We propose a new subgradient method for the minimization of nonsmooth convex functions over a convex set. To speed up computations we use adaptive approximate projections only requiring to move within a certain distance of the exact…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…
To solve deep metric learning problems and producing feature embeddings, current methodologies will commonly use a triplet model to minimise the relative distance between samples from the same class and maximise the relative distance…
We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…
Bregman divergences play a pivotal role in statistics, machine learning and computational information geometry. Particularly in the context of machine learning, they are central to clustering, exponential families, parameter estimation and…
The split Bregman (SB) method [T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2 (2009), pp. 323-43] is a fast splitting-based algorithm that solves image reconstruction problems with general l1, e.g., total-variation (TV) and compressed…
Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…
We propose an algorithm that produces a non-decreasing sequence of subsolutions for a class of optimal control problems distinguished by the property that the associated Bellman operators preserve convexity. In addition to a theoretical…
Projected gradient descent has been proved efficient in many optimization and machine learning problems. The weighted $\ell_1$ ball has been shown effective in sparse system identification and features selection. In this paper we propose…
In this draft, fault diagnosis in nonlinear dynamic systems is addressed. The objective of this work is to establish a framework, in which not only model-based but also data-driven and machine learning based fault diagnosis strategies can…
Distance metric learning (DML) approaches learn a transformation to a representation space where distance is in correspondence with a predefined notion of similarity. While such models offer a number of compelling benefits, it has been…
Motivated by a constrained minimization problem, it is studied the gradient flows with respect to Hessian Riemannian metrics induced by convex functions of Legendre type. The first result characterizes Hessian Riemannian structures on…
Inherent in virtually every iterative machine learning algorithm is the problem of hyper-parameter tuning, which includes three major design parameters: (a) the complexity of the model, e.g., the number of neurons in a neural network, (b)…
In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems, for which we have access to exact information of constraints and noisy function values of the objective. We propose a Bregman linearized augmented…
Distance metric learning (DML) has been studied extensively in the past decades for its superior performance with distance-based algorithms. Most of the existing methods propose to learn a distance metric with pairwise or triplet…
In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…
This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…