Related papers: Sparse hierarchical interaction learning with epig…

In many statistical learning problems, it is desired that the optimal solution conforms to an a priori known sparsity structure represented by a directed acyclic graph. Inducing such structures by means of convex regularizers requires…

Sketching techniques have become popular for scaling up machine learning algorithms by reducing the sample size or dimensionality of massive data sets, while still maintaining the statistical power of big data. In this paper, we study…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…

This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed…

Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, often solved by minimizing a non-smooth penalized co-log-likelihood function. Although the solution is easily interpretable with…

Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a…

We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with…

In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…

We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…

This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must…

In this paper, we develop a parameterized proximal point algorithm (P-PPA) for solving a class of separable convex programming problems subject to linear and convex constraints. The proposed algorithm is provable to be globally convergent…

We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible…

We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting…

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

Hierarchical reinforcement learning (HRL) improves the efficiency of long-horizon reinforcement-learning tasks with sparse rewards by decomposing the task into a hierarchy of subgoals. The main challenge of HRL is efficient discovery of the…

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…

Many statistical learning problems can be posed as minimization of a sum of two convex functions, one typically a composition of non-smooth and linear functions. Examples include regression under structured sparsity assumptions. Popular…