Related papers: Unveiling The Tree: A Convex Framework for Sparse …
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…
A decision tree is commonly restricted to use a single hyperplane to split the covariate space at each of its internal nodes. It often requires a large number of nodes to achieve high accuracy, hurting its interpretability. In this paper,…
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…
We consider the projected gradient algorithm for the nonconvex best subset selection problem that minimizes a given empirical loss function under an $\ell_0$-norm constraint. Through decomposing the feasible set of the given sparsity…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
In an ordinary feature selection procedure, a set of important features is obtained by solving an optimization problem such as the Lasso regression problem, and we expect that the obtained features explain the data well. In this study,…
In many modern applications, including analysis of gene expression and text documents, the data are noisy, high-dimensional, and unordered--with no particular meaning to the given order of the variables. Yet, successful learning is often…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…
This paper focuses on the development of novel greedy techniques for distributed learning under sparsity constraints. Greedy techniques have widely been used in centralized systems due to their low computational requirements and at the same…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
We introduce a code generator that converts unoptimized C++ code operating on sparse data into vectorized and parallel CPU or GPU kernels. Our approach unrolls the computation into a massive expression graph, performs redundant expression…
The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP)…
In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…
Many path planning algorithms are based on sampling the state space. While this approach is very simple, it can become costly when the obstacles are unknown, since samples hitting these obstacles are wasted. The goal of this paper is to…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. We consider a relaxed version of this problem in the setting of local algorithms. The relaxation is that the constructed subgraph is a sparse spanning…