相关论文: Subset Selection for Matrices with Fixed Blocks
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
A principled approach to characterize the hidden structure of networks is to formulate generative models, and then infer their parameters from data. When the desired structure is composed of modules or "communities", a suitable choice for…
Prototype is widely used to represent internal structure of category for few-shot learning, which was proposed as a simple inductive bias to address the issue of overfitting. However, since prototype representation is normally averaged from…
We consider the following problem: Given a matrix A, find minimal subsets of columns of A with cardinality no larger than a given bound that are linear dependent or nearly so. This problem arises in various forms in optimization, electrical…
Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…
Pattern set mining, which is the task of finding a good set of patterns instead of all patterns, is a fundamental problem in data mining. Many different definitions of what constitutes a good set have been proposed in recent years. In this…
While variable selection is essential to optimize the learning complexity by prioritizing features, automating the selection process is preferred since it requires laborious efforts with intensive analysis otherwise. However, it is not an…
Pseudospectra and structured pseudospectra are important tools for the analysis of matrices. Their computation, however, can be very demanding for all but small matrices. A new approach to compute approximations of pseudospectra and…
Model selection is an indispensable part of data analysis dealing very frequently with fitting and prediction purposes. In this paper, we tackle the problem of model selection in a general linear regression where the parameter matrix…
The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…
In this paper, we propose a fast algorithm for element selection, a multiplication-free form of dimension reduction that produces a dimension-reduced vector by simply selecting a subset of elements from the input. Dimension reduction is a…
Farkas' lemma for semidefinite programming characterizes semidefinite feasibility of linear matrix pencils in terms of an alternative spectrahedron. In the well-studied special case of linear programming, a theorem by Gleeson and Ryan…
While semidefinite programming (SDP) problems are polynomially solvable in theory, it is often difficult to solve large SDP instances in practice. One technique to address this issue is to relax the global positive-semidefiniteness (PSD)…
We study the problem of maximizing a monotone submodular set function subject to linear packing constraints. An instance of this problem consists of a matrix $A \in [0,1]^{m \times n}$, a vector $b \in [1,\infty)^m$, and a monotone…
Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…
We present a new algorithm for spectral clustering based on a column-pivoted QR factorization that may be directly used for cluster assignment or to provide an initial guess for k-means. Our algorithm is simple to implement, direct, and…
This paper introduces a framework to study discrete optimization problems which are parametric in the following sense: their constraint matrices correspond to matrices over the ring $\mathbb{Z}[x]$ of polynomials in one variable. We…
In this paper, we propose a new wrapper feature selection approach with partially labeled training examples where unlabeled observations are pseudo-labeled using the predictions of an initial classifier trained on the labeled training set.…
Feature selection aims to identify the most pattern-discriminative feature subset. In prior literature, filter (e.g., backward elimination) and embedded (e.g., Lasso) methods have hyperparameters (e.g., top-K, score thresholding) and tie to…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…