Related papers: Optimal Solutions for Sparse Principal Component A…
The topic of this tutorial is Least Squares Sparse Principal Components Analysis (LS SPCA) which is a simple method for computing approximated Principal Components which are combinations of only a few of the observed variables. Analogously…
We consider the Sparse Principal Component Analysis (SPCA) problem under the well-known spiked covariance model. Recent work has shown that the SPCA problem can be reformulated as a Mixed Integer Program (MIP) and can be solved to global…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
We address the curse of dimensionality in dynamic covariance estimation by modeling the underlying co-volatility dynamics of a time series vector through latent time-varying stochastic factors. The use of a global-local shrinkage prior for…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
Optimization problems involving mixed variables (i.e., variables of numerical and categorical nature) can be challenging to solve, especially in the presence of mixed-variable constraints. Moreover, when the objective function is the result…
We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
Accurate prediction of user consumption is a key part not only in understanding consumer flexibility and behavior patterns, but in the design of robust and efficient energy saving programs as well. Existing prediction methods usually have…
We study sparse principal component analysis in the high-dimensional, sample-limited regime, aiming to recover a leading component supported on a few coordinates. Despite extensive progress, most methods and analyses are tailored to the…
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…
This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…
Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our…
As a popular tool for producing meaningful and interpretable models, large-scale sparse learning works efficiently when the underlying structures are indeed or close to sparse. However, naively applying the existing regularization methods…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…
We study the problem of sparse tensor principal component analysis: given a tensor $\pmb Y = \pmb W + \lambda x^{\otimes p}$ with $\pmb W \in \otimes^p\mathbb{R}^n$ having i.i.d. Gaussian entries, the goal is to recover the $k$-sparse unit…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems. Unfortunately, the straightforward application of classical gradient-based…