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We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…
Motivated by $\ell_p$-optimization arising from sparse optimization, high dimensional data analytics and statistics, this paper studies sparse properties of a wide range of $p$-norm based optimization problems with $p > 1$, including…
Sparse graphs built by sparse representation has been demonstrated to be effective in clustering high-dimensional data. Albeit the compelling empirical performance, the vanilla sparse graph ignores the geometric information of the data by…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
Deep neural networks with lots of parameters are typically used for large-scale computer vision tasks such as image classification. This is a result of using dense matrix multiplications and convolutions. However, sparse computations are…
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Nonnegative matrix factorization arises widely in machine learning and data analysis. In this paper, for a given factorization of rank r, we consider the sparse stochastic matrix factorization (SSMF) of decomposing a prescribed m-by-n…
The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…
Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional rank regularized problem to a low-dimensional factorized…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
Images have become an important data source in many scientific and commercial domains. Analysis and exploration of image collections often requires the retrieval of the best subregions matching a given query. The support of such…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
The Sparse Generalized Eigenvalue Problem (sGEP), a pervasive challenge in statistical learning methods including sparse principal component analysis, sparse Fisher's discriminant analysis, and sparse canonical correlation analysis,…
Despite its important applications in Machine Learning, min-max optimization of nonconvex-nonconcave objectives remains elusive. Not only are there no known first-order methods converging even to approximate local min-max points, but the…
This thesis presents two similarity-based approaches to sparse data problems. The first approach is to build soft, hierarchical clusters: soft, because each event belongs to each cluster with some probability; hierarchical, because cluster…