Related papers: $\ell_1$-norm constrained multi-block sparse canon…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
This work develops a sparse and outlier-insensitive method to fit a one-dimensional subspace that can be used as a replacement for eigenvector methods such as principal component analysis (PCA). The method is insensitive to outlier…
Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome…
Canonical correlation analysis (CCA) has proven an effective tool for two-view dimension reduction due to its profound theoretical foundation and success in practical applications. In respect of multi-view learning, however, it is limited…
This paper considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and…
This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…
Sparse estimation for Gaussian graphical models is a crucial technique for making the relationships among numerous observed variables more interpretable and quantifiable. Various methods have been proposed, including graphical lasso, which…
For high dimensional sparse linear regression problems, we propose a sequential convex relaxation algorithm (iSCRA-TL1) by solving inexactly a sequence of truncated $\ell_1$-norm regularized minimization problems, in which the working index…
This work focuses on a class of general decentralized constraint-coupled optimization problems. We propose a novel nested primal-dual gradient algorithm (NPGA), which can achieve linear convergence under the weakest known condition, and its…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…
Canonical Correlation Analysis (CCA) is a statistical technique used to extract common information from multiple data sources or views. It has been used in various representation learning problems, such as dimensionality reduction, word…
In this paper, we aim at solving the cardinality constrained high-order portfolio optimization, i.e., mean-variance-skewness-kurtosis model with cardinality constraint (MVSKC). Optimization for the MVSKC model is of great difficulty in two…
A new approach to the sparse Canonical Correlation Analysis (sCCA)is proposed with the aim of discovering interpretable associations in very high-dimensional multi-view, i.e.observations of multiple sets of variables on the same subjects,…
The $\ell_0$-constrained mean-CVaR model poses a significant challenge due to its NP-hard nature, typically tackled through combinatorial methods characterized by high computational demands. From a markedly different perspective, we propose…
Regularized Generalized Canonical Correlation Analysis (RGCCA) is a general statistical framework for multi-block data analysis. RGCCA enables deciphering relationships between several sets of variables and subsumes many well-known…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
We consider estimation in a high-dimensional linear model with strongly correlated variables. We propose to cluster the variables first and do subsequent sparse estimation such as the Lasso for cluster-representatives or the group Lasso…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…
Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep…