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We compute approximate solutions to L0 regularized linear regression using L1 regularization, also known as the Lasso, as an initialization step. Our algorithm, the Lass-0 (Lass-zero), uses a computationally efficient stepwise search to determine a locally optimal L0 solution given any L1 regularization solution. We present theoretical results of consistency under orthogonality and appropriate handling of redundant features. Empirically, we use synthetic data to demonstrate that Lass-0 solutions are closer to the true sparse support than L1 regularization models. Additionally, in real-world data Lass-0 finds more parsimonious solutions than L1 regularization while maintaining similar predictive accuracy.
Quantifying uncertainty in predictions or, more generally, estimating the posterior conditional distribution, is a core challenge in machine learning and statistics. We introduce Convex Nonparanormal Regression (CNR), a conditional nonparanormal appr
Non-convex sparse minimization (NSM), or $ell_0$-constrained minimization of convex loss functions, is an important optimization problem that has many machine learning applications. NSM is generally NP-hard, and so to exactly solve NSM is almost impo
In this paper, we propose texttt{FedGLOMO}, the first (first-order) FL algorithm that achieves the optimal iteration complexity (i.e matching the known lower bound) on smooth non-convex objectives -- without using clients full gradient in each round.
When we are interested in high-dimensional system and focus on classification performance, the $ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different co
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the regression coeffic