Related papers: The solution path of the generalized lasso

Generalized linear model or GLM constitutes a large class of models and essentially extends the ordinary linear regression by connecting the mean of the response variable with the covariate through appropriate link functions. On the other…

We propose a new algorithm for solving the graph-fused lasso (GFL), a method for parameter estimation that operates under the assumption that the signal tends to be locally constant over a predefined graph structure. Our key insight is to…

We consider the generic regularized optimization problem $\hat{\mathsf{\beta}}(\lambda)=\arg \min_{\beta}L({\sf{y}},X{\sf{\beta}})+\lambda J({\sf{\beta}})$. Efron, Hastie, Johnstone and Tibshirani [Ann. Statist. 32 (2004) 407--499] have…

Learning under distribution shifts is a challenging task. One principled approach is to exploit the invariance principle via the structural causal models. However, the invariance principle is violated when the response is intervened, making…

This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…

Imposition of a lasso penalty shrinks parameter estimates toward zero and performs continuous model selection. Lasso penalized regression is capable of handling linear regression problems where the number of predictors far exceeds the…

Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…

We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…

In this work we establish the equivalence of algorithmic regularization and explicit convex penalization for generic convex losses. We introduce a geometric condition for the optimization path of a convex function, and show that if such a…

The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lov\'asz (1980)…

Many Machine Learning algorithms are formulated as regularized optimization problems, but their performance hinges on a regularization parameter that needs to be calibrated to each application at hand. In this paper, we propose a general…

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…

In this paper we develop inference for high dimensional linear models, with serially correlated errors. We examine Lasso under the assumption of strong mixing in the covariates and error process, allowing for fatter tails in their…

The generalized lasso is a natural generalization of the celebrated lasso approach to handle structural regularization problems. Many important methods and applications fall into this framework, including fused lasso, clustered lasso, and…

We apply the network Lasso to solve binary classification and clustering problems for network-structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data with an intrinsic network structure. The resulting…

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

rdering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an $\ell_1$ norm…

We consider the problem of estimation of a covariance matrix for Gaussian data in a high dimensional setting. Existing approaches include maximum likelihood estimation under a pre-specified sparsity pattern, l_1-penalized loglikelihood…

Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free…

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…