arXiv research

DFR reduces the computational cost of sparse-group lasso and adaptive sparse-group lasso.

In high dimensional settings, sparse structures are crucial for efficiency, either in term of memory, computation or performance. In some contexts, it is natural to handle more refined structures than pure sparsity, such as for instance group sparsity. Sparse-Group Lasso has recently been introduced in the context of l…

The sparse group lasso optimization problem is solved using a coordinate gradient descent algorithm. The algorithm is applicable to a broad class of convex loss functions. Convergence of the algorithm is established, and the algorithm is used to investigate the performance of the multinomial sparse group lasso classifi…

New theorem for generalized group sparsity improves consistency and convergence rates.

Paper introduces machine learning for time series data, improving nowcasting accuracy.

A new method solves large-scale sparse group square-root Lasso problems efficiently.

We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured model -- an actively studied topic in statistics and machine learning. In the noi…

The paper improves machine learning for heavy-tailed panel data.

New method for inferring time series graph from sparse-group log-sum penalty.

Study high-dimensional Granger causality tests for VIX and financial news.

Paper develops a new estimator for high-dimensional panel data with common shocks.

Proposes a boosting framework for sparsity in grouped covariates.

Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or not selected. In many applications, however, this can be too restrictive. In th…

The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…

Genome-wide association studies (GWA studies or GWAS) investigate the relationships between genetic variants such as single-nucleotide polymorphisms (SNPs) and individual traits. Recently, incorporating biological priors together with machine learning methods in GWA studies has attracted increasing attention. However, …

Paper uses machine learning for nowcasting corporate earnings from mixed-frequency data.

Unified analysis of multi-attribute graph learning with non-convex penalties.

In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose $y = Az + η$ where $A$ satisfies the restricted isometry property (RIP) with a sufficiently small constant, and $\Vert η\Vert_2 \leq ε$. Then minimizing $\Vert z \Vert_1$ subject to $\Vert y - Az \Ver…

New bounds for Lasso and Group Lasso in high dimensions derived.

Categorical regressor variables are usually handled by introducing a set of indicator variables, and imposing a linear constraint to ensure identifiability in the presence of an intercept, or equivalently, using one of various coding schemes. As proposed in Yuan and Lin [J. R. Statist. Soc. B, 68 (2006), 49-67], the gr…

Sparse graph learning for dependent time series using ADMM.

Guided adaptive shrinkage uses co-data to improve feature selection in genomic studies.

While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating structured VAR (vector auto-regressive models), where the structure can be capture…

We study a family of sparse estimators defined as minimizers of some empirical Lipschitz loss function -- which include the hinge loss, the logistic loss and the quantile regression loss -- with a convex, sparse or group-sparse regularization. In particular, we consider the L1 norm on the coefficients, its sorted Slope…

Study improves carbon price forecasting using quantile regression and feature selection.

A method for inferring graph from multivariate time series using ADMM.

The paper examines how to protect LASSO-based feature selection from adversarial attacks.

Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose using $l_1/l_2$ regularization upon the activation possibilities of hidden unit…

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on "superposition-structured" models where mul…

Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes --- Hawkes process. We reveal the relationship between Hawkes process's impact function and its Granger caus…

In genomic analysis, biomarker discovery, image recognition, and other systems involving machine learning, input variables can often be organized into different groups by their source or semantic category. Eliminating some groups of variables can expedite the process of data acquisition and avoid over-fitting. Research…

In high dimensional regression settings, sparsity enforcing penalties have proved useful to regularize the data-fitting term. A recently introduced technique called screening rules propose to ignore some variables in the optimization leveraging the expected sparsity of the solutions and consequently leading to faster s…

Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this work we combine the sparsity-inducing property of the Lasso model at the indivi…

In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is $\ell_1$-norm minimization. Upper bounds for the $\ell_2$- norm of the error between the true and estimated vectors are given in [1] and reviewed in [2], while bounds for the $\ell_…

The paper examines Adaptive Lasso and Transfer Lasso, highlighting their differences and proposing a new method.

We consider the problem of matrix completion with side information (\textit{inductive matrix completion}). In real-world applications many side-channel features are typically non-informative making feature selection an important part of the problem. We incorporate feature selection into inductive matrix completion by p…

In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the $\ell_1$- and $\ell_2$-norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…

We present a Bayesian method for feature selection in the presence of grouping information with sparsity on the between- and within group level. Instead of using a stochastic algorithm for parameter inference, we employ expectation propagation, which is a deterministic and fast algorithm. Available methods for feature …

Paper analyzes adaptive Lasso for high-dimensional diffusion processes, improving support recovery and bias.

Paper proposes a method to efficiently estimate structural breaks in cointegrating regressions.

sgboost reduces variable selection bias in boosting with balanced group selection.

Paper proposes a new sparse group k-max regularization for sparsity constraints.

We derive new theoretical results on the properties of the adaptive least absolute shrinkage and selection operator (adaptive lasso) for time series regression models. In particular, we investigate the question of how to conduct finite sample inference on the parameters given an adaptive lasso model for some fixed valu…

We study the distribution of the adaptive LASSO estimator (Zou (2006)) in finite samples as well as in the large-sample limit. The large-sample distributions are derived both for the case where the adaptive LASSO estimator is tuned to perform conservative model selection as well as for the case where the tuning results…

New robust estimator for high-dimensional data with outliers and leverage points.

Paper proposes a new method combining random forests and Lasso selection.

Paper analyzes adaptive ISTA with MAD for LASSO problem.