Related papers: An Alternative Graphical Lasso Algorithm for Preci…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
Continuous-time trajectory representations are a powerful tool that can be used to address several issues in many practical simultaneous localization and mapping (SLAM) scenarios, like continuously collected measurements distorted by robot…
In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental…
In recent years, there is a growing interest in combining techniques attributed to the areas of Statistics and Machine Learning in order to obtain the benefits of both approaches. In this article, the statistical technique lasso for…
We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but…
The estimation problem in a high regression model with structured sparsity is investigated. An algorithm using a two steps block thresholding procedure called GR-LOL is provided. Convergence rates are produced: they depend on simple…
We improve upon the two-stage sparse vector autoregression (sVAR) method in Davis et al. (2016) by proposing an alternative two-stage modified sVAR method which relies on time series graphical lasso to estimate sparse inverse spectral…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee…
Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…
We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…
This article explores the estimation of precision matrices in high-dimensional Gaussian graphical models. We address the challenge of improving the accuracy of maximum likelihood-based precision estimation through penalization.…
In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…
The Lasso is a method for high-dimensional regression, which is now commonly used when the number of covariates $p$ is of the same order or larger than the number of observations $n$. Classical asymptotic normality theory does not apply to…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
L1 -penalized regression methods such as the Lasso (Tibshirani 1996) that achieve both variable selection and shrinkage have been very popular. An extension of this method is the Fused Lasso (Tibshirani and Wang 2007), which allows for the…
In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the…
Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…