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Vector autoregressive (VAR) models are widely used for causal discovery and forecasting in multivariate time series analysis. In the high-dimensional setting, which is increasingly common in fields such as neuroscience and econometrics,…
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…
Sparseness of the regression coefficient vector is often a desirable property, since, among other benefits, sparseness improves interpretability. In practice, many true regression coefficients might be negligibly small, but non-zero, which…
We propose a supervised learning algorithm for machine learning applications. Contrary to the model developing in the classical methods, which treat training, validation, and test as separate steps, in the presented approach, there is a…
Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…
Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where $\Lop\Lo/N^\alpha$ is…
A prevalent feature of high-dimensional data is the dependence among covariates, and model selection is known to be challenging when covariates are highly correlated. To perform model selection for the high-dimensional Cox proportional…
Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a…
We consider (nonparametric) sparse (generalized) additive models (SpAM) for classification. The design of a SpAM classifier is based on minimizing the logistic loss with a sparse group Lasso/Slope-type penalties on the coefficients of…
Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…
We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
Latent reasoning represents a new development in Transformer language models that has shown potential in compressing reasoning lengths compared to chain-of-thought reasoning. By directly passing the information-rich previous final latent…
We study the problem of regression in a generalized linear model (GLM) with multiple signals and latent variables. This model, which we call a matrix GLM, covers many widely studied problems in statistical learning, including mixed linear…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…
In semi-supervised learning, the prevailing understanding suggests that observing additional unlabeled samples improves estimation accuracy for linear parameters only in the case of model misspecification. In this work, we challenge such a…
Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…
Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…
In the AGEMAP genomics study, researchers were interested in detecting genes related to age in a variety of tissue types. After not finding many age-related genes in some of the analyzed tissue types, the study was criticized for having low…
Random Forests (RF) is a popular machine learning method for classification and regression problems. It involves a bagging application to decision tree models. One of the primary advantages of the Random Forests model is the reduction in…