Related papers: Generalized Invariant Matching Property via LASSO
Due to the ability of deep neural nets to learn rich representations, recent advances in unsupervised domain adaptation have focused on learning domain-invariant features that achieve a small error on the source domain. The hope is that the…
We study the problem of consistently recovering the sparsity pattern of a regression parameter vector from correlated observations governed by deterministic missing data patterns using Lasso. We consider the case in which the observed…
We describe a simple, efficient, permutation based procedure for selecting the penalty parameter in the LASSO. The procedure, which is intended for applications where variable selection is the primary focus, can be applied in a variety of…
In many high dimensional classification or regression problems set in a biological context, the complete identification of the set of informative features is often as important as predictive accuracy, since this can provide mechanistic…
Sparse linear regression is a fundamental problem in high-dimensional statistics, but strikingly little is known about how to efficiently solve it without restrictive conditions on the design matrix. We consider the (correlated) random…
In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a…
This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…
This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that…
Learning using statistical invariants (LUSI) is a new learning paradigm, which adopts weak convergence mechanism, and can be applied to a wider range of classification problems. However, the computation cost of invariant matrices in LUSI is…
One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics,…
This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing,…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…
One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find \textit{invariant representations} of the data. These are representations of the covariates such that…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
Generalizing manipulation skills to new situations requires extracting invariant patterns from demonstrations. For example, the robot needs to understand the demonstrations at a higher level while being invariant to the appearance of the…
Given a collection of images, humans are able to discover landmarks by modeling the shared geometric structure across instances. This idea of geometric equivariance has been widely used for the unsupervised discovery of object landmark…
In this paper we present a world model, which learns causal features using the invariance principle. In particular, we use contrastive unsupervised learning to learn the invariant causal features, which enforces invariance across…
Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…