Related papers: SpinSVAR: Estimating Structural Vector Autoregress…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…
** This article is published (open-access). ** A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
This paper presents a novel projection-based adaptive algorithm for sparse signal and system identification. The sequentially observed data are used to generate an equivalent sequence of closed convex sets, namely hyperslabs. Each hyperslab…
Many theoretical results for the lasso require the samples to be iid. Recent work has provided guarantees for the lasso assuming that the time series is generated by a sparse Vector Auto-Regressive (VAR) model with Gaussian innovations.…
This paper presents a novel approach for approximate integration over the uncertainty of noise and signal variances in Gaussian process (GP) regression. Our efficient and straightforward approach can also be applied to integration over…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
For regression model selection via maximum likelihood estimation, we adopt a vector representation of candidate models and study the likelihood ratio confidence region for the regression parameter vector of a full model. We show that when…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
We propose a high-dimensional structural vector autoregression framework with a factor structure in the error terms that accommodates a large number of linear inequality restrictions on both impact impulse responses and structural shocks.…
There exist endless examples of dynamical systems with vast available data and unsatisfying mathematical descriptions. Sparse regression applied to symbolic libraries has quickly emerged as a powerful tool for learning governing equations…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
A structural vector autoregressive (SVAR) process is a linear causal model for variables that evolve over a discrete set of time points and between which there may be lagged and instantaneous effects. The qualitative causal structure of an…
In practical regression applications, multiple covariates are often measured, but not all may be associated with the response variable. Identifying and including only the relevant covariates in the model is crucial for improving prediction…
The article considers the problem of estimating a high-dimensional sparse parameter in the presence of side information that encodes the sparsity structure. We develop a general framework that involves first using an auxiliary sequence to…
Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world…
The Vector AutoRegressive (VAR) model is fundamental to the study of multivariate time series. Although VAR models are intensively investigated by many researchers, practitioners often show more interest in analyzing VARX models that…
Simultaneous feature selection and non-linear function estimation is challenging in modeling, especially in high-dimensional settings where the number of variables exceeds the available sample size. In this article, we investigate the…
We develop a new framework for learning variational autoencoders and other deep generative models that balances generative and discriminative goals. Our framework optimizes model parameters to maximize a variational lower bound on the…