Related papers: Matrix-Variate Regressions and Envelope Models
Multi-step forecasting is often described through a simple rule of thumb: recursive strategies are said to have high bias and low variance, while direct strategies are said to have low bias and high variance. We revisit this belief by…
Mixture models are widely used to fit complex and multimodal datasets. In this paper we study mixtures with high dimensional sparse latent parameter vectors and consider the problem of support recovery of those vectors. While parameter…
Recent alignment techniques, such as reinforcement learning from human feedback, have been widely adopted to align large language models with human preferences by learning and leveraging reward models. In practice, these models often…
In this paper, we present several estimators of the diagonal elements of the inverse of the covariance matrix, called precision matrix, of a sample of iid random vectors. The focus is on high dimensional vectors having a sparse precision…
In the analysis of multivariate spatial and univariate spatio-temporal data, it is commonly recognized that asymmetric dependence may exist, which can be addressed using an asymmetric (matrix or space-time, respectively) covariance function…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex,…
Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…
Traditional methods for covariate adjustment of treatment means in designed experiments are inherently conditional on the observed covariate values. In order to develop a coherent general methodology for analysis of covariance, we propose a…
Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…
Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
A dynamic factor model with factor series following a VAR$(p)$ model is shown to have a VARMA$(p,p)$ model representation. Reduced-rank structures are identified for the VAR and VMA components of the resulting VARMA model. It is also shown…
Discrete choice models are commonly used by applied statisticians in numerous fields, such as marketing, economics, finance, and operations research. When agents in discrete choice models are assumed to have differing preferences, exact…
We develop an envelope model for joint mean and covariance regression in the large $p$, small $n$ setting. In contrast to existing envelope methods, which improve mean estimates by incorporating estimates of the covariance structure, we…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…
We consider the problem of reconstructing the signal and the hidden variables from observations coming from a multi-layer network with rotationally invariant weight matrices. The multi-layer structure models inference from deep generative…
We extend the standard VAR to jointly model the dynamics of binary, censored and continuous variables, and develop an efficient estimation approach that scales well to high-dimensional settings. In an out-of-sample forecasting exercise, we…
The current canonical approach to publishing cross-section data is to unfold the reconstructed distributions. Detector effects like efficiency and smearing are undone mathematically, yielding distributions in true event properties. This is…