Related papers: An Interpretable and Sparse Neural Network Model f…
Sparse matrix computations are ubiquitous in scientific computing. With the recent interest in scientific machine learning, it is natural to ask how sparse matrix computations can leverage neural networks (NN). Unfortunately, multi-layer…
Tucker decomposition is the cornerstone of modern machine learning on tensorial data analysis, which have attracted considerable attention for multiway feature extraction, compressive sensing, and tensor completion. The most challenging…
Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…
Inferring the connectivity of neural circuits from incomplete observations is a fundamental challenge in neuroscience. We present a covariance-based method for estimating the weight matrix of a recurrent neural network from sparse, partial…
Learning Granger causality from event sequences is a challenging but essential task across various applications. Most existing methods rely on the assumption that event sequences are independent and identically distributed (i.i.d.).…
High dimensional vector autoregressive (VAR) models require a large number of parameters to be estimated and may suffer of inferential problems. We propose a new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional VAR…
Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC)…
Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
Sparse Gaussian graphical models characterize sparse dependence relationships between random variables in a network. To estimate multiple related Gaussian graphical models on the same set of variables, we formulate a hierarchical model,…
Granger causality is a statistical notion of causal influence based on prediction via vector autoregression. For Gaussian variables it is equivalent to transfer entropy, an information-theoretic measure of time-directed information transfer…
Latent confounding has been a long-standing obstacle for causal reasoning from observational data. One popular approach is to model the data using acyclic directed mixed graphs (ADMGs), which describe ancestral relations between variables…
High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…
Sparse inverse covariance estimation (i.e., edge de-tection) is an important research problem in recent years, wherethe goal is to discover the direct connections between a set ofnodes in a networked system based upon the observed…
This paper proposes a new approach for testing Granger non-causality on panel data. Instead of aggregating panel member statistics, we aggregate their corresponding p-values and show that the resulting p-value approximately bounds the type…
We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a…
Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence…
The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered…
Many communications and sensing applications hinge on the detection of a signal in a noisy, interference-heavy environment. Signal processing theory yields techniques such as the generalized likelihood ratio test (GLRT) to perform detection…
Understanding the causal interaction of time series variables can contribute to time series data analysis for many real-world applications, such as climate forecasting and extreme weather alerts. However, causal relationships are difficult…