相关论文: The trace norm constrained matrix-variate Gaussian…

Current causal discovery approaches require restrictive model assumptions in the absence of interventional data to ensure structure identifiability. These assumptions often do not hold in real-world applications leading to a loss of…

Multitask learning, i.e. taking advantage of the relatedness of individual tasks in order to improve performance on all of them, is a core challenge in the field of machine learning. We focus on matrix regression tasks where the rank of the…

In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…

In this paper, we consider a Bayesian bi-level variable selection problem in high-dimensional regressions. In many practical situations, it is natural to assign group membership to each predictor. Examples include that genetic variants can…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

High-dimensional health and surveillance studies often involve many collinear predictors, multiple correlated outcomes of different types, and latent heterogeneity across observational units. We propose a Bayesian latent-cluster…

With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…

This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…

In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy…

Bipartite ranking, which aims to learn a scoring function that ranks positive individuals higher than negative ones from labeled data, is widely adopted in various applications where sample prioritization is needed. Recently, there have…

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…

Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows…

We consider the problem of unveiling the implicit network structure of node interactions (such as user interactions in a social network), based only on high-frequency timestamps. Our inference is based on the minimization of the…

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…

Inferring predictive maps between multiple input and multiple output variables or tasks has innumerable applications in data science. Multi-task learning attempts to learn the maps to several output tasks simultaneously with information…

Using the $\ell_1$-norm to regularize the estimation of the parameter vector of a linear model leads to an unstable estimator when covariates are highly correlated. In this paper, we introduce a new penalty function which takes into account…

Extrinsic Gaussian process regression methods, such as wrapped Gaussian process, have been developed to analyze manifold data. However, there is a lack of intrinsic Gaussian process methods for studying complex data with manifold-valued…