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Many Bayesian statistical inference problems come down to computing a maximum a-posteriori (MAP) assignment of latent variables. Yet, standard methods for estimating the MAP assignment do not have a finite time guarantee that the algorithm…
The singular values of a product of $M$ independent Ginibre matrices of size $N\times N$ form a determinantal point process. Near the soft edge, as both $M$ and $N$ go to infinity in such a way that $M/N\to \alpha$, $\alpha>0$, a scaling…
We develop an efficient posterior sampling scheme for the Poisson INGARCH models. The proposed method is based on the approximation of the posterior density that exploits the Poisson limit of the negative binomial distribution. It allows us…
Predicting with missing inputs challenges even parametric models, as parameter estimation alone is insufficient for prediction on incomplete data. While several works study prediction in linear models, we focus on logistic models, where…
The inferential models (IM) framework provides prior-free, frequency-calibrated, posterior probabilistic inference. The key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown…
Recovering sparse conditional independence graphs from data is a fundamental problem in machine learning with wide applications. A popular formulation of the problem is an $\ell_1$ regularized maximum likelihood estimation. Many convex…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
In applications of Gaussian processes where quantification of uncertainty is a strict requirement, it is necessary to accurately characterize the posterior distribution over Gaussian process covariance parameters. Normally, this is done by…
Latent manifolds provide a compact characterization of neural population activity and of shared co-variability across brain areas. Nonetheless, existing statistical tools for extracting neural manifolds face limitations in terms of…
We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian…
In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its…
Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…
In many contexts, there is interest in selecting the most important variables from a very large collection, commonly referred to as support recovery or variable, feature or subset selection. There is an enormous literature proposing a rich…
Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper…
Tabling in logic programming has been used to eliminate redundant computation and also to stop infinite loop. In this paper we investigate another possibility of tabling, i.e. to compute an infinite sum of probabilities for probabilistic…
This paper focuses on the convergence certificates of the majorized proximal alternating minimization (PAM) method with subspace correction, proposed in \cite{TaoQianPan22} for the column $\ell_{2,0}$-norm regularized factorization model…
The Gaussian Elimination with Partial Pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases the loss of precision in GEPP due to roundoff errors can be very significant, empirical…
Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
In this paper, we consider the problem of recovering random graph signals from nonlinear measurements. We formulate the maximum a-posteriori probability (MAP) estimator, which results in a nonconvex optimization problem. Conventional…