arXiv research

Develops MGQDA for multi-group classification with theoretical guarantees and practical applications.

New method uses latent variables to estimate treatment effects from single-arm trials.

New models automate support group formation in online health communities.

Word embeddings are a powerful approach for analyzing language, and exponential family embeddings (EFE) extend them to other types of data. Here we develop structured exponential family embeddings (S-EFE), a method for discovering embeddings that vary across related groups of data. We study how the word usage of U.S. C…

Neural models improve GLMMs for complex data.

Significant pattern mining, the problem of finding itemsets that are significantly enriched in one class of objects, is statistically challenging, as the large space of candidate patterns leads to an enormous multiple testing problem. Recently, the concept of testability was proposed as one approach to correct for mult…

CMDE uses deep learning to estimate causal effects from complex data.

Group factor analysis (GFA) methods have been widely used to infer the common structure and the group-specific signals from multiple related datasets in various fields including systems biology and neuroimaging. To date, most available GFA models require Gibbs sampling or slice sampling to perform inference, which prev…

Flexible Cox model for time-dependent covariates with complex sparsity patterns.

This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class covariance, which is proportional to the between-class covariance in the conjugate prior. …

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral dens…

Method estimates shared and study-specific factors for multi-study data.

Bayesian data selection framework ensures fairness in machine learning models.

CSTs improve stability in covariance spectrum analysis without training.

Bayesian nonparametric approach for clustering non-exchangeable groups.

SharedRep-RLHF learns shared traits for diverse groups, improving fairness and performance.

The BNS invariant is applied to Kähler groups in new proofs and results.

We show that a twistor construction of Hitchin and Ward can be adapted to study unitons (harmonic spheres in a unitary group). Specifically, we show that unitons are equivalent to holomorphic bundles with extra structure over a rational ruled surface with energy given by Chern class. This equivalence allows us to confi…

Study improves conformal prediction for missing covariate data.

Due to the escalating growth of big data sets in recent years, new Bayesian Markov chain Monte Carlo (MCMC) parallel computing methods have been developed. These methods partition large data sets by observations into subsets. However, for Bayesian nested hierarchical models, typically only a few parameters are common f…

Spatially constrained Gaussian mixture models reduce covariance complexity.

Matrix completion has a long-time history of usage as the core technique of recommender systems. In particular, 1-bit matrix completion, which considers the prediction as a ``Recommended'' or ``Not Recommended'' question, has proved its significance and validity in the field. However, while customers and products aggre…

Bayesian model clusters brain activity time series.

CondMTL improves toxicity detection by learning group-specific representations.

Generative models improve MRI reconstruction by learning image structure.

A central goal of algorithmic fairness is to reduce bias in automated decision making. An unavoidable tension exists between accuracy gains obtained by using sensitive information (e.g., gender or ethnic group) as part of a statistical model, and any commitment to protect these characteristics. Often, due to biases pre…

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two no…

This work develops a model to distinguish network and covariate information.

We study inequalities related to the heat kernel for the hypoelliptic sublaplacian on an H-type Lie group. Specifically, we obtain precise pointwise upper and lower bounds on the heat kernel function itself. We then apply these bounds to derive an estimate on the gradient of solutions of the heat equation, which is kno…

The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in the inverse covariance matrix, commonly referred to as the precision matrix, cor…

Paper proposes a new method for sparse covariance Cholesky factor estimation.

Study of CB generating sets for infinite-type surfaces.

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold $M$ homeomorphic to the interior of a compact manifold, and a set $X \subset M$ homeomorphic to the uni…

We address the problem of predicting spatio-temporal processes with temporal patterns that vary across spatial regions, when data is obtained as a stream. That is, when the training dataset is augmented sequentially. Specifically, we develop a localized spatio-temporal covariance model of the process that can capture s…

Optimal classifiers derived from GMMs are approximated by deep neural networks.

MSFA clusters high-dimensional spatial data using spline-based covariance structures.

Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.

Kernel transfer operators, which can be regarded as approximations of transfer operators such as the Perron-Frobenius or Koopman operator in reproducing kernel Hilbert spaces, are defined in terms of covariance and cross-covariance operators and have been shown to be closely related to the conditional mean embedding fr…

Using a data set which includes all transactions among banks in the Italian money market, we study their trading strategies and the dependence among them. We use the Fourier method to compute the variance-covariance matrix of trading strategies. Our results indicate that well defined patterns arise. Two main communitie…

Study addresses covariate mismatch in federated learning, improving model accuracy.

Study examines APOE's impact on AD progression using a novel DEBM approach.

Proposes a new model to analyze mortgage delinquency transitions.

The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatmen…

Paper tackles fairness in CCA by minimizing correlation disparity error.

The paper improves matrix completion with auxiliary covariates using LS estimation.

Graphical models improve portfolio optimization for financial time series.

Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to recover such model structures from large covariance matrix estimation. We propos…

BiLiNGAM model reveals brain emotion circuit development in adolescents.