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Regression models are popular tools in empirical sciences to infer the influence of a set of variables onto a dependent variable given an experimental dataset. In neuroscience and cognitive psychology, Generalized Linear Models (GLMs)…
The Expectation-Maximization algorithm is perhaps the most broadly used algorithm for inference of latent variable problems. A theoretical understanding of its performance, however, largely remains lacking. Recent results established that…
Variational inference methods for latent variable statistical models have gained popularity because they are relatively fast, can handle large data sets, and have deterministic convergence guarantees. However, in practice it is unclear…
Precisely estimating out-of-sample upper quantiles is very important in risk assessment and in engineering practice for structural design to prevent a greater disaster. For this purpose, the generalized extreme value (GEV) distribution has…
Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…
Deep generative networks provide a powerful tool for modeling complex data in a wide range of applications. In inverse problems that use these networks as generative priors on data, one must often perform inference of the inputs of the…
This work establishes regularity conditions for consistency and asymptotic normality of the multiple parameter maximum likelihood estimator(MLE) from censored data, where the censoring mechanism is in the form of $1$-bit measurements. The…
This paper proposes a new approach for Bayesian and maximum likelihood parameter estimation for stationary Gaussian processes observed on a large lattice with missing values. We propose an MCMC approach for Bayesian inference, and a Monte…
High-dimensional biomedical studies require models that are simultaneously accurate, sparse, and interpretable, yet exact best subset selection for generalized linear models is computationally intractable. We develop a scalable method that…
Molecular profiling data (e.g., gene expression) has been used for clinical risk prediction and biomarker discovery. However, it is necessary to integrate other prior knowledge like biological pathways or gene interaction networks to…
This paper considers generalized least squares (GLS) estimation for linear panel data models. By estimating the large error covariance matrix consistently, the proposed feasible GLS (FGLS) estimator is more efficient than the ordinary least…
We study the excess mean square error (EMSE) above the minimum mean square error (MMSE) in large linear systems where the posterior mean estimator (PME) is evaluated with a postulated prior that differs from the true prior of the input…
This paper investigates the minimum mean square error (MMSE) estimation of x, given the observation y = Hx+n, when x and n are independent and Gaussian Mixture (GM) distributed. The introduction of GM distributions, represents a…
Multidimensional scaling (MDS) is widely used to reconstruct a low-dimensional representation of high-dimensional data while preserving pairwise distances. However, Bayesian MDS approaches based on Markov chain Monte Carlo (MCMC) face…
In practice, there often exist unobserved variables, also termed hidden variables, associated with both the response and covariates. Existing works in the literature mostly focus on linear regression with hidden variables. However, when the…
Generalized Linear Model (or GLM) extends the ordinary linear regression by linking the mean of the response variable to covariates through appropriate link functions. GLM is widely used in the analysis of datasets arising from diverse…
The accuracy and precision of high-energy spallation models are key issues for the design and development of new applications and experiments. We present a method to estimate model parameters and associated uncertainties by leveraging the…
Modern biomedical datasets are increasingly high dimensional and exhibit complex correlation structures. Generalized Linear Mixed Models (GLMMs) have long been employed to account for such dependencies. However, proper specification of the…
The scalability of Generalized Linear Models (GLMs) for large-scale, high-dimensional data often forces a trade-off between computational feasibility and statistical accuracy, particularly for inference on pre-specified parameters. While…
Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…