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Consider two batches of independent or interdependent exponentiated location-scale distributed heterogeneous random variables. This article investigates ordering results for the second-order statistics from these batches when a vector of…
Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…
We consider a small area estimation model under square-root transformation in the presence of functional measurement error. When measurement error is present, the Bayes predictor can no longer be used as it depends on the covariates even if…
Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…
In this work, we propose low-complexity adaptive biased estimation algorithms, called group-based shrinkage estimators (GSEs), for parameter estimation and interference suppression scenarios with mechanisms to automatically adjust the…
We propose a new prediction method for multivariate linear regression problems where the number of features is less than the sample size but the number of outcomes is extremely large. Many popular procedures, such as penalized regression…
This report first provides a brief overview of a number of supervised learning algorithms for regression tasks. Among those are neural networks, regression trees, and the recently introduced Nexting. Nexting has been presented in the…
The problem of preferential sampling in geostatistics arises when the choise of location to be sampled is made with information about the phenomena in the study. The geostatistical model under preferential sampling deals with this problem,…
Sparse reduced rank regression is an essential statistical learning method. In the contemporary literature, estimation is typically formulated as a nonconvex optimization that often yields to a local optimum in numerical computation. Yet,…
Spectral learning recently generated lots of excitement in machine learning, largely because it is the first known method to produce consistent estimates (under suitable conditions) for several latent variable models. In contrast, maximum…
In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder.…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
This article is devoted to the analysis of semilinear, parabolic, Stochastic Partial Differential Equations, with slow and fast time scales. Asymptotically, an averaging principle holds: the slow component converges to the solution of…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…
In regression with random design, we study the problem of selecting a model that performs well for out-of-sample prediction. We do not assume that any of the candidate models under consideration are correct. Our analysis is based on…
In online classification, a learner is presented with a sequence of examples and aims to predict their labels in an online fashion so as to minimize the total number of mistakes. In the self-directed variant, the learner knows in advance…
Weather forecasts are typically given in the form of forecast ensembles obtained from multiple runs of numerical weather prediction models with varying initial conditions and physics parameterizations. Such ensemble predictions tend to be…
Solving optimization problems with unknown parameters often requires learning a predictive model to predict the values of the unknown parameters and then solving the problem using these values. Recent work has shown that including the…
In this paper, we present a generalized estimating equations based estimation approach and a variable selection procedure for single-index models when the observed data are clustered. Unlike the case of independent observations,…
In this paper, we focus on the variable selection techniques for a class of semiparametric spatial regression models which allow one to study the effects of explanatory variables in the presence of the spatial information. The spatial…