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A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the…
Medical image segmentation is one of the domains where sufficient annotated data is not available. This necessitates the application of low-data frameworks like few-shot learning. Contemporary prototype-based frameworks often do not account…
We propose a closed-form spectral framework for relative log-density estimation in linearly parameterized probabilistic models, including unnormalized and conditional models. This is achieved by representing the Kullback-Leibler (KL)…
Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…
We study partially linear models in settings where observations are arranged in independent groups but may exhibit within-group dependence. Existing approaches estimate linear model parameters through weighted least squares, with optimal…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
Data remap between non-matching meshes is a critical step in multiphysics coupling using a partitioned approach. The data fields being transferred often have jumps in function values or derivatives. It is important but very challenging to…
A Covariance-on-Covariance regression model is introduced in this manuscript. It is assumed that there exists (at least) a pair of linear projections on outcome covariance matrices and predictor covariance matrices such that a log-linear…
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…
The function-on-function regression model is fundamental for analyzing relationships between functional covariates and responses. However, most existing function-on-function regression methodologies assume independence between observations,…
We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We…
A joint conditional autoregressive expectile and Expected Shortfall framework is proposed. The framework is extended through incorporating a measurement equation which models the contemporaneous dependence between the realized measures and…
Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…
The tuning parameter selection strategy for penalized estimation is crucial to identify a model that is both interpretable and predictive. However, popular strategies (e.g., minimizing average squared prediction error via cross-validation)…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…
We consider the problem of learning an unknown, possibly nonlinear operator between separable Hilbert spaces from supervised data. Inputs are drawn from a prescribed probability measure on the input space, and outputs are (possibly noisy)…
We consider the problem of estimating the probability density function of a circular random variable observed under censoring. To this end, we introduce a projection estimator constructed via a regression approach on linear sieves. We first…
Maximum likelihood estimation of large Markov-switching vector autoregressions (MS-VARs) can be challenging or infeasible due to parameter proliferation. To accommodate situations where dimensionality may be of comparable order to or…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
In constrained stochastic optimization, one naturally expects that imposing a stricter feasible set does not increase the statistical risk of an estimator defined by projection onto that set. In this paper, we show that this intuition can…