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Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…
Under a smart grid paradigm, there has been an increase in sensor installations to enhance situational awareness. The measurements from these sensors can be leveraged for real-time monitoring, control, and protection. However, these…
Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more…
The pseudo likelihood method of Besag(1974), has remained a popular method for estimating Markov random field on a very large lattice, despite various documented deficiencies. This is partly because it remains the only computationally…
We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…
In many applications involving large dataset or online updating, stochastic gradient descent (SGD) provides a scalable way to compute parameter estimates and has gained increasing popularity due to its numerical convenience and memory…
Nonparametric density estimation is considered for a discretely observed stationary continuous-time process. For each of three given time sampling procedures either random or deterministic, we establish that histograms and frequency…
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…
Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity…
Recently-developed genotype imputation methods are a powerful tool for detecting untyped genetic variants that affect disease susceptibility in genetic association studies. However, existing imputation methods require individual-level…
4D millimeter-wave (mmWave) radars are sensors that provide robustness against adverse weather conditions (rain, snow, fog, etc.), and as such they are increasingly used for odometry and SLAM (Simultaneous Location and Mapping). However,…
A procedure based on a Mixture Density Model for correcting experimental data for distortions due to finite resolution and limited detector acceptance is presented. Addressing the case that the solution is known to be non-negative, in the…
We introduce a framework for subspace methods which approximate the spectra of self-adjoint, unbounded operators in a local region. Using the projection-valued measure, we derive integrated spectral inequalities that also apply to unbounded…
In the context of multivariate nonparametric regression with missing covariates, we propose Pattern Embedded Neural Networks (PENNs), which can be applied in conjunction with any existing imputation technique. In addition to a neural…
Fitting parametric models by optimizing frequency domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators are a prominent example in this context. Under weak conditions and…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
One of the goals in the development of large scale electronic structure methods is to perform calculations explicitly for a localised region of a system, while still taking into account the rest of the system outside of this region. An…
We conduct a study of the aliased spectral densities of Mat\'ern covariance functions on a regular grid of points, providing clarity on the properties of a popular approximation based on stochastic partial differential equations; while…
A systematic and easy-to-use method is developed to calculate directly the doubly heavy hadron spectral density in the coordinate space. The correlation function is expressed in terms of hypergeometric functions, and the spectral density is…