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Cosmological $N$-body simulations provide numerical predictions of the structure of the Universe against which to compare data from ongoing and future surveys, but the growing volume of the Universe mapped by surveys requires…
Estimating graphical model structure from high-dimensional and undersampled data is a fundamental problem in many scientific fields. Existing approaches, such as GLASSO, latent variable GLASSO, and latent tree models, suffer from high…
Three-dimensional (3D) medical image enhancement, including denoising and super-resolution, is critical for clinical diagnosis in CT, PET, and MRI. Although diffusion models have shown remarkable success in 2D medical imaging, scaling them…
Upcoming and existing large-scale surveys of galaxies require accurate theoretical predictions of the dark matter clustering statistics for thousands of mock galaxy catalogs. We demonstrate that this goal can be achieve with our new…
Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…
Functional connectivity estimates are highly sensitive to analysis choices and can be dominated by noise when the number of sampled time points is small relative to network dimensionality. This issue is particularly acute in fMRI, where…
Magnetic field inhomogeneity estimation is important in some types of magnetic resonance imaging (MRI), including field-corrected reconstruction for fast MRI with long readout times, and chemical shift based water-fat imaging. Regularized…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
In this paper, we consider voxel selection for functional Magnetic Resonance Imaging (fMRI) brain data with the aim of finding a more complete set of probably correlated discriminative voxels, thus improving interpretation of the discovered…
The operation of a novel nonvolatile memory device based on a conductive ferroelectric/non-ferroelectric thin film multilayer stack is simulated numerically. The simulation involves the self-consistent steady state solution of Poisson's…
Ongoing and upcoming wide-field surveys at different wavelengths will measure the distribution of galaxy clusters with unprecedented precision, demanding accurate models for the two-point correlation function (2PCF) covariance. In this…
Understanding protein flexibility and its dynamic interactions with other molecules is essential for studying protein function. Although cryogenic electron microscopy(cryo-EM) provides an opportunity to observe macromolecular dynamics…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such…
Cosmological observables rely heavily on summary statistics such as two-point correlation functions. In many practical cases (e.g. the weak-lensing cosmic shear), those correlation functions are estimated from a finite, discrete sample of…
Anatomy is undergoing a renaissance driven by availability of large digital data sets generated by light microscopy. A central computational task is to map individual data volumes to standardized templates. This is accomplished by…
Statistical inference of the dependence between objects often relies on covariance matrices. Unless the number of features (e.g. data points) is much larger than the number of objects, covariance matrix cleaning is necessary to reduce…
The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix…
In this paper, we develop econometric tools to analyze the integrated volatility of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent…
In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique…