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Applying convolutional neural networks to large images is computationally expensive because the amount of computation scales linearly with the number of image pixels. We present a novel recurrent neural network model that is capable of…
Diffracted scattering and occlusion are important acoustic effects in interactive auralization and noise control applications, typically requiring expensive numerical simulation. We propose training a convolutional neural network to map…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…
Selectivity estimation aims at estimating the number of database objects that satisfy a selection criterion. Answering this problem accurately and efficiently is essential to many applications, such as density estimation, outlier detection,…
Many approaches to 3D image segmentation are based on hierarchical clustering of supervoxels into image regions. Here we describe a distributed algorithm capable of handling a tremendous number of supervoxels. The algorithm works…
We present a Fourier-based approach for high-dimensional function approximation. To this end, we analyze the truncated ANOVA (analysis of variance) decomposition and learn the anisotropic smoothness properties of the target function from…
Kernel based regularized interpolation is a well known technique to approximate a continuous multivariate function using a set of scattered data points and the corresponding function evaluations, or data values. This method has some…
Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over…
Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…
We present a paralell approach to discrete geometry: the first one introduces Voronoi cell complexes from statistical tessellations in order to know the mean scalar curvature in term of the mean number of edges of a cell. The second one…
Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these "sacrifices" do not always require more…
We study multiscale scattered data interpolation schemes for globally supported radial basis functions with focus on the Mat\'ern class. The multiscale approximation is constructed through a sequence of residual corrections, where radial…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…
3D microscopy is key in the investigation of diverse biological systems, and the ever increasing availability of large datasets demands automatic cell identification methods that not only are accurate, but also can imply the uncertainty in…
We tackle the problem of estimating the spatial distribution of mobile phones from Mobile Network Operator (MNO) data, namely Call Detail Record (CDR) or signalling data. The process of transforming MNO data to a density map requires…
Diffusion MRI offers a unique probe into neural microstructure and connectivity in the developing brain. However, analysis of neonatal brain imaging data is complicated by inevitable subject motion, leading to a series of scattered slices…
We develop and analyze an asynchronous algorithm for distributed convex optimization when the objective writes a sum of smooth functions, local to each worker, and a non-smooth function. Unlike many existing methods, our distributed…