Related papers: The Delaunay Density Diagnostic
Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena…
The goal of supervised feature selection is to find a subset of input features that are responsible for predicting output values. The least absolute shrinkage and selection operator (Lasso) allows computationally efficient feature selection…
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…
This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…
A major bottleneck of pedestrian detection lies on the sharp performance deterioration in the presence of small-size pedestrians that are relatively far from the camera. Motivated by the observation that pedestrians of disparate spatial…
Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Finding a suitable density function is essential for density-based clustering algorithms such as DBSCAN and DPC. A naive density corresponding to the indicator function of a unit $d$-dimensional Euclidean ball is commonly used in these…
We present a new image scaling method both for downscaling and upscaling, running with any scale factor or desired size. The resized image is achieved by sampling a bivariate polynomial which globally interpolates the data at the new scale.…
A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…
Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable…
Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…
The effect of uncertainties and noise on a quantity of interest (model output) is often better described by its probability density function (PDF) than by its moments. Although density estimation is a common task, the adequacy of…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We study the problem of discovering joinable datasets at scale. This is, how to automatically discover pairs of attributes in a massive collection of independent, heterogeneous datasets that can be joined. Exact (e.g., based on distinct…
Diffusion Probabilistic Field (DPF) models the distribution of continuous functions defined over metric spaces. While DPF shows great potential for unifying data generation of various modalities including images, videos, and 3D geometry, it…
Assessing whether a sample survey credibly represents the population is a critical question for ensuring the validity of downstream research. Generally, this problem reduces to estimating the distance between two high-dimensional…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
Saliency methods can make deep neural network predictions more interpretable by identifying a set of critical features in an input sample, such as pixels that contribute most strongly to a prediction made by an image classifier.…