Related papers: A Distance Measure for Random Permutation Set: Fro…
Permutation codes, in the form of rank modulation, have shown promise for applications such as flash memory. One of the metrics recently suggested as appropriate for rank modulation is the Ulam metric, which measures the minimum…
Many learning problems require predicting how populations evolve under an unknown transformation. A natural representation for such populations is a probability measure, with point clouds as a key example. In this work, we study the…
Dempster-Shafer theory (D-S theory) is widely used in decision making under the uncertain environment. Ranking basic belief assignments (BBAs) now is an open issue. Existing evidence distance measures cannot rank the BBAs in the situations…
Recent technological advancements have led to the generation of huge amounts of data over the web, such as text, image, audio and video. Most of this data is high dimensional and sparse, for e.g., the bag-of-words representation used for…
We examine the integrated squared difference, also known as the L2 distance (L2D), between two probability densities. Such a distance metric allows for comparison of differences between pairs of distributions or changes in a distribution…
Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without…
Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions,…
We present several natural notions of distance between spectral density functions of (discrete-time) random processes. They are motivated by certain filtering problems. First we quantify the degradation of performance of a predictor which…
In a conventional supervised learning setting, a machine learning model has access to examples of all object classes that are desired to be recognized during the inference stage. This results in a fixed model that lacks the flexibility to…
This paper presents a new distance metric to compare two continuous probability density functions. The main advantage of this metric is that, unlike other statistical measurements, it can provide an analytic, closed-form expression for a…
We introduce an \verb|R| package, called \verb|MPS|, for computing the probability density function, computing the cumulative distribution function, computing the quantile function, simulating random variables, and estimating the parameters…
We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by…
Ranked set sampling (RSS) is a stratified sampling method that improves efficiency over simple random sampling (SRS) by utilizing auxiliary information for ranking and stratification. While balanced RSS (BRSS) assumes equal allocation…
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
Accurate approximation of probability measures is essential in numerical applications. This paper explores the quantization of probability measures using the maximum mean discrepancy (MMD) distance as a guiding metric. We first investigate…
We describe a data-driven method for inferring the camera viewpoints given multiple images of an arbitrary object. This task is a core component of classic geometric pipelines such as SfM and SLAM, and also serves as a vital pre-processing…
In this work, we derive Robertson-Heisenberg like uncertainty relation for two incompatible observables in a pre- and post-selected (PPS) system. The newly defined standard deviation and the uncertainty relation in the PPS system have…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
Perceptual similarity scores that align with human vision are critical for both training and evaluating computer vision models. Deep perceptual losses, such as LPIPS, achieve good alignment but rely on complex, highly non-linear…