Related papers: Quantile absolute deviation
Anomaly detection (AD) is a crucial task in machine learning with various applications, such as detecting emerging diseases, identifying financial frauds, and detecting fake news. However, obtaining complete, accurate, and precise labels…
Smooth Estimation of probability density and distribution functions from its sample is an attractive and an important problem that has applications in several fields such as, business, medicine, and environment. This article introduces a…
Self-diffusion coefficients, $D^*$, are routinely estimated from molecular dynamics simulations by fitting a linear model to the observed mean-squared displacements (MSDs) of mobile species. MSDs derived from simulation exhibit statistical…
Diffusion models have shown superior performance on unsupervised anomaly detection tasks. Since trained with normal data only, diffusion models tend to reconstruct normal counterparts of test images with certain noises added. However, these…
We present a general model on the simulation of the measurement-device independent quantum key distribution (MDI-QKD). It can be used to predict experimental observations of a MDI-QKD with linear channel loss, simulating corresponding…
In this paper, we investigate the robust models for $\Lambda$-quantiles with partial information regarding the loss distribution, where $\Lambda$-quantiles extend the classical quantiles by replacing the fixed probability level with a…
Comparing $K$-sample distributions is a fundamental problem in data science that arises in a wide variety of fields and applications. In this article, we introduce a maximum-of-differences approach to make such comparisons. Specifically, we…
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…
Estimating the proportion of signals hidden in a large amount of noise variables is of interest in many scientific inquires. In this paper, we consider realistic but theoretically challenging settings with arbitrary covariance dependence…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
Zhang (2019) presented a general estimation approach based on the Gaussian distribution for general parametric models where the likelihood of the data is difficult to obtain or unknown, but the mean and variance-covariance matrix are known.…
Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue…
We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…
A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.
This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…
We study a distributed estimation problem in which two remotely located parties, Alice and Bob, observe an unlimited number of i.i.d. samples corresponding to two different parts of a random vector. Alice can send $k$ bits on average to…
While conditional diffusion models are known to have good coverage of the data distribution, they still face limitations in output diversity, particularly when sampled with a high classifier-free guidance scale for optimal image quality or…
Probabilistic methods have attracted much interest in fault detection design, but its need for complete distributional knowledge is seldomly fulfilled. This has spurred endeavors in distributionally robust fault detection (DRFD) design,…
In this work, we give efficient algorithms for privately estimating a Gaussian distribution in both pure and approximate differential privacy (DP) models with optimal dependence on the dimension in the sample complexity. In the pure DP…