Related papers: Generalized Uniformity Testing
We present a novel family of nonparametric omnibus tests of the hypothesis that two unknown but estimable functions are equal in distribution when applied to the observed data structure. We developed these tests, which represent a…
One fundamental goal in any learning algorithm is to mitigate its risk for overfitting. Mathematically, this requires that the learning algorithm enjoys a small generalization risk, which is defined either in expectation or in probability.…
Aimed at explaining the surprisingly good generalization behavior of overparameterized deep networks, recent works have developed a variety of generalization bounds for deep learning, all based on the fundamental learning-theoretic…
The primary problem in property testing is to decide whether a given function satisfies a certain property, or is far from any function satisfying it. This crucially requires a notion of distance between functions. The most prevalent notion…
Universal anomaly detection still remains a challenging problem in machine learning and medical image analysis. It is possible to learn an expected distribution from a single class of normative samples, e.g., through epistemic uncertainty…
Distributed learning facilitates the scaling-up of data processing by distributing the computational burden over several nodes. Despite the vast interest in distributed learning, generalization performance of such approaches is not well…
A theoretical framework is developed to describe the transformation that distributes probability density functions uniformly over space. In one dimension, the cumulative distribution can be used, but does not generalize to higher…
We investigate the problem of testing the equivalence between two discrete histograms. A {\em $k$-histogram} over $[n]$ is a probability distribution that is piecewise constant over some set of $k$ intervals over $[n]$. Histograms have been…
A machine learning model that generalizes well should obtain low errors on unseen test examples. Thus, if we learn an optimal model in training data, it could have better generalization performance in testing tasks. However, learning such a…
Distribution shift is an important concern in deep image classification, produced either by corruption of the source images, or a complete change, with the solution involving domain adaptation. While the primary goal is to improve accuracy…
The problem of universal outlying sequence detection is studied, where the goal is to detect outlying sequences among $M$ sequences of samples. A sequence is considered as outlying if the observations therein are generated by a distribution…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
Time series classification is an important problem in real world. Due to its non-stationary property that the distribution changes over time, it remains challenging to build models for generalization to unseen distributions. In this paper,…
Given samples from an unknown distribution $p$ and a description of a distribution $q$, are $p$ and $q$ close or far? This question of "identity testing" has received significant attention in the case of testing whether $p$ and $q$ are…
Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an…
In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…
Testing procedures for assessing specific parametric model forms, or for checking the plausibility of simplifying assumptions, play a central role in the mathematical treatment of the uncertain. No certain answers are obtained by testing…
A central question in random matrix theory is universality. When an emergent phenomena is observed from a large collection of chosen random variables it is natural to ask if this behavior is specific to the chosen random variable or if the…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…