Related papers: Learning $k$-Modal Distributions via Testing
We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…
We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…
A remarkable recent paper by Rubinfeld and Vasilyan (2022) initiated the study of \emph{testable learning}, where the goal is to replace hard-to-verify distributional assumptions (such as Gaussianity) with efficiently testable ones and to…
Given i.i.d.~samples from an unknown distribution $P$, the goal of distribution learning is to recover the parameters of a distribution that is close to $P$. When $P$ belongs to the class of product distributions on the Boolean hypercube…
Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…
We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…
We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…
Multi-distribution learning (MDL), which seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions, has emerged as a unified framework in response to the evolving demand for robustness,…
We conduct a KL-divergence based procedure for testing elliptical distributions. The procedure simultaneously takes into account the two defining properties of an elliptically distributed random vector: independence between length and…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
The k-nearest-neighbor method performs classification tasks for a query sample based on the information contained in its neighborhood. Previous studies into the k-nearest-neighbor algorithm usually achieved the decision value for a class by…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of $2$-outcome POVMs. However, these shadow tomography…
Learning a robust classifier from a few samples remains a key challenge in machine learning. A major thrust of research has been focused on developing $k$-nearest neighbor ($k$-NN) based algorithms combined with metric learning that…
In learning theory, a standard assumption is that the data is generated from a finite mixture model. But what happens when the number of components is not known in advance? The problem of estimating the number of components, also called…
Distribution testing deals with what information can be deduced about an unknown distribution over $\{1,\ldots,n\}$, where the algorithm is only allowed to obtain a relatively small number of independent samples from the distribution. In…
Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…
This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set…
We consider the problem of learning parametric distributions from their quantized samples in a network. Specifically, $n$ agents or sensors observe independent samples of an unknown parametric distribution; and each of them uses $k$ bits to…
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…