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In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the approximation results in total variation…
Instance discriminative self-supervised representation learning has been attracted attention thanks to its unsupervised nature and informative feature representation for downstream tasks. In practice, it commonly uses a larger number of…
In the setting where we have $n$ independent observations of a random variable $X$, we derive explicit error bounds in total variation distance when approximating the number of observations equal to the maximum of the sample (in the case…
Reliable measures of statistical dependence could be useful tools for learning independent features and performing tasks like source separation using Independent Component Analysis (ICA). Unfortunately, many of such measures, like the…
Sparse additive models have attracted much attention in high-dimensional data analysis due to their flexible representation and strong interpretability. However, most existing models are limited to single-level learning under the…
Well-spread samples are desirable in many disciplines because they improve estimation when target variables exhibit spatial structure. This paper introduces an integrated methodological framework for spreading samples over the population's…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…
Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
One of the central objectives of modern risk management is to find a set of risks where the probability of multiple simultaneous catastrophic events is negligible. That is, risks are taken only when their joint behavior seems sufficiently…
Reinforcement learning algorithms are typically limited to learning a single solution for a specified task, even though diverse solutions often exist. Recent studies showed that learning a set of diverse solutions is beneficial because…
The independent component model is a latent variable model where the components of the observed random vector are linear combinations of latent independent variables. The aim is to find an estimate for a transformation matrix back to…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
Let $X,X_1,...,X_n$ be independent identically distributed random variables. The paper deals with the question about the behavior of the concentration function of the random variable $\sum_{k=1}^{n}a_k X_k$ according to the arithmetic…
Active statistical inference is a new method for inference with AI-assisted data collection. Given a budget on the number of labeled data points that can be collected and assuming access to an AI predictive model, the basic idea is to…
This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined…
For zero-error function computation over directed acyclic networks, existing upper and lower bounds on the computation capacity are known to be loose. In this work we consider the problem of computing the arithmetic sum over a specific…
In this paper, we analyze and study a hybrid model for testing and learning probability distributions. Here, in addition to samples, the testing algorithm is provided with one of two different types of oracles to the unknown distribution…
A novel, non-trivial, probabilistic upper bound on the entropy of an unknown one-dimensional distribution, given the support of the distribution and a sample from that distribution, is presented. No knowledge beyond the support of the…