Related papers: Learning Powers of Poisson Binomial Distributions

As was noted already by A. N. Kolmogorov, any random variable has a Bernoulli component. This observation provides a tool for the extension of results which are known for Bernoulli random variables to arbitrary distributions. Two…

It appeared recently that the underlying degree distribution of networks may play a crucial role concerning their robustness. Empiric and analytic results have been obtained, based on asymptotic and mean-field approximations. Previous work…

This article is devoted to the problem of predicting the value taken by a random permutation $\Sigma$, describing the preferences of an individual over a set of numbered items $\{1,\; \ldots,\; n\}$ say, based on the observation of an…

In this note we present an algorithm to obtain a uniform lower bound on Hausdorff dimension of the stationary measure of an affine iterated function scheme with similarities, the best known example of which is Bernoulli convolution. The…

We study the problem of covering and learning sums $X = X_1 + \cdots + X_n$ of independent integer-valued random variables $X_i$ (SIIRVs) with unbounded, or even infinite, support. De et al. at FOCS 2018, showed that the maximum value of…

A Bernoulli factory is an algorithmic procedure for exact sampling of certain random variables having only Bernoulli access to their parameters. Bernoulli access to a parameter $p \in [0,1]$ means the algorithm does not know $p$, but has…

Recent advancements in quantum technologies have opened new horizons for exploring the physical world in ways once deemed impossible. Central to these breakthroughs is the concept of quantum advantage, where quantum systems outperform their…

We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…

We present new sampling methods in finite population that allow to control the joint inclusion probabilities of units and especially the spreading of sampled units in the population. They are based on the use of renewal chains and…

Poisson subsampling is the default sampling scheme in differentially private machine learning, largely because its unstructured randomness yields tractable privacy amplification analyses. Yet this same randomness introduces substantial…

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

We show how to compute any symmetric Boolean function on $n$ variables over any field (as well as the integers) with a probabilistic polynomial of degree $O(\sqrt{n \log(1/\epsilon)})$ and error at most $\epsilon$. The degree dependence on…

Sum-product networks (SPNs) are probabilistic models characterized by exact and fast evaluation of fundamental probabilistic operations. Its superior computational tractability has led to applications in many fields, such as machine…

Consider the family of power divergence statistics based on $n$ trials, each leading to one of $r$ possible outcomes. This includes the log-likelihood ratio and Pearson's statistic as important special cases. It is known that in certain…

We consider quantum, nondterministic and probabilistic versions of known computational model Ordered Read-$k$-times Branching Programs or Ordered Binary Decision Diagrams with repeated test ($k$-QOBDD, $k$-NOBDD and $k$-POBDD). We show…

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…

This paper considers a variation of the full-information secretary problem where the random variables to be observed are independent but not necessary identically distributed. The main result is a sharp lower bound for the optimal win…

We study the {\em Budgeted Dominating Set} (BDS) problem on uncertain graphs, namely, graphs with a probability distribution $p$ associated with the edges, such that an edge $e$ exists in the graph with probability $p(e)$. The input to the…

In this work, we investigated the feasibility of applying deep learning techniques to solve Poisson's equation. A deep convolutional neural network is set up to predict the distribution of electric potential in 2D or 3D cases. With proper…

The lack of well-calibrated confidence estimates makes neural networks inadequate in safety-critical domains such as autonomous driving or healthcare. In these settings, having the ability to abstain from making a prediction on…