Related papers: Entropy, Optimization and Counting
Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…
We study which outcomes are implementable by disclosing coarse statistics of a data-generating process rather than its full distribution. Players observe data whose joint distribution is only partially known: they know the expectations of…
Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…
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…
We study the fundamental task of estimating the median of an underlying distribution from a finite number of samples, under pure differential privacy constraints. We focus on distributions satisfying the minimal assumption that they have a…
Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm use a sample drawn according to some probability distribution for approximating the location of an…
We study the mean estimation problem under communication and local differential privacy constraints. While previous work has proposed \emph{order}-optimal algorithms for the same problem (i.e., asymptotically optimal as we spend more bits),…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
It is known that if a 2-universal hash function $H$ is applied to elements of a {\em block source} $(X_1,...,X_T)$, where each item $X_i$ has enough min-entropy conditioned on the previous items, then the output distribution…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
We provide a near-optimal, computationally efficient algorithm for the unit-demand pricing problem, where a seller wants to price n items to optimize revenue against a unit-demand buyer whose values for the items are independently drawn…
Data partitioning that maximizes/minimizes the Shannon entropy, or more generally the R\'enyi entropy is a crucial subroutine in data compression, columnar storage, and cardinality estimation algorithms. These partition algorithms can be…
In this work, we treat the problem of multi-task submodular optimization from the perspective of local distributional robustness within the neighborhood of a reference distribution which assigns an importance score to each task. We…
The best practical techniques for exact solution of instances of the constrained maximum-entropy sampling problem, a discrete-optimization problem arising in the design of experiments, are via a branch-and-bound framework, working with a…
The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision…
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities and covariance…
To efficiently evaluate system reliability based on Monte Carlo simulation, importance sampling is used widely. The optimal importance sampling density was derived in 1950s for the deterministic simulation model, which maps an input to an…
Let X_1, ..., X_n be a sequence of n classical random variables and consider a sample of r positions selected at random. Then, except with (exponentially in r) small probability, the min-entropy of the sample is not smaller than, roughly, a…