相关论文: A Probabilistic Upper Bound on Differential Entrop…

Dependence among marginally constrained observations can break a finite-sample barrier. To formalize this phenomenon, we introduce the \emph{minimum list entropy coupling} $H(P\|Q_1,\dots,Q_m)$, the minimum conditional entropy…

The generalized covariant entropy bound is the conjecture that the entropy of the matter present on any non-expanding null hypersurface L will not exceed the difference between the areas, in Planck units, of the initial and final spatial…

Stochastic programming is often challenged by epistemic uncertainty, where critical probability distributions are poorly characterized or unknown due to a lack of data. To address this, we pioneer a novel framework for stochastic…

The sensitivities revealed by a sensitivity analysis of a probabilistic network typically depend on the entered evidence. For a real-life network therefore, the analysis is performed a number of times, with different evidence. Although…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

Adaptivity is an important feature of data analysis---the choice of questions to ask about a dataset often depends on previous interactions with the same dataset. However, statistical validity is typically studied in a nonadaptive model,…

Entropy production is a key quantity characterizing nonequilibrium systems. However, it can often be difficult to compute in practice, as it requires detailed information about the system and the dynamics it undergoes. This becomes even…

Modern deep neural networks are well known to be brittle in the face of unknown data instances and recognition of the latter remains a challenge. Although it is inevitable for continual-learning systems to encounter such unseen concepts,…

Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$? This fundamental question has…

We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…

Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known…

In the last three decades, several measures of complexity have been proposed. Up to this point, most of such measures have only been developed for finite spaces. In these scenarios the baseline distribution is uniform. This makes sense…

The outputs of non-linear feed-forward neural network are positive, which could be treated as probability when they are normalized to one. If we take Entropy-Based Principle into consideration, the outputs for each sample could be…

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

We observe an infinite sequence of independent identically distributed random variables $X_1,X_2,\ldots$ drawn from an unknown distribution $p$ over $[n]$, and our goal is to estimate the entropy $H(p)=-\mathbb{E}[\log p(X)]$ within an…

We introduce a novel notion of invariance feedback entropy to quantify the state information that is required by any controller that enforces a given subset of the state space to be invariant. We establish a number of elementary properties,…

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…

This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…

A probability distribution over the Boolean cube is monotone if flipping the value of a coordinate from zero to one can only increase the probability of an element. Given samples of an unknown monotone distribution over the Boolean cube, we…

We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…