相关论文: Probability and Ambiguity

The aim of this paper is to provide a new perspective on finite element accuracy. Starting from a geometrical reading of the Bramble-Hilbert lemma, we recall the two probabilistic laws we got in previous works that estimate the relative…

To generate "accurate" scene graphs, almost all existing methods predict pairwise relationships in a deterministic manner. However, we argue that visual relationships are often semantically ambiguous. Specifically, inspired by linguistic…

This paper studies distributionally robust optimization for a rich class of risk measures with ambiguity sets defined by $\phi$-divergences. The risk measures are allowed to be non-linear in probabilities, are represented by Choquet…

We derive two probabilistic bounds for the relative forward error in the floating point summation of $n$ real numbers, by representing the roundoffs as independent, zero-mean, bounded random variables. The first probabilistic bound is based…

This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with…

We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no…

Computing the probability of evidence even with known error bounds is NP-hard. In this paper we address this hard problem by settling on an easier problem. We propose an approximation which provides high confidence lower bounds on…

The celebrated union-closed conjecture is concerned with the cardinalities of various subsets of the Boolean $d$-cube. The cardinality of such a set is equivalent, up to a constant, to its measure under the uniform distribution, so we can…

Let a stick be broken at random at n-1 points to form n pieces. We consider three problems on forming k-gons with k out of these n pieces, and show how a statistical approach, through a linear transformation of variables, yields simple…

We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs "true" with probability p, we have that the…

This paper provides a non-robust interpretation of the distributionally robust optimization (DRO) problem by relating the distributional uncertainties to the chance probabilities. Our analysis allows a decision-maker to interpret the size…

Simpson's paradox and collapsibility are two closely related concepts in the context of data analysis. While the knowledge about the occurrence of Simpson's paradox helps a statistician to draw correct and meaningful conclusions, the…

We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, splitting number, and the existence of certain…

We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…

In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…

The established language for statistical testing --- significance levels, power, and p-values --- is overly complicated and deceptively conclusive. Even teachers of statistics and scientists who use statistics misinterpret the results of…

Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…

We propose a new approach to solve the classical Monty Hall problem in its general form. The solution is based on basic tools of probability theory, by defining three elementary events which decompose the sample space into a partition. The…

The primary objective of this paper is to revisit Simpson's paradox using a statistical misspecification perspective. It is argued that the reversal of statistical associations is sometimes spurious, stemming from invalid probabilistic…

Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…