Related papers: A Cancellation Law for Probabilistic Processes
This paper investigates weighted approximations for studentized $U$-statistics type processes, both with symmetric and antisymmetric kernels, only under the assumption that the distribution of the projection variate is in the domain of…
We present a rejection method based on recursive covering of the probability density function with equal tiles. The concept works for any probability density function that is pointwise computable or representable by tabular data. By the…
Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not.…
We study the problem of assessing the robustness of counterfactual explanations for deep learning models. We focus on $\textit{plausible model shifts}$ altering model parameters and propose a novel framework to reason about the robustness…
Strong negative dependence properties have recently been proved for the symmetric exclusion process. In this paper, we apply these results to prove convergence to the Poisson and normal distributions for various functionals of the process.
An elementary recursive relation for M$\ddot{\mathrm{o}}$bius function $\mu (n)$ is introduced by two simple ways. With this recursive relation, $\mu (n)$ can be calculated without directly knowing the factorization of the $n$. $\mu (1)…
We introduce multinomial and $r$-variants of several classic objects of combinatorial probability, such as the random recursive and Hoppe trees, random set partitions and compositions, the Chinese restaurant process, Feller's coupling, and…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
While for deterministic systems, a counterexample to a property can simply be an error trace, counterexamples in probabilistic systems are necessarily more complex. For instance, a set of erroneous traces with a sufficient cumulative…
The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic…
In this paper we propose a framework for combining Disjunctive Logic Programming and Poole's Probabilistic Horn Abduction. We use the concept of hypothesis to specify the probability structure. We consider the case in which probabilistic…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…
In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…
Dilation is a puzzling phenomenon within Imprecise Probability theory: when it obtains, our uncertainty evaluation on event $A$ is vaguer after conditioning $A$ on $B$, whatever is event $B$ in a given partition $\mathcal{B}$. In this paper…
We introduce two extensions of the $\lambda$-calculus with a probabilistic choice operator, $\Lambda_\oplus^{cbv}$ and $\Lambda_\oplus^{cbn}$, modeling respectively call-by-value and call-by-name probabilistic computation. We prove that…
We present new results on the relation between purely symbolic context-free parsing strategies and their probabilistic counter-parts. Such parsing strategies are seen as constructions of push-down devices from grammars. We show that…
In this second paper in the series, we investigate occurrence frequencies of apparent unipolar processes, cancellation, and emergence of patch structures in quiet regions. Apparent unipolar events are considerably more frequent than…