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Motivated by the abundance of uncertain event data from multiple sources including physical devices and sensors, this paper presents the task of relating a stochastic process observation to a process model that can be rendered from a…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
In reinforcement learning episodes, the rewards and punishments are often non-deterministic, and there are invariably stochastic elements governing the underlying situation. Such stochastic elements are often numerous and cannot be known in…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…
Formal reasoning about hashing-based probabilistic data structures often requires reasoning about random variables where when one variable gets larger (such as the number of elements hashed into one bucket), the others tend to be smaller…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…
The sequence of so-called signature moments describes the laws of many stochastic processes in analogy with how the sequence of moments describes the laws of vector-valued random variables. However, even for vector-valued random variables,…
For fragments L of first-order logic (FO) with counting quantifiers, we consider the definability problem, which asks whether a given L-formula can be equivalently expressed by a formula in some fragment of L without counting, and the more…
The logit model is often used to analyze experimental data. However, randomization does not justify the model, so the usual estimators can be inconsistent. A consistent estimator is proposed. Neyman's non-parametric setup is used as a…
In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We…
Social dynamics determined by voting in a stochastic environment is analyzed for a society composed of two cohesive groups of similar size. Within the model of random walks determined by voting, explicit formulas are derived for the capital…
In the simplest sequential decision problem for an ergodic stochastic process X, at each time n a decision u_n is made as a function of past observations X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is known that…
This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is…
The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…
The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This…
We develop a new technique for proving distribution testing lower bounds for properties defined by inequalities involving the bin probabilities of the distribution in question. Using this technique we obtain new lower bounds for…
We present Polaris, a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs…