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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…
Associative memory refers to the ability to relate a memory with an input and targets the restoration of corrupted patterns. It has been intensively studied in classical physical systems, as in neural networks where an attractor dynamics…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
Practitioners use Hidden Markov Models (HMMs) in different problems for about sixty years. Besides, Conditional Random Fields (CRFs) are an alternative to HMMs and appear in the literature as different and somewhat concurrent models. We…
In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niew\k{e}g\l owski (2015). Here, we turn our attention to the study of Markov consistency and…
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these…
Probabilistic hyperproperties describe probabilistic relations between multiple sets of executions in a stochastic system. Prominent examples include information-theoretic characterizations of security and privacy policies. However, model…
We study the properties of a subclass of stochastic processes called discrete time nonlinear Markov chains with an aggregator, which naturally appear in various topics such as strategic queueing systems, inventory dynamics, opinion…
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation…
The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive model able to generate sequences with a given autocorrelation structure. While a first-order Markov Chain model generates new…
For a linear combination of random variables, fix some confidence level and consider the quantile of the combination at this level. We are interested in the partial derivatives of the quantile with respect to the weights of the random…
As a fundamental problem in many different fields, link prediction aims to estimate the likelihood of an existing link between two nodes based on the observed information. Since this problem is related to many applications ranging from…
Characterizing the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterizing all information inequalities. The majority of…
Continuous-time Markov chains are frequently used as stochastic models for chemical reaction networks, especially in the growing field of systems biology. A fundamental problem for these Stochastic Chemical Reaction Networks (SCRNs) is to…
Reasoning is the ability to integrate internal states and external inputs in a meaningful and semantically consistent flow. Contemporary machine learning (ML) systems increasingly rely on such sequential reasoning, from language…
The covariance matrix of measurements of Markov random fields (processes) has useful properties that allow to develop effective computational algorithms for many problems in the study of Markov fields on the basis of field observations…
Superadditivity relations characterize the distributions of coherence in multipartite quantum systems. In this work, we investigate the superadditivity relations related to the $l_1$-norm of coherence $C_{l_1}$ in multiqubit quantum…