Related papers: Belief Propagation as Diffusion
We define two algorithms for propagating information in classification problems with pairwise relationships. The algorithms are based on contraction maps and are related to non-linear diffusion and random walks on graphs. The approach is…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…
Predicting the distribution of future states in a stochastic system, known as belief propagation, is fundamental to reasoning under uncertainty. However, nonlinear dynamics often make analytical belief propagation intractable, requiring…
Undirected graphical models are a widely used class of probabilistic models in machine learning that capture prior knowledge or putative pairwise interactions between variables. Those interactions are encoded in a graph for pairwise…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
We study the stochastic block model with two communities where vertices contain side information in the form of a vertex label. These vertex labels may have arbitrary label distributions, depending on the community memberships. We analyze a…
Since their introduction, Boolean networks have been traditionally studied in view of their rich dynamical behavior under different update protocols and for their qualitative analogy with cell regulatory networks. More recently, tools…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
Gaussian belief propagation (BP) is a computationally efficient method to approximate the marginal distribution and has been widely used for inference with high dimensional data as well as distributed estimation in large-scale networks.…
Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on…
A new approximation of the cluster variational method is introduced for the three-dimensional Ising model on the simple cubic lattice. The maximal cluster is, as far as we know, the largest ever used in this method. A message-passing…
The article considers parameter estimation constructing such as quasi-maximum likelyhood estimation and one step estimation in statistical models generated by solution of stochastic differential equation. It has been developed a software…
How can we tell when accounts are fake or real in a social network? And how can we tell which accounts belong to liberal, conservative or centrist users? Often, we can answer such questions and label nodes in a network based on the labels…
A systematic study of the probability distribution of superimposed random codes is presented through the use of generating functions. Special attention is paid to the cases of either uniformly distributed but not necessarily independent or…
Systems such as sensor networks and teams of autonomous robots consist of multiple autonomous entities that interact with each other in a distributed, asynchronous manner. These entities need to keep track of the state of the system as it…
The spread of new ideas, behaviors or technologies has been extensively studied using epidemic models. Here we consider a model of diffusion where the individuals' behavior is the result of a strategic choice. We study a simple coordination…
In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…
We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…
Diffusion probabilistic models have made their way into a number of high-profile applications since their inception. In particular, there has been a wave of research into using diffusion models in the prediction and design of biomolecular…