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Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
We consider the problem of distributedly estimating Gaussian processes in multi-agent frameworks. Each agent collects few measurements and aims to collaboratively reconstruct a common estimate based on all data. Agents are assumed with…
Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls…
The random dot product graph is a popular model for network data with extensions that accommodate dynamic (time-varying) networks. However, two significant deficiencies exist in the dynamic random dot product graph literature: (1) no…
Distributed aggregation allows the derivation of a given global aggregate property from many individual local values in nodes of an interconnected network system. Simple aggregates such as minima/maxima, counts, sums and averages have been…
In analogy to superstatistics, which connects Boltzmann-Gibbs statistical mechanics to its generalizations through temperature fluctuations, complex networks are constructed from the fluctuating Erdos-Renyi random graphs. Here, using the…
Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit…
We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU…
Gaussian belief propagation (BP) has been widely used for distributed estimation in large-scale networks such as the smart grid, communication networks, and social networks, where local measurements/observations are scattered over a wide…
Belief propagation is a fundamental message-passing algorithm for numerous applications in machine learning. It is known that belief propagation algorithm is exact on tree graphs. However, belief propagation is run on loopy graphs in most…
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…
Distributed averaging is among the most relevant cooperative control problems, with applications in sensor and robotic networks, distributed signal processing, data fusion, and load balancing. Consensus and gossip algorithms have been…
This work studies the problem of stochastic dynamic filtering and state propagation with complex beliefs. The main contribution is GP-SUM, a filtering algorithm tailored to dynamic systems and observation models expressed as Gaussian…
We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and…
We consider the problem of maximum likelihood estimation in linear models represented by factor graphs and solved via the Gaussian belief propagation algorithm. Motivated by massive internet of things (IoT) networks and edge computing, we…
Belief Propagation (BP) is an efficient message-passing algorithm widely used for inference in graphical models and for solving various problems in statistical physics. However, BP often yields inaccurate estimates of order parameters and…
A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean squared displacement, yet with a non-Gaussian distribution of increments. Based on the…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
In this paper, a network-based stochastic information propagation model is developed. The information flow is modeled by a probabilistic differential equation system. The numerical solution of these equations leads to the expected number of…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…