Related papers: Loop Series Expansions for Tensor Networks
Belief propagation (BP) is a powerful tool to solve distributed inference problems, though it is limited by short cycles in the corresponding factor graph. Such cycles may lead to incorrect solutions or oscillatory behavior. Only for…
The Bethe approximation, or loopy belief propagation algorithm is a successful method for approximating partition functions of probabilistic models associated with a graph. Chertkov and Chernyak derived an interesting formula called Loop…
In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a…
This paper presents a new deterministic approximation technique in Bayesian networks. This method, "Expectation Propagation", unifies two previous techniques: assumed-density filtering, an extension of the Kalman filter, and loopy belief…
Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate…
Belief propagation (BP) is a message-passing heuristic for statistical inference in graphical models such as Bayesian networks and Markov random fields. BP is used to compute marginal distributions or maximum likelihood assignments and has…
The belief propagation (BP) algorithm is an efficient way to solve "inference" problems in graphical models, such as Bayesian networks and Markov random fields. The system-state probability distribution of CSMA wireless networks is a Markov…
We use series expansions to study dynamics of equilibrium and non-equilibrium systems on networks. This analytical method enables us to include detailed non-universal effects of the network structure. We show that even low order…
Belief propagation -- a powerful heuristic method to solve inference problems involving a large number of random variables -- was recently generalized to quantum theory. Like its classical counterpart, this algorithm is exact on trees when…
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.…
The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing…
Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…
Describing nonequilibrium quantum dynamics remains a significant computational challenge due to the growth of spatial entanglement. The tensor network influence functional (TN-IF) approach mitigates this problem for computing the time…
We derive a Belief-Propagation algorithm for counting large loops in a directed network. We evaluate the distribution of the number of small loops in a directed random network with given degree sequence. We apply the algorithm to a few…
Traditional learning methods for training Markov random fields require doing inference over all variables to compute the likelihood gradient. The iteration complexity for those methods therefore scales with the size of the graphical models.…
We address the question of convergence in the loopy belief propagation (LBP) algorithm. Specifically, we relate convergence of LBP to the existence of a weak limit for a sequence of Gibbs measures defined on the LBP s associated computation…
We introduce a new cluster-cumulant expansion (CCE) based on the fixed points of iterative belief propagation (IBP). This expansion is similar in spirit to the loop-series (LS) recently introduced in [1]. However, in contrast to the latter,…
We present a new decoder for the surface code, which combines the accuracy of the tensor-network decoders with the efficiency and parallelism of the belief-propagation algorithm. Our main idea is to replace the expensive tensor-network…
Recent works have shown that interval bound propagation (IBP) can be used to train verifiably robust neural networks. Reseachers observe an intriguing phenomenon on these IBP trained networks: CROWN, a bounding method based on tight linear…
Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of…