Factorsnetworks

Factorsnetworks are probabilistic graphical models that express the joint distribution of a set of variables by decomposing it into a network of local factors. The framework generalizes traditional factor graphs by making factor connections reflect modular interactions among variables. In a factorsnetwork, variable nodes represent random variables, while factor nodes encode compatibility constraints or likelihoods over small subsets of variables. The network structure specifies which variables participate in each factor, enabling flexible modeling of dependencies across domains.

Factors can take parametric, piecewise, or learned forms. The same factor may be shared across configurations, supporting modularity and transfer learning. Factors can be static or dynamic, allowing the network to adapt as data arrives or as the system changes.

Inference combines standard graphical-model techniques with network-aware approximations. Exact inference is often intractable in richly connected graphs, so practitioners use message passing, variational methods, or Monte Carlo sampling. Sparsity and locality of factors are important for tractable computation.

Applications include social network analysis, sensor networks, biology, finance, and recommender systems, where localized interactions govern outcomes. The framework supports probabilistic reasoning and constraint-based modeling, enabling predictive analytics and generative processes. Factorsnetworks are related to factor graphs, Bayesian networks, and Markov random fields, differing mainly in emphasis on a modular networked factor structure.