Bayesian Tensor Network with Polynomial Complexity for Probabilistic Machine Learning
This work addresses the computational bottleneck in probabilistic machine learning for applications like image recognition, though it appears incremental as it builds on existing tensor network concepts.
The authors tackled the exponential cost of modeling conditional probabilities for multiple events by proposing a Bayesian tensor network (BTN) with polynomial complexity, achieving competitive performance in image recognition tasks using simple tree structures.
It is known that describing or calculating the conditional probabilities of multiple events is exponentially expensive. In this work, Bayesian tensor network (BTN) is proposed to efficiently capture the conditional probabilities of multiple sets of events with polynomial complexity. BTN is a directed acyclic graphical model that forms a subset of TN. To testify its validity for exponentially many events, BTN is implemented to the image recognition, where the classification is mapped to capturing the conditional probabilities in an exponentially large sample space. Competitive performance is achieved by the BTN with simple tree network structures. Analogous to the tensor network simulations of quantum systems, the validity of the simple-tree BTN implies an ``area law'' of fluctuations in image recognition problems.