Incremental Dynamic Construction of Layered Polytree Networks

TL;DR

This paper presents a deterministic algorithm for incrementally extending layered polytree belief networks while preserving their structure, enabling efficient dynamic updates and probabilistic inference in various AI applications.

Contribution

It introduces a novel incremental extension algorithm for singly connected polytree networks that maintains structure and efficiency during dynamic modifications.

Findings

Algorithm guarantees single node addition complexity proportional to network size.

Maintains polytree structure after incremental modifications.

Supports probabilistic inference similarly to existing exact algorithms.

Abstract

Certain classes of problems, including perceptual data understanding, robotics, discovery, and learning, can be represented as incremental, dynamically constructed belief networks. These automatically constructed networks can be dynamically extended and modified as evidence of new individuals becomes available. The main result of this paper is the incremental extension of the singly connected polytree network in such a way that the network retains its singly connected polytree structure after the changes. The algorithm is deterministic and is guaranteed to have a complexity of single node addition that is at most of order proportional to the number of nodes (or size) of the network. Additional speed-up can be achieved by maintaining the path information. Despite its incremental and dynamic nature, the algorithm can also be used for probabilistic inference in belief networks in a fashion similar to other exact inference algorithms.