Active Inference for Binary Symmetric Hidden Markov Models
This work addresses a specific inference problem in machine learning, focusing on binary symmetric HMMs, and is incremental as it builds on existing active inference methods with a specialized analytical solution.
The paper tackles the active maximum a posteriori inference problem for binary symmetric Hidden Markov Models by developing an analytical approach to select states for labeling to improve estimation accuracy, resulting in a closed-form solution that relates error reduction to model parameters and identifies optimal schemes.
We consider active maximum a posteriori (MAP) inference problem for Hidden Markov Models (HMM), where, given an initial MAP estimate of the hidden sequence, we select to label certain states in the sequence to improve the estimation accuracy of the remaining states. We develop an analytical approach to this problem for the case of binary symmetric HMMs, and obtain a closed form solution that relates the expected error reduction to model parameters under the specified active inference scheme. We then use this solution to determine most optimal active inference scheme in terms of error reduction, and examine the relation of those schemes to heuristic principles of uncertainty reduction and solution unicity.