Behavior Detection Using Confidence Intervals of Hidden Markov Models

Abstract

Markov models are commonly used to analyze real-world problems. Their combination of discrete states and stochastic transitions is suited to applications with deterministic and stochastic components. Hidden Markov models (HMMs) are a class of Markov models commonly used in pattern recognition. Currently, HMMs recognize patterns using a maximum-likelihood approach. One major drawback with this approach is that data observations are mapped to HMMs without considering the number of data samples available. Another problem is that this approach is only useful for choosing between HMMs. It does not provide a criterion for determining whether or not a given HMM adequately matches the data stream. In this paper, we recognize complex behaviors using HMMs and confidence intervals. The certainty of a data match increases with the number of data samples considered. Receiver operating characteristic curves are used to find the optimal threshold for either accepting or rejecting an HMM description. We present one example using a family of HMMs to show the utility of the proposed approach. A second example using models extracted from a database of consumer purchases provides additional evidence that this approach can perform better than existing techniques.