Deep Neural Networks for the Sequential Probability Ratio Test on Non-i.i.d. Data Series

Classifying sequential data as early as and as accurately as possible is a challenging yet critical problem, especially when a sampling cost is high. One algorithm that achieves this goal is the sequential probability ratio test (SPRT), which is known as Bayes-optimal: it can keep the expected number of data samples as small as possible, given the desired error upper-bound. The SPRT has recently been found to be the best model that explains the activities of the neurons in the primate parietal cortex that are thought to mediate our complex decision-making processes. However, the original SPRT makes two critical assumptions that limit its application in real-world scenarios: (i) samples are independently and identically distributed, and (ii) the likelihood of the data being derived from each class can be calculated precisely. Here, we propose the SPRT-TANDEM, a deep neural network-based SPRT algorithm that overcomes the above two obstacles. The SPRT-TANDEM estimates the log-likelihood ratio of two alternative hypotheses by leveraging a novel Loss function for Log-Likelihood Ratio estimation (LLLR), while allowing for correlations up to $N (\in \mathbb{N})$ preceding samples. In tests on one original and two public video databases, Nosaic MNIST, UCF101, and SiW, the SPRT-TANDEM achieves statistically significantly better classification accuracy than other baseline classifiers, with a smaller number of data samples. The code and Nosaic MNIST are publicly available at https://github.com/TaikiMiyagawa/SPRT-TANDEM.