Toward Asymptotic Optimality: Sequential Unsupervised Regression of Density Ratio for Early Classification

Theoretically-inspired sequential density ratio estimation (SDRE) algorithms are proposed for the early classification of time series. Conventional SDRE algorithms can fail to estimate DRs precisely due to the internal overnormalization problem, which prevents the DR-based sequential algorithm, Sequential Probability Ratio Test (SPRT), from reaching its asymptotic Bayes optimality. Two novel SPRT-based algorithms, B2Bsqrt-TANDEM and TANDEMformer, are designed to avoid the overnormalization problem for precise unsupervised regression of SDRs. The two algorithms statistically significantly reduce DR estimation errors and classification errors on an artificial sequential Gaussian dataset and real datasets (SiW, UCF101, and HMDB51), respectively. The code is available at: https://github.com/Akinori-F-Ebihara/LLR_saturation_problem.

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.

Specular- and Diffuse-reflection-based Face Liveness Detection for Mobile Devices

In light of the rising demand for biometric-authentication systems, preventing face spoofing attacks is a critical issue for the safe deployment of face recognition systems. Here, we propose an efficient liveness detection algorithm that requires minimal hardware and only a small database, making it suitable for resource-constrained devices such as mobile phones. Utilizing one monocular visible light camera, the proposed algorithm takes two facial photos, one taken with a flash, the other without a flash. The proposed $SpecDiff$ descriptor is constructed by leveraging two types of reflection: (i) specular reflections from the iris region that have a specific intensity distribution depending on liveness, and (ii) diffuse reflections from the entire face region that represents the 3D structure of a subject's face. Classifiers trained with $SpecDiff$ descriptor outperforms other flash-based liveness detection algorithms on both an in-house database and on publicly available NUAA and Replay-Attack databases. Moreover, the proposed algorithm achieves comparable accuracy to that of an end-to-end, deep neural network classifier, while being approximately ten-times faster execution speed.