Time-sensitive machine learning benefits from Sequential Probability Ratio Test (SPRT), which provides an optimal stopping time for early classification of time series. However, in *finite horizon* scenarios, where input lengths are finite, determining the optimal stopping rule becomes computationally intensive due to the need for *backward induction*, limiting practical applicability. We thus introduce FIRMBOUND, an SPRT-based framework that efficiently estimates the solution to backward induction from training data, bridging the gap between optimal stopping theory and real-world deployment. It employs *density ratio estimation* and *convex function learning* to provide statistically consistent estimators for sufficient statistic and conditional expectation, both essential for solving backward induction; consequently, FIRMBOUND minimizes Bayes risk to reach optimality. Additionally, we present a faster alternative using Gaussian process regression, which significantly reduces training time while retaining low deployment overhead, albeit with potential compromise in statistical consistency. Experiments across independent and identically distributed (i.i.d.), non-i.i.d., binary, multiclass, synthetic, and real-world datasets show that FIRMBOUND achieves optimalities in the sense of Bayes risk and speed-accuracy tradeoff. Furthermore, it advances the tradeoff boundary toward optimality when possible and reduces decision-time variance, ensuring reliable decision-making. Code is included in the supplementary materials.

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.

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 face presentation attack detection (PAD) 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 PAD algorithms on both an in-house database and on publicly available NUAA, Replay-Attack, and SiW databases. Moreover, the proposed algorithm achieves statistically significantly better accuracy to that of an end-to-end, deep neural network classifier, while being approximately six-times faster execution speed. The code is publicly available at https://github.com/Akinori-F-Ebihara/SpecDiff-spoofing-detector.

Many of the existing tracking methods do not estimate the object scale (width, height), only the location (x, y). In this paper we present a method which can accurately estimate the object scale given the location. The proposed approach works by cascading two methods together; such that each method refines the estimate by removing the false scale samples. Our method does not depend on the tracking technique and can be applied with any tracking system. We apply our approach to an existing tracker and compare the performance on benchmark sequences. The proposed method outperforms the existing tracker, while hardly affecting the speed.

A method for feature point tracking with partial occlusion handling is proposed. Occlusion causes distortion of entire face shape and not just the occluded part. To address this multiple models are learnt using regression, each aligning some part of the complete feature point set. A ranking SVM is then used to select the best feature points from among the aligned parts. The proposed method gives improved results compared to state of the art methods.