Toward Asymptotic Optimality: Sequential Unsupervised Regression of Density Ratio for Early Classification
This work improves early classification for time series applications, but it is incremental as it builds on existing SPRT-based methods to fix a specific bottleneck.
The paper tackles the problem of early classification of time series by addressing the overnormalization issue in sequential density ratio estimation, which prevents asymptotic optimality. The proposed B2Bsqrt-TANDEM and TANDEMformer algorithms significantly reduce density ratio estimation and classification errors on artificial and real datasets.
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.