Learning the Optimal Stopping for Early Classification within Finite Horizons via Sequential Probability Ratio Test

• URL: http://arxiv.org/abs/2501.18059v1
• Date: Wed, 29 Jan 2025 23:54:46 GMT
• Title: Learning the Optimal Stopping for Early Classification within Finite Horizons via Sequential Probability Ratio Test
• Authors: Akinori F. Ebihara, Taiki Miyagawa, Kazuyuki Sakurai, Hitoshi Imaoka,
• Abstract summary: Time-sensitive machine learning benefits from Sequential Probability Ratio Test (SPRT), which provides an optimal stopping time for early classification of time series. In finite horizon scenarios, where input lengths are finite, determining the optimal stopping rule becomes computationally intensive due to the need for backward induction. We introduce FIRMBOUND, an SPRT-based framework that efficiently estimates the solution to backward induction from training data.
• Score: 11.199585259018459
• License:
• Abstract: 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 publicly available at https://github.com/Akinori-F-Ebihara/FIRMBOUND

Related papers

• Tube Loss: A Novel Approach for Prediction Interval Estimation and probabilistic forecasting [17.472882720712118]
  This paper proposes a novel loss function, called 'Tube Loss', for simultaneous estimation of bounds of a Prediction Interval (PI) in the regression setup. Pis obtained by minimizing the empirical risk based on the Tube Loss are shown to be of better quality than the PIs obtained by the existing methods.
  arXiv  Detail & Related papers  (2024-12-08T15:17:53Z)
• Statistical Inference for Temporal Difference Learning with Linear Function Approximation [62.69448336714418]
  We study the consistency properties of TD learning with Polyak-Ruppert averaging and linear function approximation. First, we derive a novel high-dimensional probability convergence guarantee that depends explicitly on the variance and holds under weak conditions. We further establish refined high-dimensional Berry-Esseen bounds over the class of convex sets that guarantee faster rates than those in the literature.
  arXiv  Detail & Related papers  (2024-10-21T15:34:44Z)
• Conformal Thresholded Intervals for Efficient Regression [9.559062601251464]
  Conformal Thresholded Intervals (CTI) is a novel conformal regression method that aims to produce the smallest possible prediction set with guaranteed coverage. CTI constructs prediction sets by thresholding the estimated conditional interquantile intervals based on their length. CTI achieves superior performance compared to state-of-the-art conformal regression methods across various datasets.
  arXiv  Detail & Related papers  (2024-07-19T17:47:08Z)
• Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise [51.87307904567702]
  Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the distribution of outputs. We propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint. We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities.
  arXiv  Detail & Related papers  (2024-06-05T13:36:38Z)
• High Confidence Level Inference is Almost Free using Parallel Stochastic Optimization [16.38026811561888]
  This paper introduces a novel inference method focused on constructing confidence intervals with efficient computation and fast convergence to the nominal level. Our method requires minimal additional computation and memory beyond the standard updating of estimates, making the inference process almost cost-free.
  arXiv  Detail & Related papers  (2024-01-17T17:11:45Z)
• A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport [92.96250725599958]
  Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. We show that our SSN method achieves a global convergence rate of $O (1/sqrtk)$, and a local quadratic convergence rate under standard regularity conditions.
  arXiv  Detail & Related papers  (2023-10-21T18:48:45Z)
• Calibrating Neural Simulation-Based Inference with Differentiable Coverage Probability [50.44439018155837]
  We propose to include a calibration term directly into the training objective of the neural model. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference.
  arXiv  Detail & Related papers  (2023-10-20T10:20:45Z)
• Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels [57.46832672991433]
  We propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS) We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We develop an expectation-propagation expectation-maximization algorithm for efficient posterior inference and function estimation.
  arXiv  Detail & Related papers  (2023-10-09T03:55:09Z)
• Improved uncertainty quantification for neural networks with Bayesian last layer [0.0]
  Uncertainty quantification is an important task in machine learning. We present a reformulation of the log-marginal likelihood of a NN with BLL which allows for efficient training using backpropagation.
  arXiv  Detail & Related papers  (2023-02-21T20:23:56Z)
• Gaining Outlier Resistance with Progressive Quantiles: Fast Algorithms and Theoretical Studies [1.6457778420360534]
  A framework of outlier-resistant estimation is introduced to robustify arbitrarily loss function. A new technique is proposed to alleviate the requirement on starting point such that on regular datasets the number of data reestimations can be substantially reduced. The obtained estimators, though not necessarily globally or even globally, enjoymax optimality in both low dimensions.
  arXiv  Detail & Related papers  (2021-12-15T20:35:21Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.