Sequential probability ratio test

About: Sequential probability ratio test is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22355 citations.

Minimum-sample SPRT for sensor or operating point selection in a single- or multisensor environment

Abstract: This paper describes a technique for employing the sequential probability ratio test (SPRT) in a single or multisensor environment. The technique minimizes the number of sensor decisions required to declare the null or alternative hypothesis when there is a choice of different sensors or sensor operating points. Thus the technique will be dubbed the Minimum-Sample SPRT (MS-SPRT). The first step of the MS-SPRT requires an off-line optimization of the choice of sensors across all possible values of the alternative hypothesis probability. The second step of the technique involves the application of two Kalman filters to estimate the probability of the alternative hypothesis and to optimize a set of sensor probabilities. The sensor probabilities determine the optimal sensor choice that minimizes the expected number of samples before a decision is made. Three examples are given using simulated data. In the first example, it is shown that the MS-SPRT is not necessary. The second example shows the usefulness of the MS-SPRT when there is a step discontinuity in the null/alternative hypothesis probabilities. In the third example, the MS-SPRT facilitates the use of the proper sensor for a probabilistic variation in the hypothesis probabilities.

Sequential cooperative spectrum sensing in cognitive radio networks: Optimal selection of secondary users and their spectral measurements

Abstract: In this paper we consider the problem of spectrum sensing in cognitive radio networks which involves detection of primary (licensed) users (PUs) by secondary (unlicensed) users (SUs), who are interested in transmitting their data opportunistically. To facilitate accurate detection of PUs by the fusion center (FC) based on the energy measurements received from the chosen set of SUs, we formulate an optimization problem for selection of SUs and the number of samples they need to collect of the underlying spectrum. By assuming that the FC uses a sequential probability ratio test (SPRT) for performing spectrum sensing we formulate the problem of joint optimization over subset of SUs and the number of samples each of the SU in the chosen subset needs to collect, so that a composite cost function is maximized. For the computation of the optimal subset of SUs and the number of samples each SU has to collect we propose an algorithm based on DSO, in which optimization over the subset of SUs and the number of samples is done successively till convergence to the optimal set of values is achieved. Our simulation results demonstrate the efficacy of the proposed optimization approach based on SPRT as against that of a fixed sample size test at the FC. Specifically, the average number of samples required for an SPRT is much lower than that of a fixed sample size test for given values of probability of detection and probability of false alarm. The simulation results also confirm tracking ability of the proposed DSO based algorithms, in response to variations in the corresponding channel gains between the SUs and the FC.

The Power of Log-Sum-Exp: Sequential Density Ratio Matrix Estimation for Speed-Accuracy Optimization

Abstract: We propose a model for multiclass classification of time series to make a prediction as early and as accurate as possible. The matrix sequential probability ratio test (MSPRT) is known to be asymptotically optimal for this setting, but contains a critical assumption that hinders broad real-world applications; the MSPRT requires the underlying probability density. To address this problem, we propose to solve density ratio matrix estimation (DRME), a novel type of density ratio estimation that consists of estimating matrices of multiple density ratios with constraints and thus is more challenging than the conventional density ratio estimation. We propose a log-sum-exp-type loss function (LSEL) for solving DRME and prove the following: (i) the LSEL provides the true density ratio matrix as the sample size of the training set increases (consistency); (ii) it assigns larger gradients to harder classes (hard class weighting effect); and (iii) it provides discriminative scores even on class-imbalanced datasets (guess-aversion). Our overall architecture for early classification, MSPRT-TANDEM, statistically significantly outperforms baseline models on four datasets including action recognition, especially in the early stage of sequential observations. Our code and datasets are publicly available at: this https URL.