Binary Hypothesis Testing Research Articles

Distributed Hypothesis Testing Based on Unequal-Error Protection Codes

Coding and testing schemes for binary hypothesis testing over noisy networks are proposed and their corresponding type-II error exponents are derived. When communication is over a discrete memoryless channel (DMC), our scheme combines Shimokawa-Han-Amari's hypothesis testing scheme with Borade-Nakiboglu-Zheng's unequal error protection (UEP) for channel coding where source and channel codewords are simultaneously decoded. The resulting exponent is optimal for the newly introduced class of generalized testing against conditional independence. When communication is over a multi-access channel (MAC), our scheme combines hybrid coding with UEP. The resulting error exponent over the MAC is optimal in the case of generalized testing against conditional independence with independent observations at the two sensors when the MAC decomposes into two individual DMCs. In this case, separate source-channel coding is sufficient and no UEP is required. This same conclusion holds also under arbitrarily correlated sensor observations when testing is against independence.

Privacy-Aware Distributed Hypothesis Testing.

A distributed binary hypothesis testing (HT) problem involving two parties, a remote observer and a detector, is studied. The remote observer has access to a discrete memoryless source, and communicates its observations to the detector via a rate-limited noiseless channel. The detector observes another discrete memoryless source, and performs a binary hypothesis test on the joint distribution of its own observations with those of the observer. While the goal of the observer is to maximize the type II error exponent of the test for a given type I error probability constraint, it also wants to keep a private part of its observations as oblivious to the detector as possible. Considering both equivocation and average distortion under a causal disclosure assumption as possible measures of privacy, the trade-off between the communication rate from the observer to the detector, the type II error exponent, and privacy is studied. For the general HT problem, we establish single-letter inner bounds on both the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs. Subsequently, single-letter characterizations for both trade-offs are obtained (i) for testing against conditional independence of the observer’s observations from those of the detector, given some additional side information at the detector; and (ii) when the communication rate constraint over the channel is zero. Finally, we show by providing a counter-example where the strong converse which holds for distributed HT without a privacy constraint does not hold when a privacy constraint is imposed. This implies that in general, the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs are not independent of the type I error probability constraint.

Optimal Stopping and Worker Selection in Crowdsourcing: an Adaptive Sequential Probability Ratio Test Framework

In this study, we solve a class of multiple testing problems under a Bayesian sequential decision framework. Our work is motivated by binary labeling tasks in crowdsourcing, where a requestor needs to simultaneously choose a worker to provide a label and decide when to stop collecting labels, under a certain budget constraint. We begin by using a binary hypothesis testing problem to determine the true label of a single object, and provide an optimal solution by casting it under an adaptive sequential probability ratio test framework. Then, we characterize the structure of the optimal solution, that is, the optimal adaptive sequential design, which minimizes the Bayes risk using a log-likelihood ratio statistic. We also develop a dynamic programming algorithm to efficiently compute the optimal solution. For the multiple testing problem, we propose an empirical Bayes approach for estimating the class priors, and show that the average loss of our method converges to the minimal Bayes risk under the true model. Experiments on both simulated and real data show the robustness of our method, as well as its superiority over existing methods in terms of its labeling accuracy.

Optimal Linear Cooperation for Signal Classification in Cognitive Communication Networks

Signal classification plays an important role in cognitive communication networks to identify and avoid interference. Contrary to traditional cooperative spectrum sensing based on binary hypothesis testing, we study a network of cognitive radios that jointly perform linear cooperation based signal classification via M-ary hypothesis testing. To maximize the probability of successful classification subject to constraints on individual probabilities of misclassification, we divide the problem into M independent binary hypothesis testing subproblems in parallel before selecting the hypothesis that is most likely true. Furthermore, we consider a problem that maximizes the probability of successful classification subject to a constraint on the total probability of misclassification. We reformulate such an optimization problem into two different subproblems, where the optimal solution is obtained by alternating the two optimization sub-problems iteratively. Numerical simulations demonstrate the near-optimality of the proposed methods with low computational complexity for the cooperative signal classification problems.

A Gradient-Based Method for Robust SensorSelection in Hypothesis Testing.

This paper considers the binary Gaussian distribution robust hypothesis testing under a Bayesian optimal criterion in the wireless sensor network (WSN). The distribution covariance matrix under each hypothesis is known, while the distribution mean vector under each hypothesis drifts in an ellipsoidal uncertainty set. Because of the limited bandwidth and energy, we aim at seeking a subset of p out of m sensors such that the best detection performance is achieved. In this setup, the minimax robust sensor selection problem is proposed to deal with the uncertainties of distribution means. Following a popular method, minimizing the maximum overall error probability with respect to the selection matrix can be approximated by maximizing the minimum Chernoff distance between the distributions of the selected measurements under null hypothesis and alternative hypothesis to be detected. Then, we utilize Danskin’s theorem to compute the gradient of the objective function of the converted maximization problem, and apply the orthogonal constraint-preserving gradient algorithm (OCPGA) to solve the relaxed maximization problem without 0/1 constraints. It is shown that the OCPGA can obtain a stationary point of the relaxed problem. Meanwhile, we provide the computational complexity of the OCPGA, which is much lower than that of the existing greedy algorithm. Finally, numerical simulations illustrate that, after the same projection and refinement phases, the OCPGA-based method can obtain better solutions than the greedy algorithm-based method but with up to shorter runtimes. Particularly, for small-scale problems, the OCPGA -based method is able to attain the globally optimal solution.

ADHD classification by dual subspace learning using resting-state functional connectivity.

As one of the most common neurobehavioral diseases in school-age children, Attention Deficit Hyperactivity Disorder (ADHD) has been increasingly studied in recent years. But it is still a challenge problem to accurately identify ADHD patients from healthy persons. To address this issue, we propose a dual subspace classification algorithm by using individual resting-state Functional Connectivity (FC). In detail, two subspaces respectively containing ADHD and healthy control features, called as dual subspaces, are learned with several subspace measures, wherein a modified graph embedding measure is employed to enhance the intra-class relationship of these features. Therefore, given a subject (used as test data) with its FCs, the basic classification principle is to compare its projected component energy of FCs on each subspace and then predict the ADHD or control label according to the subspace with larger energy. However, this principle in practice works with low efficiency, since the dual subspaces are unstably obtained from ADHD databases of small size. Thereby, we present an ADHD classification framework by a binary hypothesis testing of test data. Here, the FCs of test data with its ADHD or control label hypothesis are employed in the discriminative FC selection of training data to promote the stability of dual subspaces. For each hypothesis, the dual subspaces are learned from the selected FCs of training data. The total projected energy of these FCs is also calculated on the subspaces. Sequentially, the energy comparison is carried out under the binary hypotheses. The ADHD or control label is finally predicted for test data with the hypothesis of larger total energy. In the experiments on ADHD-200 dataset, our method achieves a significant classification performance compared with several state-of-the-art machine learning and deep learning methods, where our accuracy is about 90 % for most of ADHD databases in the leave-one-out cross-validation test.

An automatic detection method for 40-Hz auditory steady state response and its application in prognosis of comatose patients

ObjectiveWe proposed a 40-Hz auditory steady-state response (ASSR) automatic detection method, and studied the prognosis of comatose patients by combining the 40-Hz ASSR detection results of multiple paradigms of auditory stimulation. MethodsThe 40-Hz ASSR elicitation experiments were carried out on 32 comatose patients, with the detection results used as prognosis predictors. To achieve automatic detection, the detection was modeled as a binary hypothesis test for a sinusoidal waveform with unknown amplitude and phase, based on the generalized likelihood ratio test (GLRT). The patients were followed up for 6 months, and each patient’s outcome was classified as either favorable outcome (severe disability, moderate disability or good recovery) or unfavorable outcome (vegetative state/unresponsive wakefulness syndrome or death) according to the Glasgow outcome scale (GOS). The performance of the prognosis predictors was assessed using the area under the receiver operating characteristic curve (AUC-ROC). ResultsThe largest AUC in univariate analysis involving a single stimulation paradigm was 0.849, while the AUC obtained by combining multiple predictors was increased to 0.966. ConclusionsFor comatose patients, the absence of 40-Hz ASSR in multiple stimulation paradigms may indicate an unfavorable prognosis. Furthermore, the combination of multiple auditory stimulation paradigms may increase the outcome prediction accuracy. SignificanceThe combination of multi-paradigm 40-Hz ASSR automatic detection results may provide a feasible automatic outcome prediction method for comatose patients.

Netted Radar Tracking with Multiple Simultaneous Transmissions against Combined PDS Interception

One of the advantages of a netted airborne radar system (NARS) is escaping interception of the passive detection system (PDS) while tracking a target. A significant tactic to realize tracking without PDS interception is to study the low probability of interception (LPI) time of NARS. Firstly, this paper analyses the power, frequency, and platform interception probabilities of a combined PDS consisting of a radar-warning receiver (RWR) and an electronic support measurement (ESM). Secondly, this paper takes interactive multiple models (IMM) to describe the target tracking process and introduces a binary hypothesis test for chi square as well as noncentralized chi square distributions as a detection criterion of NARS during target tracking after the design of adaptive dwell time and the maximum illumination interval algorithm. Finally, based on experiential moving platform interception probabilities of a RWR and an ESM, a simplified math model is presented to estimate LPI time of NARS when the parameters are partially known. Simulations illustrate that the simultaneous management of radiation power and time is crucial for NARS against combined PDS interception.

High-Accuracy Classification of Attention Deficit Hyperactivity Disorder With l 2,1-Norm Linear Discriminant Analysis and Binary Hypothesis Testing

Attention Deficit Hyperactivity Disorder (ADHD) is a high incidence of neurobehavioral disease in school-age children. Its neurobiological diagnosis (or classification) is meaningful for clinicians to give proper treatment for ADHD patients. The existing ADHD classification methods suffer from two problems, i.e., insufficient data and noise disturbance. In this paper, a high-accuracy classification method is proposed by using brain Functional Connectivity (FC) as ADHD features, where an ${l_{2,1}}$ -norm Linear Discriminant Analysis (LDA) model and a binary hypothesis testing framework are effectively employed. In detail, we introduce a binary hypothesis testing framework to cope with insufficient data of ADHD database. The FCs of test data (without seeing its label) are used for training and thus affect the subspace learning of training data under binary hypotheses. On other hand, the ${l_{2,1}}$ -norm LDA model generates a subspace to represent ADHD features, aiming to overcome noise disturbance. By robustly learning ADHD features, the subspace energy difference between binary hypotheses becomes more discriminative. Thereby, the true hypothesis can be rightly estimated with its larger subspace energy, which provides reliable evidence to predict the label of test data. By the test on ADHD-200 database, it shows that our method outperforms other state-of-the-art methods with the significant average accuracy of 97.6%. Moreover, the corresponding result analysis with ADHD symptom score and the explanation of discriminative FCs between ADHD and healthy control groups are given, which further verifies the validity of our classification method.

On Safeguarding Visible Light Communication Systems Against Attacks by Active Adversaries

We consider an indoor visible light communication (VLC) system comprising of a transmitter (Alice) and a receiver (Bob). The communication from Alice to Bob is prone to active attacks by a malicious node (Eve) installed nearby. Specifically, when the VLC channel contains idle slots, Eve launches impersonation attack—thus, the VLC channel becomes orthogonal multiple access (OMA). On the other hand, when the VLC channel remains fully occupied by Alice, Eve is left with no choice other than to transmit simultaneously and this constitutes a jamming attack—thus, the VLC channel becomes non-orthogonal multiple access (NOMA). To thwart the impersonation attack, Bob authenticates the received packets via binary hypothesis testing (BHT) by utilizing the channel gain as the transmit device fingerprint. As for the jamming attack, Bob treats Eve’s interference as Gaussian noise to recover the data sent by Alice. We further study two different physical scenarios: a room and a corridor, respectively. In the former, Bob remains static, while in the latter, Bob is mobile. Thus, for the corridor scenario, Bob tracks Alice’s channel via a linear Kalman filter whose prediction is then fed to the BHT as the ground truth. Simulation results show that: i) for OMA VLC, authentication becomes more effective as Eve’s distance to Bob becomes more dissimilar to Alice’s distance to Bob; ii) for NOMA VLC, the average decoding error probability increases approximately logarithmically with the increase in the interference power of Eve.

Target Detection With Imperfect Waveform Separation in Distributed MIMO Radar

This paper considers target detection in distributed multiple-input multiple-output (MIMO) radar with imperfect waveform separation at local receivers. The problem is formulated as a binary composite hypothesis testing problem, where target residuals due to imperfect waveform separation are explicitly modeled as a subspace component in the alternative hypothesis, while disturbances including the clutter and thermal noise are present under both hypotheses. Under assumptions of fluctuating and non-fluctuating target amplitude over a scan, e.g., Swerling models, we particularly consider a distributed hybrid-order Gaussian (DHOG) signal model and develop the generalized likelihood ratio test (GLRT) which relies on the maximum likelihood (ML) estimation of the target amplitude and the residual covariance matrix under the alternative hypothesis. The Cramer-Rao bounds (CRBs) on estimating the target amplitude and residual subspace covariance matrix are derived. Simulation results in both local and distributed scenarios confirm the effectiveness of the proposed GLRT and show improved performance in terms of receiver operating characteristic (ROC) by exploiting the existence of target residual component.

Sensor Selection and Design for Binary Hypothesis Testing in the Presence of a Cost Constraint

We consider a sensor selection problem for binary hypothesis testing with cost-constrained measurements. Random outputs related to a parameter vector of interest are assumed to be generated by a linear system corrupted with Gaussian noise. The aim is to decide on the state of the parameter vector based on a set of measurements collected by a limited number of sensors. The cost of each sensor measurement is determined by the number of amplitude levels that can reliably be distinguished. By imposing constraints on the total cost, and the maximum number of sensors that can be employed, a sensor selection problem is formulated in order to maximize the detection performance for binary hypothesis testing. By characterizing the form of the solution corresponding to a relaxed version of the optimization problem, a computationally efficient algorithm with near optimal performance is proposed. In addition to the case of fixed sensor measurement costs, we also consider the case where they are subject to design. In particular, the problem of allocating the total cost budget to a limited number of sensors is addressed by designing the measurement accuracy (i.e., the noise variance) of each sensor to be employed in the detection procedure. The optimal solution is obtained in closed form. Numerical examples are presented to corroborate the proposed methods.

Prospect Theoretic Utility Based Human Decision Making in Multi-Agent Systems

This paper studies human decision making via a utility based approach in a binary hypothesis testing framework that includes the consideration of individual behavioral disparity. Unlike rational decision makers who make decisions so as to maximize their expected utility, humans tend to maximize their subjective utilities, which are usually distorted due to cognitive biases. We use the value function and the probability weighting function from prospect theory to model human cognitive biases and obtain their subjective utility function in decision making. First, we show that the decision rule which maximizes the subjective utility function reduces to a likelihood ratio test (LRT). Second, to capture the unreliable nature of human decision making behavior, we model the decision threshold of a human as a Gaussian random variable, whose mean is determined by his/her cognitive bias, and the variance represents the uncertainty of the agent while making a decision. This human decision making framework under behavioral biases incorporates both cognitive biases and uncertainties. We consider several decision fusion scenarios that include humans. Extensive numerical results are provided throughout the paper to illustrate the impact of human behavioral biases on the performance of the decision making systems.

Single-Pulse Simultaneous Target Detection and Angle Estimation in a Multichannel Phased Array Radar

This paper is focused on simultaneous target detection and angle estimation with a multichannel phased array radar. Resorting to a linearized expression for the array steering vector around the beam pointing direction, the problem is formulated as a composite binary hypothesis test where the unknowns, under the alternative hypothesis, include the target directional cosines displacements with respect to the array nominal coarse pointing direction. The problem is handled via the Generalized Likelihood Ratio (GLR) criterion (both one-step and two-step) where decision statistics leveraging the Maximum Likelihood Estimates (MLEs) of the parameters are compared with a detection threshold. If crossed, target presence is declared and the MLEs of the aforementioned displacements directly provide target angular position with respect to the pointing direction. From the analytic point of view, ML estimation involves a constrained fractional quadratic optimization problem whose optimal solution can be found via the Dinkelbach's algorithm or approximated through a fast-converging procedure based on a Coordinate Descent (CD) optimization. The performance analysis of the proposed architectures as well as the corresponding discussion is developed in terms of computational complexity, Constant False Alarm Rate (CFAR) behavior, detection performance, and angular estimation accuracy, also in comparison with some counterparts available in the open literature and theoretical benchmark limits.

Optimal Decision Rules for Simple Hypothesis Testing Under General Criterion Involving Error Probabilities

The problem of simple $M-$ ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule can be characterized as a randomization among at most two deterministic decision rules, each of the form reminiscent to Bayes rule, if the boundary points corresponding to each rule have zero probability under each hypothesis. Otherwise, a randomization among at most $M(M-1)+1$ deterministic decision rules is sufficient. The form of the deterministic decision rules are explicitly specified. Likelihood ratios are shown to be sufficient statistics. Classical performance measures including Bayesian, minimax, Neyman-Pearson, generalized Neyman-Pearson, restricted Bayesian, and prospect theory based approaches are all covered under the proposed formulation. A numerical example is presented for prospect theory based binary hypothesis testing.

Virtual Dimensionality of Hyperspectral Data: Use of Multiple Hypothesis Testing for Controlling Type-I Error

Estimating the number of materials present in a scene is the fundamental step in many hyperspectral remote sensing applications. The virtual dimensionality (VD) estimates the number of spectrally distinct materials in the hyperspectral data. The VD is generally considered as the number of signal sources under binary hypothesis, based on the Neyman-Pearson detection criteria. We observe that the hypothesis testing procedure used in many approaches is prone to inflated Type-I (false positive) error. This is due to carrying out the binary hypothesis test individually on each band image, i.e., more than 200 images in hyperspectral data. In this article, we propose multiple hypothesis testing to control the expected proportion of falsely rejected null hypotheses, i.e., false discovery rate (FDR), and in turn, improve the probability of better performance in estimating the VD. To this end, we employ Benjamini and Hochberg procedure that controls the FDR. We provide multiple hypothesis testing-based algorithms to estimate VD wherein the hypothesis can be formulated according to eigenanalysis, the target specified by statistical approach, and by geometric analysis. The efficacies of the proposed algorithms are evaluated by estimating the number of endmembers for the spectral unmixing application. We conduct experiments on four synthetic hyperspectral data sets at different noise levels as well as on two well-known real hyperspectral datasets. Time complexity and execution time are discussed to study the algorithmic aspects while sensitivity analyses of parameters are carried out for better performance analysis of the proposed approach. We found that the use of multiple hypothesis testing improves estimation of number of endmembers in hyperspectral data.

Distributed Hypothesis Testing Over Discrete Memoryless Channels

A distributed binary hypothesis testing (HT) problem involving two parties, one referred to as the observer and the other as the detector is studied. The observer observes a discrete memoryless source (DMS) and communicates its observations to the detector over a discrete memoryless channel (DMC). The detector observes another DMS correlated with that at the observer, and performs a binary hypothesis test on the joint distribution of the two DMS’s using its own observed data and the information received from the observer. The trade-off between the type I error probability and the type II error-exponent of the HT is explored. Single-letter lower bounds on the optimal type II error-exponent are obtained by using two different coding schemes, a separate HT and channel coding scheme and a joint HT and channel coding scheme based on hybrid coding for the matched bandwidth case. Exact single-letter characterization of the same is established for the special case of testing against conditional independence, and it is shown to be achieved by the separate HT and channel coding scheme. An example is provided where the joint scheme achieves a strictly better performance than the separation based scheme.

Optimal interference range for minimum Bayes risk in binomial and Poisson wireless networks

Interference is the main performance-limiting factor in most wireless networks. Protocol interference model is extensively used in the design of wireless networks. However, the setting of interference range, a crucial part of the protocol interference model, is rather heuristic and remains an open problem. In this paper, we use the stochastic geometry and the direct approach to obtain the associated feasibility distributions. After that, we use the binary hypothesis testing to achieve the Bayes risk under binomial point process (BPP) and Poisson point process (PPP), respectively. According to the first derivative of the Bayes risk, we provide the equation to achieve the optimal interference range for minimum Bayes risk. We extend the method proposed by Wildman et al. to a more general situation. Furthermore, we show that for infinite PPP, those two methods converge to the same results. Several numerical results for wireless networks under BPP, finite PPP, and infinite PPP are given. Simulation results show that in the finite wireless network, the BPP method performs better than the PPP method.

Pengaruh Motivasi dan Stres Kerja terhadap Kinerja Karyawan pada Bank Nagari Cabang Syari’ah Payakumbuh

This study aims to determine the effect of motivation and work stres on the performance of employees of Bank Nagari Branch of Payakumbuh Syari'ah. In connection with the research objectives above, it is hypothesized that "alleged motivation and work stres have a significant partial and simultaneous effect on employee performance". To conduct discussions and research, the author uses primary data directly obtained from the object of research through a list of statements or structured questionnaires that have been answered by employees, and the population of this study is Bank Nagari Employees of Payakumbuh Syari'ah Branch totaling 30 with a sample of 30 people who are determined by the Census (Total Sampling) method. Data processing using SPSS 16.0 help method. The analytical tool used was Binary Logistic Regression Analysis and Hypothesis Test namely G Test, Wald Test, and Exp (B) Test. The results of Binary Logistics Regression analysis obtained the following Equations; Y = -48.994 + 1.819X1 - 0.58X2 shows that motivation has a positive and significant effect on employee performance and job stres has a negative and significant effect on the performance of employees of Bank Nagari Payakumbuh Syari'ah Branch. The motivation variable has the Exp (B) value greater than the other variables, which is 6,163. This shows that the motivation variable has the greatest contribution in improving the performance of Bank Nagari employees at the Payakumbuh Syari'ah Branch.

Beliefs in Decision-Making Cascades

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents have their own beliefs instead of the true prior, and have nonidentical noise variances in the private signal. We focus on the Bayes risk of the last agent, where preceding agents are selfish. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The effect of nonidentical noise levels in the two-agent case is also considered and analytical properties of the optimal belief curves are given. Next, we consider a predecessor selection problem wherein the subsequent agent of a certain belief chooses a predecessor from a set of candidates with varying beliefs. We characterize the decision region for choosing such a predecessor and argue that a subsequent agent with beliefs varying from the true prior often ends up selecting a suboptimal predecessor, indicating the need for a social planner. Lastly, we discuss an augmented intelligence design problem that uses a model of human behavior from cumulative prospect theory and investigate its near-optimality and suboptimality.