Binary Hypothesis Testing Research Articles

Optimal provable robustness of quantum classification via quantum hypothesis testing

Quantum machine learning models have the potential to offer speedups and better predictive accuracy compared to their classical counterparts. However, these quantum algorithms, like their classical counterparts, have been shown to also be vulnerable to input perturbations, in particular for classification problems. These can arise either from noisy implementations or, as a worst-case type of noise, adversarial attacks. In order to develop defense mechanisms and to better understand the reliability of these algorithms, it is crucial to understand their robustness properties in the presence of natural noise sources or adversarial manipulation. From the observation that measurements involved in quantum classification algorithms are naturally probabilistic, we uncover and formalize a fundamental link between binary quantum hypothesis testing and provably robust quantum classification. This link leads to a tight robustness condition that puts constraints on the amount of noise a classifier can tolerate, independent of whether the noise source is natural or adversarial. Based on this result, we develop practical protocols to optimally certify robustness. Finally, since this is a robustness condition against worst-case types of noise, our result naturally extends to scenarios where the noise source is known. Thus, we also provide a framework to study the reliability of quantum classification protocols beyond the adversarial, worst-case noise scenarios.

Theoretical Concept Study of Cooperative Abnormality Detection and Localization in Fluidic-Medium Molecular Communication

In this paper, we propose a theoretical framework for cooperative abnormality detection and localization systems by exploiting molecular communication setup. The system consists of mobile sensors in a fluidic medium, which are injected into the medium to search the environment for abnormality. Some fusion centers (FC) are placed at specific locations in the medium, which absorb all sensors arrived at their locations, and by observing its state, each FC decides on the abnormality existence and/or its location. To reduce the effects of sensor imperfection, we propose a scheme where the sensors release some molecules (i.e., markers) into the medium after they sense an abnormality. If the goal is abnormality detection, the released molecules are used to cooperatively activate other sensors. If the goal is abnormality localization, the released molecules are used by the FCs to determine the location. In our model, both sensors' imperfection and markers background noise are taken into account. For the detection phase, we consider two sensor types based on their activation strategy by markers. To make the analysis tractable, we assume some ideal assumptions for the sensors' model. We investigate the related binary hypothesis testing problem and obtain the probabilities of false alarm and miss-detection. It is shown that using sensors with the ability of cooperatively activating each other can significantly improve the detection performance in terms of probability of error. For the localization phase, we consider two types of FCs based on their capability in reading sensors' storage levels. We study their performance and obtain the optimal and sub-optimal decision schemes and also the probability of localization error for both perfect and imperfect sensing regimes.

Adaptive strategies for clutter edge detection in radar

In this paper, the problem of the detection and localization of clutter edges within training data is addressed. This is accomplished through a procedure capable of discriminating between either a unique homogeneous set or two heterogeneous subsets within a sliding window moving over the set of range bins of interest. The problem is first formulated as a binary hypothesis test assuming that the rank of the covariance clutter component is known and solved resorting to the generalized likelihood ratio test. Then, in the case of no a priori knowledge about the rank of the clutter covariance matrix, a preliminary estimation stage relying on the model order selection rules is devised. Interestingly, the estimates provided by the detection stage can be processed by a fusion algorithm in order to improve the quality of the location estimate of the clutter edge. Finally, the performance analysis conducted in comparison with a suitable competitor highlights the effectiveness of the proposed solutions.

Autonomous Vehicles Sideslip Angle Estimation: Single Antenna GNSS/IMU Fusion With Observability Analysis

Taking advantage of available measurement in Internet of Things (IoT) for intelligent transportation systems, a sideslip angle estimation method for autonomous vehicles is presented and experimentally verified by fusing global navigation satellite system (GNSS) and inertial measurement unit (IMU), and by constructing an observability index (OI). The correlation between the vehicle sideslip error and the inertial navigation system (INS) heading error is presented first. Then, the observability for the heading error in a velocity-based Kalman filter is discussed and a novel index is defined to check the observability of the heading error. The course from a single antenna GNSS in an autonomous vehicle is augmented to estimate the heading error when the observability of the heading error is low. To reject the course measurement for scenarios that include sideslip movement, a binary hypothesis test approach is applied to indicate whether the vehicle is sidesliping. In addition, based on the OI and the sideslip indicator, a hybrid feedback strategy is designed for the heading error correction. To improve the convergence rate of the heading error in the velocity-based Kalman filter, a tuning strategy is presented. The stochastical observability of the designed Kalman observer is investigated for known and stochastic initial conditions. Finally, the proposed sideslip angle estimator is experimentally validated through a vehicle test platform in critical driving scenarios. The results confirm that the proposed OI can effectively identify when the heading error is observable, and also corroborate the effectiveness of the hybrid feedback strategy and adaptation method in the Kalman observer.

On Universality and Training in Binary Hypothesis Testing

The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For testing in the simple normal location problem (that is, testing for the mean of multivariate Gaussians), we overcome the difficulty as follows. In this problem there exists a natural “hardness” order between parameters as for different parameters the error-probabilities curves (when the parameter is known) are either identical, or one dominates the other. We can thus define minimax performance as the worst-case among parameters which are below some hardness level. Fortunately, there exists a universal minimax test, in the sense that it is minimax for all hardness levels simultaneously. Under this criterion we also find the optimal test for composite hypothesis testing with training data. THIS criterion extends to the wide class of local asymptotic normal models, in an asymptotic sense where the approximation of the error probabilities is additive. Since we have the asymptotically optimal tests for composite hypothesis testing with and without training data, we quantify the loss of universality and gain of training data for these models.

Hypothesis tests on Rayleigh wave radiation pattern shapes: a theoretical assessment of idealized source screening

SUMMARYShallow seismic sources excite Rayleigh wave ground motion with azimuthally dependent radiation patterns. We place binary hypothesis tests on theoretical models of such radiation patterns to screen cylindrically symmetric sources (like explosions) from non-symmetric sources (like non-vertical dip-slip or non-VDS faults). These models for data include sources with several unknown parameters, contaminated by Gaussian noise and embedded in a layered half-space. The generalized maximum likelihood ratio tests that we derive from these data models produce screening statistics and decision rules that depend on measured, noisy ground motion at discrete sensor locations. We explicitly quantify how the screening power of these statistics increase with the size of any dip-slip and strike-slip components of the source, relative to noise (faulting signal strength) and how they vary with network geometry. As applications of our theory, we apply these tests to (1) find optimal sensor locations that maximize the probability of screening non-circular radiation patterns and (2) invert for the largest non-VDS faulting signal that could be mistakenly attributed to an explosion with damage, at a particular attribution probability. Finally, we quantify how certain errors that are sourced by opening cracks increase screening rate errors. While such theoretical solutions are ideal and require future validation, they remain important in underground explosion monitoring scenarios because they provide fundamental physical limits on the discrimination power of tests that screen explosive from non-VDS faulting sources.

Three Variants of Differential Privacy: Lossless Conversion and Applications

We consider three different variants of differential privacy (DP), namely approximate DP, Rényi DP (RDP), and hypothesis test DP. In the first part, we develop a machinery for optimally relating approximate DP to RDP based on the joint range of two f-divergences that underlie the approximate DP and RDP. In particular, this enables us to derive the optimal approximate DP parameters of a mechanism that satisfies a given level of RDP. As an application, we apply our result to the moments accountant framework for characterizing privacy guarantees of noisy stochastic gradient descent (SGD). When compared to the state-of-the-art, our bounds may lead to about 100 more stochastic gradient descent iterations for training deep learning models for the same privacy budget. In the second part, we establish a relationship between RDP and hypothesis test DP which allows us to translate the RDP constraint into a tradeoff between type I and type II error probabilities of a certain binary hypothesis test. We then demonstrate that for noisy SGD our result leads to tighter privacy guarantees compared to the recently proposed f-DP framework for some range of parameters.

Binary Hypothesis Testing with Learning of Empirical Distributions

Binary hypothesis testing with a single observer is considered. The true distributions of the observations under either hypothesis are unknown. Empirical distributions are estimated from observations. A sequence of detection problems are solved using the sequence of empirical distributions. The convergence of the information state and optimal detection cost under empirical distributions to the information state and optimal detection cost under the true distribution are shown. Simulation results are presented and are consistent with the results mentioned earlier.

PERFORMANCE INVESTIGATION OF PHYSICAL LAYER AUTHENTICATION BASED ON STATISTICAL DECISION STRATEGIES

In this paper, physical layer authentication based on the estimated channel state information (CSI) over the subcarriers of wireless orthogonal frequency division multiplexing (OFDM) systems has been studied to provide reliable and augmented authentication solutions for wireless communication devices. The binary hypothesis test with channel-discriminative functions that are based on measuring the difference between channel features and CSI profile clustering is investigated. A comprehensive performance evaluation for the considered channel-discriminative functions in frequency-selective fading channels is presented. Simulation results demonstrated that the security performance depends on the channel frequency selectivity. The decision metrics that measure the difference between the channel features demonstrated improved performance with the increase of channel variation over the subcarriers. In contrast, the CSI profile clustering method exhibited significant degradation in the performance for moderate and severe frequency selectivity conditions. Therefore, for the clustering method the channel fingerprint should be extracted from the neighboring subcarriers, while in other methods the channel features should be extracted from disjoint pilots in order to optimize the security performance over frequency-selective channels.

Finite-Length Bounds on Hypothesis Testing Subject to Vanishing Type I Error Restrictions

A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of the optimal miss error probability -- as the sample size tends to infinity -- given some (positive) restrictions on the false alarm probabilities is a fundamental question to address in theory. Considering the more realistic context of a BHT with a finite number of observations, this paper presents a new non-asymptotic result for the scenario with monotonic (sub-exponential decreasing) restriction on the Type I error probability, which extends the result presented by Strassen in 2009. Building on the use of concentration inequalities, we offer new upper and lower bounds to the optimal Type II error probability for the case of finite observations. Finally, the derived bounds are evaluated and interpreted numerically (as a function of the number samples) for some vanishing Type I error restrictions.

On Trajectory Design for Intruder Detection in Wireless Mobile Sensor Networks

We address the problem of detecting the invasion of an intruder into a region of interest (ROI) which is monitored by a distributed bandwidth-constrained wireless mobile sensor network (WMSN). We design periodic trajectories for the mobile sensor nodes (MSNs) such that high detection probabilities are obtained while maintaining the MSNs' energy consumption low. To reduce the transmission and processing burden on the MSNs, we propose an operation algorithm based on two modes, surveying mode and confirmation mode. In the former, to efficiently detect the intruder while using little mechanical energy, we optimize the surveying path such that the sensed area is maximized. During this mode, each MSN performs local detection and switches to the confirmation mode if and only if the intruder is suspected to be present. In the confirmation mode, each MSN collects further measurements over a predefined duration to reduce the detection uncertainly. A binary local hypothesis testing is performed at each MSN and only positive test statistics are transmitted to the FC where the ultimate decision is taken. Simulations results show the merits of the proposed two-mode operation algorithm in terms of detection performance and energy efficiency.

Distributed Sequential Hypothesis Testing With Byzantine Sensors

This paper considers the problem of sequential binary hypothesis testing based on observations from a network of $m$ sensors where a subset of the sensors is compromised by a malicious adversary. The asymptotic average sample number required to reach a certain level of error probability is selected as the performance metric of the system. We propose an asymptotically optimal voting algorithm for the sensor network with a fusion center and generalize it to fully-distributed networks, where the algorithm stays asymptotically optimal under the weak assumption that the sensor network is connected. Moreover, we prove that both of the proposed algorithms are asymptotically optimal in the presence of Byzantine sensors, in the sense that each of them forms a Nash equilibrium with the worst-case attack (flip-attack). Compared to existing distributed detection strategies, the proposed scheme has a low message complexity, which is independent of the error probability and the sample number, by taking advantage of the sparsity of votes. The results are corroborated by numerical simulations.

Adaptive Radar Detection in Low-Rank Heterogeneous Clutter via Invariance Theory

This paper addresses adaptive detection of a range distributed target in the presence of dominant heterogeneous clutter, which is (possibly) low-rank and lies in a known subspace, plus Gaussian thermal noise. First, this problem is transformed into an equivalent binary hypothesis test with observations having block-diagonal covariance matrices. Then an invariance analysis is conducted on the resulting hypothesis test. Data and unknown parameters are compressed into a maximal invariant and an induced maximal invariant, respectively, w.r.t. a suitable transformation group. This suggests to focus attention on invariant detectors and to establish the relationship between invariance and constant false alarm rate (CFAR) property. According to this guideline, two tunable invariant detectors exploiting the aforementioned covariance structure are devised, and they are shown to ensure bounded CFAR and standard CFAR properties, respectively. Finally, the CFAR behavior of the proposed detectors as well as their detection performance is assessed via numerical simulations.

Ordered Transmissions Schemes for Detection in Spatially Correlated Wireless Sensor Networks

The ordered transmissions scheme requires fewer sensor nodes to transmit their measurements than the conventional unordered transmissions scheme (UTS) in which all nodes transmit. Yet, it achieves the same error probability as UTS. For the practically relevant scenario in which the measurements of the sensor nodes are spatially correlated, we present a novel correlation-aware ordered transmissions scheme (CA-OTS) for the binary hypothesis testing problem with Gaussian statistics. It uses the timer scheme to make the nodes transmit their measurements in the decreasing order of the absolute values of the measurements without any node knowing the measurements of other nodes. CA-OTS applies to the general case where the hypotheses differ in the mean vector and covariance matrix, and markedly reduces the number of transmissions. It differs from the literature that assumes that the measurements of the nodes, when conditioned on the hypotheses, are statistically independent or the covariance matrix has a special structure. When the mean vector or covariance matrix is the same for the two hypotheses, we propose novel refinements that require even fewer transmissions. We also derive insightful upper bounds for them that apply to a general product-correlation model.

Second-Order Asymptotics of Sequential Hypothesis Testing

We consider the classical sequential binary hypothesis testing problem in which there are two hypotheses governed respectively by distributions $P_{0}$ and $P_{1}$ and we would like to decide which hypothesis is true using a sequential test. It is known from the work of Wald and Wolfowitz that as the expectation of the length of the test grows, the optimal type-I and type-II error exponents approach the relative entropies $D(P_{1}\|P_{0})$ and $D(P_{0}\|P_{1})$ . We refine this result by considering the optimal backoff—or second-order asymptotics—from the corner point of the achievable exponent region $(D(P_{1}\|P_{0}),D(P_{0}\|P_{1}))$ under two different constraints on the length of the test (or the sample size). First, we consider a probabilistic constraint in which the probability that the length of test exceeds a prescribed integer $n$ is less than a certain threshold $0 . Second, the expectation of the sample size is bounded by $n$ . In both cases, and under mild conditions, the second-order asymptotics is characterized exactly. Numerical examples are provided to illustrate our results.

Blind recognition of MIMO-SFBC based on Symbolic eigenvalue*

In the blind recognition of air frequency block code signals, a blind recognition algorithm of MIMO-SFBC based on symbolic eigenvalue was proposed to solve the problems of poor recognition performance and large number of samples under the condition of low SNR. According to the symbol correlation characteristics of different air frequency block codes in frequency domain, the eigenvector sequences of different air frequency block codes are derived, symbolic eigenvalue are estimated by binary hypothesis testing, and different coding types are distinguished by decision tree classification recognition algorithm. Simulation results show that the algorithm does not need prior information such as modulation prediction, and has good recognition performance under low SNR and small sample conditions, and can be applied to engineering fields such as cognitive radio.

Reciprocity Evaluation in Heterogeneous Polarimetric SAR Images

In this letter, an automatic method to validate the reciprocity theorem on full-polarimetric heterogeneous synthetic aperture radar (SAR) data is derived. The study extends, to the more general heterogeneous scenario, the work of <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , where the conformity with the reciprocity is studied in the homogeneous case. At the design stage, it is assumed that the pixels in the polarimetric image share the same covariance structure but different power levels. Then, the dependence on nuisance parameters is removed resorting to the Principle of Invariance. The resulting problem is formalized as a binary hypothesis test and is solved through the generalized likelihood ratio test (GLRT). Tests are conducted both on simulated and real-recorded data to show the superiority of the proposed GLRT with respect to its homogeneous counterpart.

KL distance function over GLRT for a multi-antenna-based cognitive radio

ABSTRACT Cognitive Radio (CR) has been identified as a promising technology for recycling underutilized frequency bands. Proper detection of frequency voids a.k.a. spectrum sensing is the fundamental necessity to accomplish the objective. In this article, spectrum sensing for a multi-antenna based CR receiver has been considered. Initially, the performance of a Generalized Likelihood Receiver (GLR) has been demonstrated in conventional approach. Here a test statistic is formulated for binary hypothesis testing and respective false alarm and detection probabilities are calculated. Later, the same analysis has been carried out by alternative Kullback-Leibler (KL) distance function. It is shown that the proposed alternative method provides better detection probability for the same false alarm probability especially to identify weak primary signals. Numerical results are provided in support of the proposition.

Source localization in resource-constrained sensor networks based on deep learning

Source localization with a network of low-cost motes with limited processing, memory, and energy resources is considered in this paper. The state-of-the-art methods are mostly based on complicated signal processing approaches in which motes send their (processed) data to a fusion center (FC) wherein the source is localized. These methods are resource-demanding and mostly do not meet the limitations of motes and network. In this paper, we consider distributed detection where each mote performs a binary hypothesis test to detect locally the existence of a desired source and sends its (potentially erroneous) decision to FC during just one bit (1 indicates source existence and 0 otherwise). Hence, both processing and bandwidth constraints are met. We propose to use an artificial neural network (ANN) to correct erroneous local decisions. After error correction, the region affected by the source is specified by nodes with decision 1. Moreover, we propose to localize the source by deep learning in FC which converts the network of decisions 1 and 0 to a black and white image with white pixels in the locations of motes with decision 1. The proposed schemes of error correction by ANN (ECANN) and source localization with deep learning (SoLDeL) were evaluated in a fire detection application. We showed that SoLDeL performs appropriately and scales well into large networks. Moreover, the applicability of ECANN in delineation of farm management zones was illustrated.

Sensor Fusion for Distributed Detection of Mobile Intruders in Surveillance Wireless Sensor Networks

Wireless sensor networks are widely applicable in surveillance applications for intruder detection. Many research articles in the literature have focused on to generate an inference about the intruder detection and evaluated this in terms of detection probability and false alarm rate. In this paper, we have solved the problem of passive mobile intruder detection using two modalities i.e. acoustic signal model and sensing probability model. A three-level hierarchy is proposed to generate an inference about the presence of a mobile intruder. At base level the deployed sensor nodes are grouped together using k-mean clustering. For both modalities the distance between the sensor nodes and intruder is computed. At cluster head, the received signal strengths or sensing probabilities reported by the sensor nodes are employed for binary hypothesis testing. The cluster heads transmit their decisions to the fusion center for the generation of accurate inference about the intruder detection after performing Likelihood Ratio Test (LRT) on the fused decisions. Numerical analysis of received signals identify the optimum threshold value for detection probability computation. The derived fusion rule maximizes detection probability with respect to the allowable false alarm rates. The accuracy of proposed fusion rule is depending on the number of actual detections reported by the deployed sensor nodes. Simulation results also show that the derived fusion rule performs better as compared to other fusion rules in terms of sensor count, speed of mobile intruder, detection probability and detection accuracy.