Distributed Hypothesis Testing Research Articles

Event-Triggered Distributed Hypothesis Testing for Multiagent Networks Based on Observations Cumulation.

This article is concerned with the distributed hypothesis testing problem for multiagent networks, where a group of agents aim to learn an optimal hypothesis set via informative observations and event-triggered communication. Within this framework, a new event-triggered distributed hypothesis testing algorithm based on cumulation of historical observations is proposed. Theoretically, it is proven that due to the introduction of cumulation of historical observations, the proposed algorithm can always ensure the convergence whatever the event-triggered parameters are selected. This convergence result is different from that of the existing algorithm without involving historical observations, where the event-triggered parameters should satisfy a specific design condition to ensure the convergence of the algorithm. In addition, an explicit description of the convergence rate of the proposed algorithm is provided. Finally, the effectiveness of the algorithm is demonstrated through simulation examples.

Design of Bayesian evaluation test for missile damage effectiveness based on multiple damage level standards

The qualified missile damage effectiveness is an important guarantee for giving full play to combat effectiveness. In order to test whether the missile damage effectiveness meets the standard, it is particularly necessary to carry out damage effectiveness identification test research. In view of the limitation that the existing "single-shot damage probability" damage effectiveness quantitative characterization index is difficult to fully describe the missile damage effectiveness based on a single damage standard, considering the different damage level results formed by a single missile hitting the target, the damage effectiveness is characterized by the probability of occurrence of different damage level results. Missile identification from the perspective of multiple damage level standards is conducive to comprehensive inspection of missile damage effectiveness. In addition, in order to overcome the problem of insufficient information in small sample missile assembly tests, the Bayesian method is combined with the system contribution degree to fuse multi-source prior information in the identification test design, and a test scheme with full information utilization and controllable risks for both parties is designed. The example shows that compared with the quantitative characterization index of a single damage standard, this study can fully describe the missile damage effectiveness, and compared with the improved binomial distribution hypothesis test method, the superiority of this method is verified.

Distributed hypothesis testing for large dimensional two-sample mean vectors

Distributed hypothesis testing for large dimensional two-sample mean vectors

A Survey on Error Exponents in Distributed Hypothesis Testing: Connections with Information Theory, Interpretations, and Applications.

A central challenge in hypothesis testing (HT) lies in determining the optimal balance between Type I (false positive) and Type II (non-detection or false negative) error probabilities. Analyzing these errors' exponential rate of convergence, known as error exponents, provides crucial insights into system performance. Error exponents offer a lens through which we can understand how operational restrictions, such as resource constraints and impairments in communications, affect the accuracy of distributed inference in networked systems. This survey presents a comprehensive review of key results in HT, from the foundational Stein's Lemma to recent advancements in distributed HT, all unified through the framework of error exponents. We explore asymptotic and non-asymptotic results, highlighting their implications for designing robust and efficient networked systems, such as event detection through lossy wireless sensor monitoring networks, collective perception-based object detection in vehicular environments, and clock synchronization in distributed environments, among others. We show that understanding the role of error exponents provides a valuable tool for optimizing decision-making and improving the reliability of networked systems.

Study on the supercooling and crystallization mechanism of saline soil based on thermodynamic framework

Quantifying the supercooling characteristics of saline soil–water systems is essential for engineering and agriculture in cold regions. However, the crystallization mechanism of supercooling remains unclear. We conducted experimental observations to investigate the impact of salinity on the soil supercooling properties. Additionally, a freezing nucleation thermodynamic model for saline soil was established based on the Negentropic Nucleation Framework (NNF). Statistical analysis methods were employed to analyze the sensitivity of the parameters and interpret the supercooling microscopic mechanism. The results indicated that the supercooling degree distribution of saline soil is best described by a normal distribution (hypothesis testing statistic Dn=0.176). The nucleation rate was primarily controlled by water activity and activation energy of water molecules. The concentration of salt solution played a crucial role in promoting the formation and growth of crystal nuclei. However, the promoting effect decreased with increasing solution concentration when the concentration was below 0.3 mol/L. Moreover, the nucleation potential energy barrier increased with salt concentration, with NaCl environment exhibiting a higher nucleation potential energy barrier compared to Na2SO4 environment at the same salt concentration. In summary, this research provides a theoretical reference for revealing the freezing-thawing hysteretic mechanism and improving the accuracy of numerical calculation models in cold regions.

On the Optimal Error Exponent of Type-Based Distributed Hypothesis Testing.

Distributed hypothesis testing (DHT) has emerged as a significant research area, but the information-theoretic optimality of coding strategies is often typically hard to address. This paper studies the DHT problems under the type-based setting, which is requested from the popular federated learning methods. Specifically, two communication models are considered: (i) DHT problem over noiseless channels, where each node observes i.i.d. samples and sends a one-dimensional statistic of observed samples to the decision center for decision making; and (ii) DHT problem over AWGN channels, where the distributed nodes are restricted to transmit functions of the empirical distributions of the observed data sequences due to practical computational constraints. For both of these problems, we present the optimal error exponent by providing both the achievability and converse results. In addition, we offer corresponding coding strategies and decision rules. Our results not only offer coding guidance for distributed systems, but also have the potential to be applied to more complex problems, enhancing the understanding and application of DHT in various domains.

Multi-Hop Network With Multiple Decision Centers Under Expected-Rate Constraints

We consider a multi-hop distributed hypothesis testing problem with multiple decision centers (DCs) for testing against independence and where the observations obey some Markov chain. For this system, we characterize the fundamental type-II error exponents region, i.e., the type-II error exponents that the various DCs can achieve simultaneously, under expected rate-constraints. Our results show that this fundamental exponents region is boosted compared to the region under maximum-rate constraints, and that it depends on the permissible type-I error probabilities. When all DCs have equal permissible type-I error probabilities, the exponents region is rectangular and all DCs can simultaneously achieve their optimal type-II error exponents. When the DCs have different permissible type-I error probabilities, a tradeoff between the type-II error exponents at the different DCs arises. New achievability and converse proofs are presented. For the achievability, a new multiplexing and rate-sharing strategy is proposed. The converse proof is based on applying different change of measure arguments in parallel and on proving asymptotic Markov chains. For the special cases <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> ∈ {2, 3}, and for arbitrary <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> ≥ 2 when all permissible type-I error probabilities at the various DCs are equal, we provide simplified expressions for the exponents region; a similar simplification is conjectured for the general case.

Resilient distributed hypothesis testing under time-varying multi-agent networks with multiple types of adversarial agents

In this paper, the resilient distributed hypothesis testing problem under multi-agent networks is studied, where the normal agents that are not attacked aim to cooperatively learn a true state from a set of hypotheses. Different from the existing works, the considered network is heterogeneous and time-varying, and it is allowed that multiple types of agents can be attacked. Within this framework, by designing a novel filtering mechanism, an effective resilient distributed algorithm is developed to solve the considered hypothesis testing problem. In the convergence analysis of the algorithm, a key definition about the robustness of heterogeneous time-varying networks is firstly introduced, then by combining the designed filtering mechanism with a delay-based analysis approach, it is proven that the beliefs of the true state held by all normal agents converge to 1 under the proposed algorithm, which means that the normal agents successfully learn the true state. Finally, the theoretical findings are verified through simulations, and a comparison is provided to show that the proposed algorithm by utilizing the network heterogeneity may tolerate more adversarial agents than the algorithm designed in homogeneous networks.

Distributed Hypothesis Testing over a Noisy Channel: Error-Exponents Trade-Off.

A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to n independent and identically distributed samples, denoted by U and V, respectively. The observer communicates to the decision maker over a discrete memoryless channel, and the decision maker performs a binary hypothesis test on the joint probability distribution of (U,V) based on V and the noisy information received from the observer. The trade-off between the exponents of the type I and type II error probabilities is investigated. Two inner bounds are obtained, one using a separation-based scheme that involves type-based compression and unequal error-protection channel coding, and the other using a joint scheme that incorporates type-based hybrid coding. The separation-based scheme is shown to recover the inner bound obtained by Han and Kobayashi for the special case of a rate-limited noiseless channel, and also the one obtained by the authors previously for a corner point of the trade-off. Finally, we show via an example that the joint scheme achieves a strictly tighter bound than the separation-based scheme for some points of the error-exponents trade-off.

Rate-Exponent Region for a Class of Distributed Hypothesis Testing Against Conditional Independence Problems

We study a class of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -encoder hypothesis testing against conditional independence problems. Under the criterion that stipulates minimization of the Type II error subject to a (constant) upper bound <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> on the Type I error, we characterize the set of encoding rates and exponent for both discrete memoryless and memoryless vector Gaussian settings. For the DM setting, we provide a converse proof and show that it is achieved using the Quantize-Bin-Test scheme of Rahman and Wagner. For the memoryless vector Gaussian setting, we develop a tight outer bound by means of a technique that relies on the de Bruijn identity and the properties of Fisher information. In particular, the result shows that for memoryless vector Gaussian sources the rate-exponent region is exhausted using the Quantize-Bin-Test scheme with Gaussian test channels; and there is no loss in performance caused by restricting the sensors’ encoders not to employ time sharing. Furthermore, we also study a variant of the problem in which the source, not necessarily Gaussian, has finite differential entropy and the sensors’ observations noises under the null hypothesis are Gaussian. For this model, our main result is an upper bound on the exponent-rate function. The bound is shown to mirror a corresponding explicit lower bound, except that the lower bound involves the source power (variance) whereas the upper bound has the source entropy power. Part of the utility of the established bound is for investigating asymptotic exponent/rates and losses incurred by distributed detection as function of the number of sensors.

Predictors of Septic Shock or Bacteremia in Children Experiencing Febrile Neutropenia Post-Chemotherapy.

Febrile neutropenia (FN) is an early indicator of infection in oncology patients post-chemotherapy. We aimed to determine clinical predictors of septic shock and/or bacteremia in pediatric cancer patients experiencing FN and to create a model that classifies patients as low-risk for these outcomes. This is a retrospective analysis with clinical data of a cohort of pediatric oncology patients admitted during July 2015 to September 2017 with FN. One FN episode per patient was randomly selected. Statistical analyses include distribution analysis, hypothesis testing, and multivariate logistic regression to determine clinical feature association with outcomes. A total of 865 episodes of FN occurred in 429 subjects. In the 404 sampled episodes that were analyzed, 20.8% experienced outcomes of septic shock and/or bacteremia. Gram-negative bacteria count for 70% of bacteremias. Features with statistically significant influence in predicting these outcomes were hematological malignancy (P < .001), cancer relapse (P = .011), platelet count (P = .004), and age (P = .023). The multivariate logistic regression model achieves AUROC = 0.66 (95% CI 0.56-0.76). The optimal classification threshold achieves sensitivity = 0.96, specificity = 0.33, PPV = 0.40, and NPV = 0.95. This model, based on simple clinical variables, can be used to identify patients at low-risk of septic shock and/or bacteremia. The model's NPV of 95% satisfies the priority to avoid discharging patients at high-risk for adverse infection outcomes. The model will require further validation on a prospective population.

Byzantine-Resilient Distributed Hypothesis Testing With Time-Varying Network Topology

In this article, we study the problem of distributed hypothesis testing over a network of mobile agents with limited communication and sensing ranges to infer the true hypothesis collaboratively. In particular, we consider a scenario where there is an unknown subset of compromised agents that may deliberately share altered information to undermine the team objective. We propose two distributed algorithms where each agent maintains and updates two sets of beliefs (i.e., probability distributions over the hypotheses), namely <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">local</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">actual</i> beliefs (LB and AB, respectively, for brevity). In both algorithms, at every time step, each agent shares its AB with other agents within its communication range and makes a local observation to update its LB. Then, both algorithms can use the shared information to update ABs under certain conditions. One requires receiving a certain number of shared ABs at <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">each time instant</i> ; the other accumulates shared ABs <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">over time</i> and updates after the number of shared ABs exceeds a prescribed threshold. Otherwise, both algorithms rely on the agent’s current LB and AB to update the new AB. We prove under mild assumptions that the AB for every noncompromised agent converges almost surely to the true hypothesis, without requiring connectivity in the underlying time-varying network topology. Using a simulation of a team of unmanned aerial vehicles aiming to classify adversarial agents among themselves, we illustrate and compare the proposed algorithms. Finally, we show experimentally that the second algorithm consistently outperforms the first algorithm in terms of the speed of convergence.

Synthesis of new, more powerful statistical tests through multiplicative clustering of classical Frozini and Murota-Takeuchi tests with the Hurst test for the purpose of testing small samples for normality

Aim. The paper examines the problem of small sample analysis by means of synthesizing new statistical tests generated by the clustering of the Hurst statistical test with the Frozini test, as well as with the Murota-Takeuchi test. The problem of normal distribution hypothesis testing on samples of 16 to 25 experiments is solved. Such significant limitations of the sample size arise in subject areas that include biometrics, biology, medical science and economics. In this case, the problem can be solved by applying not one, but a number of statistical tests to the analysis of the same small sample. Methods. It is suggested multiplying the Hurst test outputs by the Frozini test and/or the Murota-Takeuchi test outputs. A multiplicative clustering was performed for pairs of examined tests and their combination. It was shown that for each known statistical test, an equivalent artificial neuron can be constructed. A neural network integration of about 21 classical statistical tests constructed in the last century becomes possible. It is expected that the addition of new statistical tests in the form of artificial neurons will improve the quality of multi-criteria analysis solutions. Formally, the products of non-recurrent pairs of 21 original classical statistical tests should produce 210 new statistical tests. That is significantly more than the total number of statistical tests developed in the last century for the purpose of normality testing. Results. Pairwise product of the examined tests allows reducing the probability of errors of the first and second kind by more than 1.55 times as compared to the basic Hurst test. In case of triple product of the tests, the probabilities of error decrease relative to the basic Hurst test and to the associated second test. It is noted that there is no steady improvement in the quality of the decisions made by multiplicative mathematical constructions. The probabilities of error of the new test obtained by multiplying three of the examined tests are approximately 1.5% worse as compared to those of the tests obtained by multiplying pairs of the original tests. Conclusions. By analogy with the examined tests, the proposed data processing methods can also be applied to other known statistical tests. In theory, it becomes possible to significantly increase the number of new statistical tests by multiplying their final values. Unfortunately, as the number of clustered statistical tests grows, mutual correlations between the newly synthesized tests grow as well. The latter fact limits the capabilities of the method proposed in the paper. Further research is required in order to identify the most efficient combinations of pairs, triples or large groups for known statistical tests.

On Distributed Learning With Constant Communication Bits

In this paper, we study a distributed learning problem constrained by constant communication bits. Specifically, we consider the distributed hypothesis testing (DHT) problem where two distributed nodes are constrained to transmit a constant number of bits to a central decoder. In such settings, we show that in order to achieve the optimal error exponents, it suffices to consider the empirical distributions of observed data sequences and encode them to the transmission bits. With such a coding strategy, we develop a geometric approach in the distribution spaces and establish an inner bound of error exponent regions. In particular, we show the optimal achievable error exponents and coding schemes for the following cases: (i) both nodes can transmit <inline-formula> <tex-math notation="LaTeX">$\log _{2}3$ </tex-math></inline-formula> bits; (ii) one of the nodes can transmit 1 bit, and the other node is not constrained; (iii) the joint distribution of the nodes are conditionally independent given one hypothesis. Furthermore, we provide several numerical examples for illustrating the theoretical results. Our results provide theoretical guidance for designing practical distributed learning rules, and the developed approach also reveals new potentials for establishing error exponents for DHT with more general communication constraints.

The Effect of Open-Ended Approach on Automotive Electricity Learning in SMK Negeri 3 Makassar

This study aims (1) to find out the students' capabilities in the closed-ended teaching method; (2) to find out the students' capabilities in the open-ended teaching method with a scenario; (3) to find out whether there is an effect of the open-ended teaching method with a scenario on the students' capabilities to solve automotive electrical system problems with problem-based scenarios. The research subject involved a whole class (consisting of 25 students) selected by the purposive sampling technique. The data were collected through observation, tests, interviews, and documentation, then analyzed with descriptive statistical analysis of percentages, frequency distribution tables and hypothesis testing with nonparametric statistical analysis, Mann Whitney test with SPSS-PC 20.0 for windows. The results of the data analysis showed that: (1) the students' capabilities to assemble an automotive electrical system (closed-ended teaching method) was 88%, (2) the students' capabilities to solve automotive electrical problems with a problem-based scenario (open-ended teaching method in a scenario) was 72 %, (3) the effect of the students' capabilities in assembling electricity (closed-ended teaching method) was higher than the students' capabilities to solve electrical problems (scenario of open-ended teaching).

Communication Complexity of Distributed High Dimensional Correlation Testing

We consider a two-party distributed hypothesis testing problem for correlated Gaussian random variables. For a d-dimensional random vector X and a scalar random variable Y, where X and Y are jointly Gaussian with an unknown correlation vector ρ, parties <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> observe independent copies of X and Y, respectively. The parties seek to test if their observations are correlated or not, namely they seek to test if ||ρ|| <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> exceeds τ or is it 0. To that end, they communicate interactively and declare the test output. We show that roughly order d/τ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> bits of communication are sufficient and necessary for resolving the distributed correlation testing problem above. Furthermore, we establish a lower bound of roughly d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /τ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> bits for the communication needed for distributed estimation of ρ, implying that distributed correlation testing requires less communication than distributed estimation. Both our lower bounds for testing and estimation hold for an arbitrary d and interactive communication with shared randomness, while our distributed test requires only one-way communication with shared randomness. For the one-dimensional case, with one-way communication and with probability of one of the error-types fixed, our bounds are more refined in the dependence on the other error-type and are tight even in the constant.

Distributed Hypothesis Testing over Noisy Broadcast Channels

This paper studies binary hypothesis testing with a single sensor that communicates with two decision centers over a memoryless broadcast channel. The main focus lies on the tradeoff between the two type-II error exponents achievable at the two decision centers. In our proposed scheme, we can partially mitigate this tradeoff when the transmitter has a probability larger than 1/2 to distinguish the alternate hypotheses at the decision centers, i.e., the hypotheses under which the decision centers wish to maximize their error exponents. In the cases where these hypotheses cannot be distinguished at the transmitter (because both decision centers have the same alternative hypothesis or because the transmitter’s observations have the same marginal distribution under both hypotheses), our scheme shows an important tradeoff between the two exponents. The results in this paper thus reinforce the previous conclusions drawn for a setup where communication is over a common noiseless link. Compared to such a noiseless scenario, here, however, we observe that even when the transmitter can distinguish the two hypotheses, a small exponent tradeoff can persist, simply because the noise in the channel prevents the transmitter to perfectly describe its guess of the hypothesis to the two decision centers.

Bayesian Nonparametric Unsupervised Concept Drift Detection for Data Stream Mining

Online data stream mining is of great significance in practice because of its ubiquity in many real-world scenarios, especially in the big data era. Traditional data mining algorithms cannot be directly applied to data streams due to (1) the possible change of underlying data distribution over time (i.e.,concept drift) and (2) delayed, short, or even no labels for streaming data in practice. A new research area, namedunsupervised concept drift detection, has emerged to tackle this difficulty mainly based on two-sample hypothesis tests, such as the Kolmogorov–Smirnov test. However, it is surprising that none of the existing methods in this area exploit the Bayesian nonparametric hypothesis test, which has clear interpretability and straightforward prior knowledge encoding ability and no strict or unrealistic requirement of prefixing the form for the underlying data distribution. In this article, we present a Bayesian nonparametric unsupervised concept drift detection method based on the Polya tree hypothesis test. The basic idea is to decompose the underlying data distribution into a multi-resolution representation that transforms the whole distribution hypothesis test into recursive and simple binomial tests. Also, an incremental mechanism is especially designed to improve its efficiency in the stream setting. The method effectively detect drifts, and it also locates where a drift happens and the posteriors of hypotheses. The experiments on synthetic data verify the desired properties of the proposed method, and the experiments on real-world data show the better performance of the method for data stream mining compared with its frequentist counterpart in the literature.

Distributed Hypothesis Testing With Variable-Length Coding

The problem of distributed testing against independence with variable-length coding is considered when the average and not the maximum communication load is constrained as in previous works. The paper characterizes the optimum type-II error exponent of a single-sensor single-decision center system given a maximum type-I error probability when communication is either over a noise-free rate-R link or over a noisy discrete memoryless channel (DMC) with stop-feedback. Specifically, let E denote the maximum allowed type-I error probability. Then the optimum exponent of the system with a rate-R link under a constraint on the average communication load coincides with the optimum exponent of such a system with a rate R/(1-ε) link under a maximum communication load constraint. A strong converse thus does not hold under an average communication load constraint. A similar observation also holds for testing against independence over DMCs. With variable-length coding and stopfeedback and under an average communication load constraint, the optimum type-II error exponent over a DMC of capacity C equals the optimum exponent under fixed-length coding and a maximum communication load constraint when communication is over a DMC of capacity C/(1 - ε).

Distributed Hypothesis Testing: Cooperation and Concurrent Detection

A single-sensor two-detectors system is considered where the sensor communicates with both detectors and Detector 1 communicates with Detector 2, all over noise-free rate-limited links. The sensor and both detectors observe discrete memoryless source sequences whose joint probability mass function depends on a binary hypothesis. The goal at each detector is to guess the binary hypothesis in a way that, for increasing observation lengths, the probability of error under one of the hypotheses decays to zero with largest possible exponential decay, whereas the probability of error under the other hypothesis can decay to zero or to a small positive number arbitrarily slow. For the setting with positive communication rates from the sensor to the detectors and when both detectors are interested in maximizing the error exponent under the same hypothesis, we characterize the set of all possible exponents in a special case of testing against independence. In this case the cooperation link allows Detector 2 to increase its Type-II error exponent by an amount that is equal to the exponent attained at Detector 1. We also provide a general inner bound on the set of achievable error exponents that shows a tradeoff between the exponents at the two detectors in most cases. When the two detectors aim at maximizing the error exponent under different hypotheses and the distribution at the Sensor is different under the two hypotheses, then we show that such a tradeoff does not exist. We propose a general scheme that allows each detector to attain the same exponent as if it was the only detector in the system. For the setting with zero-rate communication on both links, we exactly characterize the set of possible exponents and the gain brought up by cooperation, in function of the number of bits that are sent over the two links. Notice that, for this setting, tradeoffs between the exponents achieved at the two detectors arise only in few particular cases. In all other cases, each detector achieves the same performance as if it were the only detector in the system.