Hellinger Distance Research Articles

Contrasting occupancy models with presence-only models: Does accounting for detection lead to better predictions?

Species distribution models are popular statistical tools for inferring potential distribution range of species across space and time and are extensively used in conservation planning. Models based on presence-only data (e.g., MaxEnt) are widely used; however, these models assume perfect species detectability. Occupancy modelling is considered a better modelling technique since it accounts for species detectability. Presence-only models are relatively simpler, requiring only presence locations, while occupancy models are data hungry models requiring detection/non-detection data from multiple visits to the survey sites. We utilized data from the Kerala Bird Atlas (India) and modelled current distribution for 109 species using MaxEnt and occupancy approaches. MaxEnt performed well even with less occurrences, while occupancy model failed for species with fewer than 40 records. In terms of evaluation metrics, AUC and Root Mean Square Error, both models performed relatively better for species with low occurrences than those with high occurrences (generalist species). The comparison metrics (Relative-rank scores, Root Mean Square Error, Hellinger distance and Expectation of Shared Presences) were significantly correlated with the number of occurrences; MaxEnt and occupancy based SDMs for widespread species had more concordance than SDMs of narrowly distributed species. There was some discordance between algorithms with regards to diversity hotspot. Selection of best combination of variables and correction for overprediction can help improve performances of both models and improve consistency between them. Given the data hungry nature of occupancy models and marginal difference with the MaxEnt models; it appears that latter is better suited for predicting the distribution of rare species and studies dealing with cumulative data from multiple species.

Bayesian approach for limited-aperture inverse acoustic scattering with total variation prior

In this work, we apply the Bayesian approach for the acoustic scattering problem to reconstruct the shape of a sound-soft obstacle using the limited-aperture far-field measure data. A novel total variation prior scheme is developed for the obstacle shape parameterization. It is imposed on the Fourier coefficients of the parameterization not the parameterization itself. Using this prior, some less smooth objects can be reconstructed. We also investigate the well-posedness in the sense of the Hellinger distance, Wasserstein distance and Kullback–Leibler divergence. Extensive numerical tests are provided to illustrate the numerical performance.

A Multi-Sensor Data-Fusion Method Based on Cloud Model and Improved Evidence Theory.

The essential factors of information-aware systems are heterogeneous multi-sensory devices. Because of the ambiguity and contradicting nature of multi-sensor data, a data-fusion method based on the cloud model and improved evidence theory is proposed. To complete the conversion from quantitative to qualitative data, the cloud model is employed to construct the basic probability assignment (BPA) function of the evidence corresponding to each data source. To address the issue that traditional evidence theory produces results that do not correspond to the facts when fusing conflicting evidence, the three measures of the Jousselme distance, cosine similarity, and the Jaccard coefficient are combined to measure the similarity of the evidence. The Hellinger distance of the interval is used to calculate the credibility of the evidence. The similarity and credibility are combined to improve the evidence, and the fusion is performed according to Dempster’s rule to finally obtain the results. The numerical example results show that the proposed improved evidence theory method has better convergence and focus, and the confidence in the correct proposition is up to 100%. Applying the proposed multi-sensor data-fusion method to early indoor fire detection, the method improves the accuracy by 0.9–6.4% and reduces the false alarm rate by 0.7–10.2% compared with traditional and other improved evidence theories, proving its validity and feasibility, which provides a certain reference value for multi-sensor information fusion.

Cross-Domain Active Learning for Electronic Nose Drift Compensation.

The problem of drift in the electronic nose (E-nose) is an important factor in the distortion of data. The existing active learning methods do not take into account the misalignment of the data feature distribution between different domains due to drift when selecting samples. For this, we proposed a cross-domain active learning (CDAL) method based on the Hellinger distance (HD) and maximum mean difference (MMD). In this framework, we weighted the HD with the MMD as a criterion for sample selection, which can reflect as much drift information as possible with as few labeled samples as possible. Overall, the CDAL framework has the following advantages: (1) CDAL combines active learning and domain adaptation to better assess the interdomain distribution differences and the amount of information contained in the selected samples. (2) The introduction of a Gaussian kernel function mapping aligns the data distribution between domains as closely as possible. (3) The combination of active learning and domain adaptation can significantly suppress the effects of time drift caused by sensor ageing, thus improving the detection accuracy of the electronic nose system for data collected at different times. The results showed that the proposed CDAL method has a better drift compensation effect compared with several recent methodological frameworks.

Local Normal Approximations and Probability Metric Bounds for the Matrix-Variate T Distribution and Its Application to Hotelling’s T Statistic

In this paper, we develop local expansions for the ratio of the centered matrix-variate T density to the centered matrix-variate normal density with the same covariances. The approximations are used to derive upper bounds on several probability metrics (such as the total variation and Hellinger distance) between the corresponding induced measures. This work extends some previous results for the univariate Student distribution to the matrix-variate setting.

An Integrated Approach for Bearing Health Indicator and Stage Division Using Improved Gaussian Mixture Model and Confidence Value

Bearing prognosis is of paramount and practical importance for rotating machinery. In this article, we propose an integrated approach for bearing performance degradation assessment. First, we propose an improved clustering algorithm, called the Hellinger distance-based regularized Gaussian mixture model (HRGMM). In this model, the Hellinger distance is incorporated to measure the similarity between probability distributions (PDs) of raw data. The manifold regularized GMM is then enhanced to differentiate bearing performance changes. Second, we construct a new health indicator (HI) that combines the Jensen–Rényi divergence and improved confidence value to normalize the difference in PDs between the test condition and healthy condition. It aims to solve the problems of the insensitivity of HI to the incipient defect and its highly fluctuating behavior as the bearing deteriorates over time. Clustering results of the experimental and real bearings show that the HRGMM successfully distinguishes different health states, damage severities, and working conditions. The results of two run-to-failure bearing tests demonstrate that, for each bearing, the HI based on HRGMM drops in a smooth and monotonic manner and accurately identify the incipient defect as the beginning of the slight degradation. Moreover, it can automatically mark the sharp state declines as the beginning of severe degradation and failure stages so that appropriate warnings can be set for follow-up maintenance.

Attention-Based LSTM Model for IFA Detection in Named Data Networking

As one of the next generation networks, Named Data Networking (NDN) performs well on content distribution. However, it is vulnerable against a new type of denial-of-service (DoS) attacks, interest flooding attacks (IFAs), one of the fatal threats to NDN. The attackers request nonexist content to occupy the Pending Interest Table (PIT), and it causes the degradation of network performance. Because of the great harm and strong concealment of this attack, it is urgent to detect and throttle the attack. This paper proposes a detection mechanism based on Long Short-Term Memory (LSTM) with attention mechanism, which uses sequence with different treatments. Once IFA is detected, the Hellinger distance is used to recognize malicious Interest prefix. The simulation results show that the proposed scheme can resist IFA effectively compared to state-of-the-art schemes.

Unsupervised Dynamic Sensor Selection for IoT-Based Predictive Maintenance of a Fleet of Public Transport Buses

In recent years, big data produced by the Internet of Things has enabled new kinds of useful applications. One such application is monitoring a fleet of vehicles in real time to predict their remaining useful life. The consensus self-organized models (COSMO) approach is an example of a predictive maintenance system. The present work proposes a novel Internet of Things based architecture for predictive maintenance that consists of three primary nodes: the vehicle node, the server leader node, and the root node, which enable on-board vehicle data processing, heavy-duty data processing, and fleet administration, respectively. A minimally viable prototype of the proposed architecture was implemented and deployed to a local bus garage in Gatineau, Canada.The present work proposes improved consensus self-organized models (ICOSMO), a fleet-wide unsupervised dynamic sensor selection algorithm. To analyze the performance of ICOSMO, a fleet simulation was implemented. The J1939 data gathered from a hybrid bus was used to generate synthetic data in the simulations. Simulation results that compared the performance of the COSMO and ICOSMO approaches revealed that in general ICOSMO improves the average area under the curve of COSMO by approximately 1.5% when using the Cosine distance and 0.6% when using Hellinger distance.

Dualities and Asymptotic Mixtures Using Functional-Order Differentiation

New definitions for fractional integro-differential operators are presented and referred to as delayed fractional operators. It is shown that delayed fractional derivatives give rise to the notion of functional order differentiation. Functional differentiation can be used to establish dualities and asymptotic mixtures between unrelated theories, something that conventional fractional or integer operators cannot do. In this paper, dualities and asymptotic mixtures are established between arbitrary functions, probability densities, the Gibbs–Shannon entropy and Hellinger distance, as well as higher-dimensional particle geometries in quantum mechanics.

Evaluation of HIV-1 integrase variability by combining computational and probabilistic approaches.

This study aimed at updating previous data on HIV-1 integrase variability, by using effective bioinformatics methods combining different statistical instruments from simple entropy and mutation rate to more specific approaches such as Hellinger distance. A total of 2133 HIV-1 integrase sequences were analyzed in: i) 1460 samples from drug-naïve [DN] individuals; ii) 386 samples from drug-experienced but INI-naïve [IN] individuals; iii) 287 samples from INI-experienced [IE] individuals. Within the three groups, 76 amino acid positions were highly conserved (≤0.2% variation, Hellinger distance: <0.25%), with 35 fully invariant positions; while, 80 positions were conserved (>0.2% to <1% variation, Hellinger distance: <1%). The H12-H16-C40-C43 and D64-D116-E152 motifs were all well conserved. Some residues were affected by dramatic changes in their mutation distributions, especially between DN and IE samples (Hellinger distance ≥1%). In particular, 15 positions (D6, S24, V31, S39, L74, A91, S119, T122, T124, T125, V126, K160, N222, S230, C280) showed a significant decrease of mutation rate in IN and/or IE samples compared to DN samples. Conversely, 8 positions showed significantly higher mutation rate in samples from treated individuals (IN and/or IE) compared to DN. Some of these positions, such as E92, T97, G140, Y143, Q148 and N155, were already known to be associated with resistance to integrase inhibitors; other positions including S24, M154, V165 and D270 are not yet documented to be associated with resistance. Our study confirms the high conservation of HIV-1 integrase and identified highly invariant positions using robust and innovative methods. The role of novel mutations located in the critical region of HIV-1 integrase deserves further investigation.

A multistage distributionally robust optimization approach to water allocation under climate uncertainty

This paper investigates a Multistage Distributionally Robust Optimization (MDRO) approach to water allocation under climate uncertainty. The MDRO is formed by creating sets of conditional distributions (called conditional ambiguity sets) on a finite scenario tree. The distributions in the conditional ambiguity sets remain close to a nominal conditional distribution according a ϕ-divergence (e.g., Kullback-Leibler divergence, Hellinger distance, Burg entropy, etc.). The paper discusses a decomposition algorithm to solve the resulting MDRO with ϕ-divergences, which uses the dual formulation and solves only linear subproblems instead of convex ones. Some properties of the algorithm such as generating feasible policies and valid upper/lower bounds are established. The paper then applies the modeling and solution techniques to allocate water in a rapidly-developing area of Tucson, Arizona. Tucson, like many arid and semi-arid regions around the world, faces considerable uncertainty in its ability to provide water for its citizens in the future. The primary sources of uncertainty in the Tucson region include (1) unpredictable population growth, (2) the availability of water from the Colorado River, and (3) the effects of climate variability on water consumption. This paper integrates forecasts for all these sources of uncertainty into a single optimization model for robust and sustainable water allocation. Then, it uses this model to analyze the value of constructing additional treatment facilities to reduce future water shortages. The results indicate that the MDRO approach can be very valuable for water managers by providing insights to minimize their risks and help them plan for the future.

Biases of the Mean and Shape Properties in CMIP6 Extreme Precipitation Over Central Asia

The global climate models (GCMs) are indispensable for accurately simulating the climate variability and change, and numerous studies have assessed climatic extreme events globally and regionally. However, the shape properties of GCM precipitation extreme simulations, such as measures of asymmetry (e.g., skewness coefficient) and measures of tail heaviness (e.g., kurtosis coefficient), have received far less attention. Here, we address this issue by comparing the performance of 22 GCMs from the Coupled Model Intercomparison Project Phase 6 (CMIP6) in reproducing the statistical properties of ground observations for the period 2001–2014 over typical arid and semiarid Central Asia. We evaluated the performance of the CMIP6 models using novel methodologies to assess biases not only in mean and variation but also in higher order L-moments which involved less bias and variance than the conventional moment approach, including 1) summary statistics as expressed by univariate analysis of L-moments and 2) the bivariate kernel densities of (mean, L-variation) and (L-skewness, L-kurtosis) using the application of the highest probability region (HPR) and applying the Hellinger distance as a measure of agreement. The results show that CMIP6 simulations can reproduce the shape properties of precipitation extremes with the observational datasets and that biases are observed when the mean and variation are examined bivariate. An ensemble mean of the CMIP6 models does not improve the performance of the variation and skewness of the simulated precipitation extremes, while it only slightly constrains the mean and kurtosis error of most metrics. Our results could provide guidance for climate research and improve the statistical properties of CMIP6 models in relation to ground observations.

Higher criticism to compare two large frequency tables, with sensitivity to possible rare and weak differences

We adapt Higher Criticism (HC) to the comparison of two frequency tables which may—or may not—exhibit moderate differences between the tables in some unknown, relatively small subset out of a large number of categories. Our analysis of the power of the proposed HC test quantifies the rarity and size of assumed differences and applies moderate deviations-analysis to determine the asymptotic powerfulness/powerlessness of our proposed HC procedure. Our analysis considers the null hypothesis of no difference in underlying generative model against a rare/weak perturbation alternative, in which the frequencies of N1−β out of the N categories are perturbed by r(logN)/2n in the Hellinger distance; here, n is the size of each sample. Our proposed Higher Criticism (HC) test for this setting uses P-values obtained from N exact binomial tests. We characterize the asymptotic performance of the HC-based test in terms of the sparsity parameter β and the perturbation intensity parameter r. Specifically, we derive a region in the (β,r)-plane where the test asymptotically has maximal power, while having asymptotically no power outside this region. Our analysis distinguishes between cases in which the counts in both tables are low, versus cases in which counts are high, corresponding to the cases of sparse and dense frequency tables. The phase transition curve of HC in the high-counts regime matches formally the curve delivered by HC in a two-sample normal means model.

Near-linear convergence of the Random Osborne algorithm for Matrix Balancing

We revisit Matrix Balancing, a pre-conditioning task used ubiquitously for computing eigenvalues and matrix exponentials. Since 1960, Osborne’s algorithm has been the practitioners’ algorithm of choice, and is now implemented in most numerical software packages. However, the theoretical properties of Osborne’s algorithm are not well understood. Here, we show that a simple random variant of Osborne’s algorithm converges in near-linear time in the input sparsity. Specifically, it balances K in {mathbb {R}}_{ge 0}^{n times n} after O(m varepsilon ^{-2} log kappa ) arithmetic operations in expectation and with high probability, where m is the number of nonzeros in K, varepsilon is the ell _1 accuracy, and kappa = sum _{ij} K_{ij} / ( min _{ij : K_{ij} ne 0} K_{ij}) measures the conditioning of K. Previous work had established near-linear runtimes either only for ell _2 accuracy (a weaker criterion which is less relevant for applications), or through an entirely different algorithm based on (currently) impractical Laplacian solvers. We further show that if the graph with adjacency matrix K is moderately connected—e.g., if K has at least one positive row/column pair—then Osborne’s algorithm initially converges exponentially fast, yielding an improved runtime O(m varepsilon ^{-1} log kappa ). We also address numerical precision issues by showing that these runtime bounds still hold when using O(log (nkappa /varepsilon ))-bit numbers. Our results are established through an intuitive potential argument that leverages a convex optimization perspective of Osborne’s algorithm, and relates the per-iteration progress to the current imbalance as measured in Hellinger distance. Unlike previous analyses, we critically exploit log-convexity of the potential. Notably, our analysis extends to other variants of Osborne’s algorithm: along the way, we also establish significantly improved runtime bounds for cyclic, greedy, and parallelized variants of Osborne’s algorithm.

An efficient geometric approach to quantum-inspired classifications

Optimal measurements for the discrimination of quantum states are useful tools for classification problems. In order to exploit the potential of quantum computers, feature vectors have to be encoded into quantum states represented by density operators. However, quantum-inspired classifiers based on nearest mean and on Helstrom state discrimination are implemented on classical computers. We show a geometric approach that improves the efficiency of quantum-inspired classification in terms of space and time acting on quantum encoding and allows one to compare classifiers correctly in the presence of multiple preparations of the same quantum state as input. We also introduce the nearest mean classification based on Bures distance, Hellinger distance and Jensen–Shannon distance comparing the performance with respect to well-known classifiers applied to benchmark datasets.

Semiparametric modelling of two-component mixtures with stochastic dominance.

In this work, we studied a two-component mixture model with stochastic dominance constraint, a model arising naturally from many genetic studies. To model the stochastic dominance, we proposed a semiparametric modelling of the log of density ratio. More specifically, when the log of the ratio of two component densities is in a linear regression form, the stochastic dominance is immediately satisfied. For the resulting semiparametric mixture model, we proposed two estimators, maximum empirical likelihood estimator (MELE) and minimum Hellinger distance estimator (MHDE), and investigated their asymptotic properties such as consistency and normality. In addition, to test the validity of the proposed semiparametric model, we developed Kolmogorov–Smirnov type tests based on the two estimators. The finite-sample performance, in terms of both efficiency and robustness, of the two estimators and the tests were examined and compared via both thorough Monte Carlo simulation studies and real data analysis.Supplementary InformationThe online version contains supplementary material available at 10.1007/s10463-022-00835-5.

A generalized Rényi divergence for multi-source information fusion with its application in EEG data analysis

The application of multisource information fusion in real-world scenarios is an emerging practice because it effectively uses consistent and complementary data to optimize decision-making. Dempster-Shafer (D-S) evidence theory is prevalent because it competently handles uncertainty problems by assigning basic probability assignments (BPAs) to multielement subsets. However, a counterintuitive result may be obtained when the evidence is highly conflicting. To overcome this flaw, this paper defines a new divergence measurement to quantify the differences between BPAs; we name this new metric the belief Rényi divergence. The belief Rényi divergence takes the number of possible hypotheses into consideration, which makes it a more rational and effective difference measurement in the realm of evidence theory. Additionally, some important properties of the belief Rényi divergence are extensively explored and proven, in which the belief Rényi divergence also connects to Kullback-Leibler divergence, Hellinger distance and χ2 divergence. Moreover, a novel multisource information fusion method is devised based on the proposed belief Rényi divergence and belief entropy. Our proposed belief Rényi divergence can efficiently model the differences between evidence, and the belief entropy is used to calculate the information volume of evidence. Thus, the proposed method can sufficiently exploit the relationships among evidence and the information volume of the evidence itself. Two case studies are illustrated to verify the effectiveness and practicality of the proposed method. Also, an experiment on an iris dataset classification is presented to verify the performance of the proposed method. In addition, an EEG data analysis application demonstrates that the proposed method can be effectively used in real-world applications.

EFFECT OF COMPLEX SAMPLE DESIGN ON DETERMINING COMMON VARIABLES IN STATISTICAL MATCHING METHOD FOR SOCIAL RESEARCH

It is of great importance for researchers to find out different ways of accessing microdata, due to the ever-increasing demand for data and the expectation of reducing the response burden and costs at the same time. In this sense, statistical matching methods have been used extensively to produce new data using existing microdata of surveys and registers recently. It has an increasing application area in social studies such as poverty, deprivation, the effects of newborn on the economic situation of the household, indebtedness and demography, due to the gradual improvement of the micro estimation levels. Selection of matching variables among common variables, at this point, is a critical step in terms of the quality of the microdata to be reached. In the study, while selecting the common variables in order to estimate consumption expenditures by using Statistics on Income and Living Conditions (2018) and Household Budget Survey (2018), weights were added to Hellinger Distance and Spearman2 applications as a new approach. In addition, the effects of design variables (stratum and cluster) were also included in the processes, taking into account the complex structure of both samples. Adding household level weights and design variables to the statistical processes changed the selected or unselected common variables dramatically.

Utility Metrics for Evaluating Synthetic Health Data Generation Methods: Validation Study.

BackgroundA regular task by developers and users of synthetic data generation (SDG) methods is to evaluate and compare the utility of these methods. Multiple utility metrics have been proposed and used to evaluate synthetic data. However, they have not been validated in general or for comparing SDG methods.ObjectiveThis study evaluates the ability of common utility metrics to rank SDG methods according to performance on a specific analytic workload. The workload of interest is the use of synthetic data for logistic regression prediction models, which is a very frequent workload in health research.MethodsWe evaluated 6 utility metrics on 30 different health data sets and 3 different SDG methods (a Bayesian network, a Generative Adversarial Network, and sequential tree synthesis). These metrics were computed by averaging across 20 synthetic data sets from the same generative model. The metrics were then tested on their ability to rank the SDG methods based on prediction performance. Prediction performance was defined as the difference between each of the area under the receiver operating characteristic curve and area under the precision-recall curve values on synthetic data logistic regression prediction models versus real data models.ResultsThe utility metric best able to rank SDG methods was the multivariate Hellinger distance based on a Gaussian copula representation of real and synthetic joint distributions.ConclusionsThis study has validated a generative model utility metric, the multivariate Hellinger distance, which can be used to reliably rank competing SDG methods on the same data set. The Hellinger distance metric can be used to evaluate and compare alternate SDG methods.

The relation between entanglement measure and coherence measure based on Hellinger distance

The relation between entanglement measure and coherence measure based on Hellinger distance