Minimum Discrimination Information Principle Research Articles

An Influencing Factors Analysis of Road Traffic Accidents Based on the Analytic Hierarchy Process and the Minimum Discrimination Information Principle

Safe traffic is an important part of sustainable transportation. Road traffic accidents lead to a large number of casualties and property losses every year. Current research mainly studies some types of traffic accidents and ignores other types of traffic accidents; therefore, taking various types of road traffic accidents as a whole, an overall study of their influencing factors is urgently needed. To improve road traffic safety, taking various types of road traffic accidents as a whole, this paper analyzes the influencing factors and finds out the causative factors of road traffic accidents. A new index system of road traffic accident influencing factors is constructed based on the existing literature and real traffic data, and their subjective weights and objective weights are obtained by the analytic hierarchy process based on the subjective data and the normalization of the actual traffic data for Yizheng City, Yangzhou, China from January 2020 to December 2020, where the subjective weights are the main weights, and comprehensive weights are obtained by the minimum discrimination information principle correcting the subjective weights with the objective weights. Finally, the global weights, their ranks, and their weight differences are obtained. The main findings are as follows: (1) compared with the real traffic data, experts generally overestimate the impact of road factors on traffic accidents and underestimate the impact of human factors on traffic accidents; (2) in the first-level, human factors and road factors are the causative factors; (3) in the second-level, “motor vehicle drivers’ misconduct”, “road condition”, and “road section” are the causative factors; and (4) in the third-level, “slippery road”, “rain and snow weather”, “intersection”, and “untimely braking” are the causative factors. The research results can provide some scientific basis for improving road traffic safety.

An Optimization Model for a Desert Railway Route Scheme Based on Interval Number and TOPSIS

The construction of desert railways inevitably destructs the environment and aggravates the wind–sand damage along the line. A reasonable railway route is an effective measure to avoid blown sand hazards, save construction costs, and reduce environmental damage. Currently, the selection methods for the railway route scheme are to analyze the qualitative indicators and quantitative indicators separately, and there are few decision-making models for the desert railway scheme. Therefore, this study aims to propose a comprehensive quantitative optimization model of the route scheme for the desert railway. Based on the design principles of hazard reduction, the evaluation index system of the desert railway route is first constructed, including railway design factors, wind-blown sand hazard factors, environmental impact factors, and operation condition factors. Subsequently, the subjective weights and objective weights are combined to obtain the comprehensive weights of the index by utilizing the principle of minimum discrimination information. Finally, the interval number is employed to quantify the linguistic fuzzy number of qualitative indicators, and the optimization model of the route scheme for the desert railway is constructed based on the technique for order preference by similarity to an ideal solution (TOPSIS). The model is verified using the Minfeng-Yuhu section in the Hotan–Ruoqiang railway as the case study. The achieved results reveal that this model enhances the accuracy and efficiency of the railway scheme decision-making and provides a theoretical basis for the optimal design and sand damage control of the desert railway.

A discrepant information selection mechanism for cooperative sensors

Aiming at the discrepancy of information raised by different fields of view of cooperative sensors, this paper proposes a fusion rule based on a new information-theoretic cost function. Specifically, the optimal function is proposed based on the principle of Minimum Discrimination Information (MDI), where the fusion weights are the functions of the label set. The solution of the optimal function exhibits the information selection mechanism, i.e., the GLMB components of the global multitarget density are selected among the local GLMB components based on their weights. Besides, to evaluate the performance of the proposed method, we also propose the overlapping indicator which assesses the similarity among the FoVs of cooperative sensors. The simulation results demonstrate that the proposed method achieves robust performance under different values of the overlapping indicator.

Diagnosis of Critical Risk Sources in the Operation Safety of the Central Route Project of South-to-North Water Diversion Based on the Improved FMEA Method

For the inaccurate description of the failure level in the traditional failure mode and effects analysis (FMEA) method, the research uses the fuzzy evidence reasoning theory to improve the traditional failure mode and effects analysis (FMEA) method. Based on the subjective weight determined by the analytic hierarchy process and the objective weight determined by the gray correlation degree method, we get the combined weight of risk factors through the principle of minimum discrimination information. Combined with the technique for order of preference by similarity to ideal solution (TOPSIS), an improved risk sequence number (IRPN) method was proposed to diagnose the key risk sources. In the case study on a canal section of the Central Route Project of South-to-North Water Diversion in Henan, the key risk factors for the operation safety of the project are identified as rainstorm and flood, geological conditions, geological disasters, and design safety coefficient, and the corresponding prevention measures are put forward to provide help for the safe operation of the Central Route Project of South-to-North Water Diversion.

An Action Principle for Biological Systems

In the analysis of physical systems, the forces and mechanics of all system changes as codified in the Newtonian laws can be redefined by the methods of Lagrange and Hamilton through an identification of the governing action principle as a more general framework for dynamics. For the living system, it is the dimensional and relational structure of its biologic continuum (both internal and external to the organism) that creates the signature informational metrics and course configurations for the action dynamics associated with any natural systems phenomena. From this dynamic information theoretic framework, an action functional can be also derived in accordance with the methods of Lagrange. The experiential process of acquiring information and translating it into actionable meaning for adaptive responses is the driving force for changes in the living system. The core axiomatic procedure of this adaptive process should include an innate action principle that can determine the system’s directional changes. This procedure for adaptive system reconciliation of divergences from steady state within the biocontinuum can be described by an information metric formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback’s Principle of Minimum Discrimination Information powered by the mechanics of survival replicator dynamics. This entropic driven trajectory naturally minimizes the biocontinuum information gradient differences like a least action principle and is an inference procedure for directional change. If the mathematical expression of this process is the Lagrangian integrand for adaptive changes within the biocontinuum, then it is also considered as an action functional for the living system.

SDGs-Based River Health Assessment for Small- and Medium-Sized Watersheds

A river health assessment index system was established, focusing on the realistic needs of county sustainable development and the refined management of small- and medium-sized watersheds. The index system takes into consideration the United Nations’ Sustainable Development Goals (SDGs) and the vulnerability characteristics of small- and medium-sized watershed ecosystems and consists of 15 indicators in four areas: clean water, sanitation, the present status of biodiversity and threats to biodiversity. This paper uses the minimum discrimination information principle to construct a dynamic combination-weighting technology composed of a subjective weighting method (document frequency method) and an objective weighting method (entropy weight method). Using the fuzzy matter-element analysis theory, a comprehensive river health assessment technology system was constructed. Baoxing County was chosen as the research area and the results reveal that: (1) Key indicators are the biodiversity index of fish, water use intensity, endemic or indicative species retention, and chemical oxygen demand (COD) emissions. (2) The Euclid approach degree of Baoxing County indicates that the entire river is in a moderate state of health. In the future, towns must take targeted measures to coordinate the relationship between the ecological environment and socio-economic development, and enhancement and releasing must be prioritised.

Distributed Multi-Sensor Fusion of PHD Filters With Different Sensor Fields of View

The paper addresses the problem of distributed multi-target tracking (MTT) in a network of sensors having different fields of view (FoVs). Probability hypothesis density (PHD) filters are running locally in every sensor for MTT. The weighted arithmetic average (WAA) fusion rule is employed to fuse the multiple local PHD densities due to its computational efficiency. First, we provide a theoretical analysis showing that the standard WAA fusion among sensors with different FoVs is unsuitable from the perspective of the principle of minimum discrimination information (PMDI). In fact, the information inconsistency among sensors due to the different FoVs unavoidably leads to an underestimation of the fused PHD. Then, motivated by the analysis, we devise two novel approaches to address the different FoV issue. The first approach accounts for the case where the sensor FoVs are known and time-invariant. The second one deals with the more complicated case where the actual sensor FoVs can be cropped due to unknown line of sight obstructions or sensors can obtain the information outside their current FoVs because of platform movement or information feedback. The essence of the proposed approaches is to perform the WAA in a more robust way by employing a set of state-dependent fusion weights which are computed online. The Gaussian mixture implementations of the proposed methods are also presented. Various simulation experiments, including a challenging tracking scenario involving six sensors with different FoVs and also random line of sight obstructions, are designed to demonstrate the efficacy of the proposed fusion approaches.

The generalised maximum α entropy principle

Generalisations of maximum entropy principle (MEP) and minimum discrimination information principle (MDIP) are described by Kapur and Kesavan (1989) . In this paper, we used generalised entropies and replaced Shannon entropy with Tsallis entropy when α = 2 . The generalisation has been achieved by the entropy maximisation postulate and examining its consequences . The inverse principles which are inherent in the maximum α entropy and minimum discrimination α entropy are made in the new methodology.

Robust Distributed Fusion With Labeled Random Finite Sets

This paper considers the problem of the distributed fusion of multi-object posteriors in the labeled random finite set filtering framework, using Generalized Covariance Intersection (GCI) method. Our analysis shows that GCI fusion with labeled multi-object densities strongly relies on label consistencies between local multi-object posteriors at different sensor nodes, and hence suffers from a severe performance degradation when perfect label consistencies are violated. Moreover, we mathematically analyze this phenomenon from the perspective of Principle of Minimum Discrimination Information and the so called yes-object probability. Inspired by the analysis, we propose a novel and general solution for the distributed fusion with labeled multi-object densities that is robust to label inconsistencies between sensors. Specifically, the labeled multi-object posteriors are firstly marginalized to their unlabeled posteriors which are then fused using GCI method. We also introduce a principled method to construct the labeled fused density and produce tracks formally. Based on the developed theoretical framework, we present tractable algorithms for the family of generalized labeled multi-Bernoulli (GLMB) filters including $\delta$-GLMB, marginalized $\delta$-GLMB and labeled multi-Bernoulli filters. The robustness and efficiency of the proposed distributed fusion algorithm are demonstrated in challenging tracking scenarios via numerical experiments.

Research on Reliability Allocation Method for NC Grinding Machine

Reliability allocation is a collection problem of engineering decision, multiple factors comprehensive balance and process optimization. Considering that both the factors that influenced the reliability allocation and their weights have the characteristics of uncertainty, which always be ignored .Therefore a subjective and objective combined weights method that combined the entropy method and Interval analysis method was proposed. Taking NC grinding machine as an example, firstly, establish the reliability objective function based on the minimum discrimination information principle, and employ the Lagrange multiplier to get the combined weights of the 6 factors. Then use the fuzzy comprehensive allocation method to obtain the reliability allocation results, which was compared with the actual accumulated data, so that the feasibility and effectiveness of this method was verified.

Rational approximations of spectral densities based on the Alpha divergence

We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by selecting the spectral density having minimum “distance” from under the constraint corresponding to imposing the given second-order statistics. We analyze the structure of the optimal solutions as the minimized “distance” varies in the Alpha divergence family. We show that the corresponding approximation problem leads to a family of rational solutions. Secondly, such a family contains the solution which generalizes the Kullback–Leibler solution proposed by Georgiou and Lindquist in 2003. Finally, numerical simulations suggest that this family contains solutions close to the non-rational solution given by the principle of minimum discrimination information.

An information-theoretical perspective on weighted ensemble forecasts

Summary This paper presents an information-theoretical method for weighting ensemble forecasts with new information. Weighted ensemble forecasts can be used to adjust the distribution that an existing ensemble of time series represents, without modifying the values in the ensemble itself. The weighting can, for example, add new seasonal forecast information in an existing ensemble of historically measured time series that represents climatic uncertainty. A recent article in this journal compared several methods to determine the weights for the ensemble members and introduced the pdf-ratio method. In this article, a new method, the minimum relative entropy update (MRE-update), is presented. Based on the principle of minimum discrimination information, an extension of the principle of maximum entropy (POME), the method ensures that no more information is added to the ensemble than is present in the forecast. This is achieved by minimizing relative entropy, with the forecast information imposed as constraints. From this same perspective, an information-theoretical view on the various weighting methods is presented. The MRE-update is compared with the existing methods and the parallels with the pdf-ratio method are analysed. The paper provides a new, information-theoretical justification for one version of the pdf-ratio method that turns out to be equivalent to the MRE-update. All other methods result in sets of ensemble weights that, seen from the information-theoretical perspective, add either too little or too much (i.e. fictitious) information to the ensemble.

The Evaluation of Drought Degree in Irrigation District Based on Variable Fuzzy Evaluation Method

In view of the disadvantages of drought evaluation methods in irrigation district, the variable fuzzy sets theory has been adopted in this paper to establish the variable fuzzy sets drought evaluation method in irrigation district. At the same time, the improved entropy method has been employed to determine the objective weights and the minimum discrimination information principle has been used to combine the subjective weights with the objective weights, which have eliminated the one-sidedness of the application of a single weighting preferred program.

Deformed statistics Kullback–Leibler divergence minimization within a scaled Bregman framework

The generalized Kullback–Leibler divergence (K–Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K–Ld)] is here reconciled with the theory of Bregman divergences for expectations defined by normal averages, within a measure-theoretic framework. Specifically, it is demonstrated that the dual generalized K–Ld is a scaled Bregman divergence. The Pythagorean theorem is derived from the minimum discrimination information principle using the dual generalized K–Ld as the measure of uncertainty, with constraints defined by normal averages. The minimization of the dual generalized K–Ld, with normal averages constraints, is shown to exhibit distinctly unique features.

A family of empirical likelihood functions and estimators for the binary response model

The minimum discrimination information principle is used to identify an appropriate parametric family of probability distributions and the corresponding maximum likelihood estimators for binary response models. Estimators in the family subsume the conventional logit model and form the basis for a set of parametric estimation alternatives with the usual asymptotic properties. Sampling experiments are used to assess finite sample performance.

Principle of Minimum Discrimination Information and Replica Dynamics

Dynamics of many complex systems can be described by replicator equations (RE). Here we present an effective method for solving a wide class of RE based on reduction theorems for models of inhomogeneous communities. The solutions of the RE minimize the discrimination information of the initial and current distributions at each point of the system trajectory, not only at the equilibrium, under time-dependent constraints. Applications to inhomogeneous versions of some conceptual models of mathematical biology (logistic and Ricker models of populations and Volterra’ models of communities) are given.

Replicator Equations and the Principle of Minimal Production of Information

Many complex systems in mathematical biology and other areas can be described by the replicator equation. We show that solutions of a wide class of replicator equations minimize the KL-divergence of the initial and current distributions under time-dependent constraints, which in their turn, can be computed explicitly at every instant due to the system dynamics. Therefore, the Kullback principle of minimum discrimination information, as well as the maximum entropy principle, for systems governed by the replicator equations can be derived from the system dynamics rather than postulated. Applications to the Malthusian inhomogeneous models, global demography, and the Eigen quasispecies equation are given.

Crop Area Distributions for Optimal Yield

In the present communication maximum entropy principle and minimum discrimination information principle have been explained and their applications in crop area distributions for optimal yield have been studied. Two solutions of a crop yield optimization problem have also been obtained.

The generalized maximum entropy principle

Generalizations of the maximum entropy principle (MEP) of E.T. Jaynes (1957) and the minimum discrimination information principle (MDIP) of S. Kullback (1959) are described. The generalizations have been achieved by enunciating the entropy maximization postulate and examining its consequences. The inverse principles which are inherent in the MEP and MDIP are made quite explicit. Several examples are given to illustrate the power and scope of the generalized maximum entropy principle that follows from the entropy maximization postulate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Constrained Discrimination via MDI Estimation: The use of Additional Information in Segmentation Analysis

The authors demonstrate a general, flexible constrained discrimination method for testing hypotheses about the segmentability of a target population using categorical descriptors when additional information is available. The method applies the principle of minimum discrimination information (MDI) to the estimation of multinomial probabilities under linear equality and inequality constraints.