Maximum Entropy Estimation Research Articles

Asymptotic Efficiency of Maximum Entropy Estimates

The problem of entropy estimation of probability density functions with allowance for real data is posed (the maximum entropy estimation (MEE) problem). Global existence conditions for the implicit dependence of Lagrange multipliers on data collection are obtained. The asymptotic efficiency of maximum entropy estimates is proved.

Identifying Significant Cost-Influencing Factors for Sustainable Development in Construction Industry Using Structural Equation Modelling

Construction projects are typically conducted in a complex and dynamic environment in which the accumulation of many interrelated factors causes high uncertainty. Many factors may have negative effects on construction projects and thus cause project cost overruns. The aim of this study is to identify significant cost-influencing factors for sustainable development in construction. Considering the effects of economic and environmental factors on project cost is indeed a challenging task due to the shortage of appropriate methodology. This study examines the relationships between cost-influencing factors and construction project cost by using a structural equation model based on the generalized maximum entropy (GME) and Bayesian estimation methods. The advantages of GME and Bayesian methods are discussed, and results obtained from the statistical analysis are provided for illustration. The results can enhance cost performance through the identification and evaluation of the cost-influencing factors. The improved project performance is considered as an important step to transit into a sustainable development in construction. The sustainable development may greatly affect the emission reduction target of the industry.

Developing nonuniform sampling strategies to improve sensitivity and resolution in 1,1-ADEQUATE experiments.

Nonuniform sampling (NUS) strategies are developed for acquiring highly resolved 1,1-ADEQUATE spectra, in both conventional and homodecoupled (HD) variants with improved sensitivity. Specifically, the quantile-directed and Poisson gap methods were critically compared for distributing the samples nonuniformly, and the quantile schedules were further optimized for weighting. Both maximum entropy and iterative soft thresholding spectral estimation algorithms were evaluated. All NUS approaches were robust when the degree of data reduction is moderate, on the order of a 50% reduction of sampling points. Further sampling reduction by NUS is facilitated by using weighted schedules designed by the quantile method, which also suppresses sampling noise well. Seed independence and the ability to specify the sample weighting in quantile scheduling are important in optimizing NUS for 1,1-ADEQUATE data acquisition. Using NUS yields an improvement in sensitivity, while also making longer evolution times accessible that would be difficult or impractical to attain by uniform sampling. Theoretical predictions for the sensitivity enhancements in these experiments are in the range of 5-20%; NUS is shown to disambiguate weak signals, reveal some n JCC correlations obscured by noise, and improve signal strength relative to uniform sampling in the same experimental time. This work presents sample schedule development for applying NUS to challenging experiments. The schedules developed here are made available for general use and should facilitate the broader utilization of ADEQUATE experiments (including 1,1-, 1,n-, and HD- variants) for challenging structure elucidation problems.

An improved method for predicting water shortage risk in the case of insufficient data and its application in Tianjin, China

It is very important to estimate the parameters of a risk prediction model in the case of small samples. This paper proposed an improved method for predicting water shortage risk in situations when insufficient data are available. The new method (maximum entropy estimation, MEE) does not require the data about water shortage risk but only a few data about the risk factors. Twelve simulations or experiments were made to evaluate the performance of MEE under different small sample size and compared with the maximum likelihood estimation (MLE) which requires a large amount of data about risk and its factors, and two models which require small samples about risk and risk factors. The result shows that MEE performs much better than MLE, and has an advantage over the two models. Water shortage risks in 2020 in all the districts or counties of Tianjin were predicted by using the new method. The result shows that the values of water shortage risk in most of the districts or counties of Tianjin are very high when the transferred and unconventional water are not used. After using the transferred and unconventional water, all the values of water shortage risk decline considerably.

Modified Entropy Estimator Using a Haar Matrix to Fit the Weibull Growth Model

It is well known that the Generalized Maximum Entropy method can be used to fit linear regression models, especially as they are not restricted by the conditions to be verified as are other classical methods. Therefore, in this paper, a new method for estimating the parameters of the four-parameter Weibull growth model was proposed using the Generalized Maximum Entropy function by fitting data based on the Haar matrix which was used in the wavelet method. The suggested and classical entropy estimators for Weibull growth model parameters were compared using simulation and the preference for the suggested method estimator was shown. The Modified Generalized Maximum Entropy estimator was applied to the real data representing annual Iraqi oil production for the period 2010–2017. Iraqi crude oil production for the year 2022 was predicted and appeared as 4.4 million bb/day.

Study on Temperature Recognition of Thermal Paint Based on Color Camera

As a temperature-sensing material, the thermal paint will show different colors at different temperatures, so the temperature of the thermal paint can be judged by observing the color. It is an efficient way to identify the color of the thermal paint by the color image, so the calibration of the color camera is very important. The main work of this paper is to calibrate a color industrial camera and compare our proposed method with several commonly used methods. Finally, it is concluded that the proposed method combining BP neural network and maximum entropy estimation works best.

Female Labor Force Participation in Five Selected Mena Countries: An Age- Period-Cohort Analysis (Algeria, Egypt, Jordan, Palestine and Tunisia)

This paper considers the female labor force participation (FLFP) behavior over the past decade in five MENA countries namely, Algeria, Egypt, Jordan, Palestine and Tunisia. Low FLFP rates in these countries, as it is in other MENA countries, are well documented. We conduct synthetic panel analysis using age-period-cohort (APC) methodology and decompose FLFP rates into age, period and cohort effects. We present our results with Hanoch-Honig/Deaton-Paxson normalization and maximum entropy estimation approaches to the APC methodology in order to observe robustness of our results. We first study the aggregate FLFP and note the differentials in age, period and cohort effects across the countries we consider.The analysis is carried also out by rural/urban regional differentiation, marital status and educational attainment. Implications of our results for possible government policies to increase FLFP rates are discussed.

Female Labor Force Participation in Five Selected MENA Countries: An Age-Period-Cohort Analysis (Algeria, Egypt, Jordan, Palestine and Tunisia)

This paper considers the female labor force participation (FLFP) behavior over the past decade in five MENA countries namely, Algeria, Egypt, Jordan, Palestine and Tunisia. Low FLFP rates in these countries, as it is in other MENA countries, are well documented. We conduct synthetic panel analysis using age-period-cohort (APC) methodology and decompose FLFP rates into age, period and cohort effects. We present our results with Hanoch-Honig/Deaton-Paxson normalization and maximum entropy estimation approaches to the APC methodology in order to observe robustness of our results. We first study the aggregate FLFP and note the differentials in age, period and cohort effects across the countries we consider.The analysis is carried also out by rural/urban regional differentiation, marital status and educational attainment. Implications of our results for possible government policies to increase FLFP rates are discussed.

Expiry Dates, Consumer Behavior, and Food Waste: How Would Italian Consumers React If There Were No Longer “Best Before” Labels?

Much research has been carried out on food losses and waste in the various stages of the food supply chain, consolidating the “fight” against food waste as one of the most important challenges in industrialized countries. Numerous different studies have focused on food waste at the household level, identifying both the multiple causes linked to this behavior and the factors that can drive towards the reduction of food waste. In this paper, a different approach was used, trying to analyze different individuals’ reactions to a concrete action consisting of removing “best before” labels from some food products, following the recent proposal by European Union to simplify date marking. How could any action in this area be implemented in every single country? Bearing in mind the general results of the cross-sectional official survey Flash Eurobarometer n. 425, the purpose of this study was to go deeper into the study of how consumers would behave if the expiry date were no longer available on a pack of spaghetti. The heterogeneity observed in the possible alternative reactions across European Union 28 countries, as well as by considering the importance played by the local context in which individuals reside led us to focus on a single country, and specifically on the Italian context, as an example of country in which citizens have a higher average level of knowledge about expiration dates than the global EU28 citizens, but where, at the same time, there is a more conservative behavior regarding using a product with no expiry date. The multinomial regression model—estimated using the generalized maximum entropy estimator—enabled us to identify different profiles and groups of individuals with which—as a suggestion to policy makers—it would be first necessary to intervene in order to standardize the level of knowledge on this specific topic. In this direction, territorial macro-areas proved to be strongly associated with the various reactions; the probability of consuming or throwing away was found to significantly differ across all the studied regional macro-areas, with a higher likelihood of throwing away the product with no best-before date in southern regions.

On the estimation of Okun’s coefficient in some countries in Latin America: a comparison between OLS and GME estimators

We explore Okun’s coefficient in several Latin American countries for the period from 1995 to 2017 and compare the results obtained using ordinary least squares (OLS) and generalised maximum entropy (GME) estimators. There are several advantages in considering the GME estimator over traditional regression approaches. First, it can estimate the parameters of an equation without imposing constraints on the probability distribution of the errors. Second, empirical and simulation studies available in the literature showed that GME worked well for ill-posed problems (e.g. when a model estimate is performed using a small sample of data). Among the main findings, we confirm the inverted relationship between changes in the unemployment rate and real gross domestic product growth in the explored countries except for Peru. Okun’s coefficient and the associated confidence intervals obtained by applying GME were very close to those obtained from OLS. Therefore, we did not observe a gain when using the GME estimator rather than the classic OLS approach.

Cell‐based maximum entropy approximants for three‐dimensional domains: Application in large strain elastodynamics using the meshless total Lagrangian explicit dynamics method

SummaryWe present the cell‐based maximum entropy (CME) approximants in E3 space by constructing the smooth approximation distance function to polyhedral surfaces. CME is a meshfree approximation method combining the properties of the maximum entropy approximants and the compact support of element‐based interpolants. The method is evaluated in problems of large strain elastodynamics for three‐dimensional (3D) continua using the well‐established meshless total Lagrangian explicit dynamics method. The accuracy and efficiency of the method is assessed in several numerical examples in terms of computational time, accuracy in boundary conditions imposition, and strain energy density error. Due to the smoothness of CME basis functions, the numerical stability in explicit time integration is preserved for large time step. The challenging task of essential boundary condition (EBC) imposition in noninterpolating meshless methods (eg, moving least squares) is eliminated in CME due to the weak Kronecker‐delta property. The EBCs are imposed directly, similar to the finite element method. CME is proven a valuable alternative to other meshless and element‐based methods for large‐scale elastodynamics in 3D. A naive implementation of the CME approximants in E3 is available to download at https://www.mountris.org/software/mlab/cme.

Determinants of non-cash payments in Asian countries

Non-cash payments, such as payment cards and digital payment, are more efficient ways to complete transactions when compared to cash payment. This study investigates the factors that influence the use of non-cash payments in 10 Asian countries, namely China, India, Indonesia, Japan, Malaysia, Philippines, Singapore, South Korea, Thailand, and Vietnam. A panel data is used in this study and the period 2016-2017 is considered. To address the ill-posed problem caused by limited observations, generalized maximum entropy (GME) estimator is employed. The purposes of the study are to identify the cross-country determinants of non-cash payments and prove that GME estimator is the most effective estimation method. The results of data show that online banking penetration and debit card penetration are important factors boosting non-cash payments. In addition, the sales of desktop-PCs and the number of individuals who overed 35 years are the determinants of non-cash payments.

Peridynamic Petrov–Galerkin method: A generalization of the peridynamic theory of correspondence materials

The Peridynamic Petrov–Galerkin (PPG) method is a meshfree approach based on the peridynamic integro-differential form of the momentum equation. The spurious oscillations in the common peridynamic correspondence formulation are investigated. They occur due to an inadmissible linearized mapping of the family deformation field. This leads to a generalized correspondence formulation, which contains the common formulation as a special case. It is based on the weak form of the peridynamic momentum equation. Test and trial function requirements are examined which ensure an exact imposition of Dirichlet and Neumann boundary conditions and Weighted Least Square (WLS) shape functions as well as Local Maximum Entropy (LME) approximants are utilized to examine the PPG Method. A consistent linearization is provided, which can also be used to speed up common implicit peridynamic correspondence codes. It is used in an implicit quasistatic framework to investigate the impact of different shape function combinations. Test cases show that low-energy modes can be prevented by the PPG Method and highlight the fast convergence and stability.

Maximum Entropy Derived Statistics of Sound-Speed Structure in a Fine-Grained Sediment Inferred From Sparse Broadband Acoustic Measurements on the New England Continental Shelf

Marginal probability distributions for parameters representing an effective sound-speed structure of a fine-grained sediment are inferred from a data ensemble maximum entropy method that utilizes a sparse spatially distributed set of received pressure time series resulting from multiple explosive sources in a shallow-water ocean environment possessing significant spatial variability of the seabed. A remote sensing seabed acoustics experiment undertaken in March 2017 off the New England Shelf was designed so that multiple independent analyses could infer the statistical properties of the seabed. The current analysis incorporates the measured horizontal variability from interpretations of a subbottom profiling survey of the experimental area. An idealized range- and azimuth-dependent parameterization of the seabed is derived from identification of horizons within the seabed that define multiple sediment layers. A sparse set of explosive charges were deployed on circular tracks with radii of about 2, 4, and 6.5 km with an acoustic array at the center to correlate a set of random measurements to physical acoustic processes that characterize the seabed. The mean values of a surface sound speed ratio and a linear sound speed gradient for the fine-grained sediment layer derived from 12 data samples processed in the 25-275-Hz band provide an estimate of the effective sound-speed structure in a 130-km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> area. The inferred sediment sound speed values are evaluated by predicting measured time series data not used in the statistical inference, and are also compared to historical measurements. Finally, the low-frequency maximum entropy estimate of the sediment sound speed along with physical measurements derived from piston core measurements are utilized to estimate the sediment grain bulk modulus.

Maximum entropy: a stochastic frontier approach for electricity distribution regulation

The literature on incentive-based regulation in the electricity sector indicates that the size of this sector in a country constrains the choice of frontier methods as well as the model specification itself to measure economic efficiency of regulated firms. The aim of this study is to propose a stochastic frontier approach with maximum entropy estimation, which is designed to extract information from limited and noisy data with minimal statements on the data generation process. Stochastic frontier analysis with generalized maximum entropy and data envelopment analysis—the latter one has been widely used by national regulators—are applied to a cross-section data on thirteen European electricity distribution companies. Technical efficiency scores and rankings of the distribution companies generated by both approaches are sensitive to model specification. Nevertheless, the stochastic frontier analysis with generalized maximum entropy results indicate that technical efficiency scores have similar distributional properties and these scores as well as the rankings of the companies are not very sensitive to the prior information. In general, the same electricity distribution companies are found to be in the highest and lowest efficient groups, reflecting weak sensitivity to the prior information considered in the estimation procedure.

Analyzing Regional Agricultural Production Responses using a Positive Mathematical Programming Method

This study constructs regional crop production models of 8 cities in Korea using the PMP Leontief-quadratic and the generalized-CES models suggested by M&eacute;rel and Bucaram (2010) and M&eacute;rel et al. (2011). A generalized maximum entropy estimation method was used to derive the set of supply elasticity estimates allowing a complete calibration of the models. We demonstrate that those two PMP models fit the Korean regional data quite well. The impacts of two policy changes, raising the rice producer price under the rice direct payment system and raising the minimum wage for hired rural labor were simulated. Our simulation results show that the policy impacts are varying over region and crop. Moreover, it is shown that the choice of the functional specification substantially affects the direction and the magnitudes of the policy impacts. More specifically, production responses are more flexible in the CES specification rather than in the Loentief specification, and the former specification suggests that a substantial increase in rural minimum wage may result in a decline in capital and labor employment in rural areas while the latter specification suggests that the overall resource use in rural areas will not be affected by the policy.

Maximum a posteriori probability estimates for quantum tomography

Using a Bayesian methodology, we introduce the maximum a posteriori~(MAP) estimator for quantum state and process tomography. The maximum likelihood, hedged maximum likelihood, maximum likelihood-maximum entropy estimator, and estimators of this general type, can be viewed as special cases of the MAP estimator. The MAP, like the Bayes mean estimator includes prior knowledge, however for cases of interest to tomography can take advantage of convex optimization tools making it numerically easier to compute. We show how the MAP and other Bayesian quantum state estimators can be corrected for noise produced if the quantum state passes through a noisy quantum channel prior to measurement.

A New Efficient Expression for the Conditional Expectation of the Blind Adaptive Deconvolution Problem Valid for the Entire Range ofSignal-to-Noise Ratio.

In the literature, we can find several blind adaptive deconvolution algorithms based on closed-form approximated expressions for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output), involving the maximum entropy density approximation technique. The main drawback of these algorithms is the heavy computational burden involved in calculating the expression for the conditional expectation. In addition, none of these techniques are applicable for signal-to-noise ratios lower than 7 dB. In this paper, I propose a new closed-form approximated expression for the conditional expectation based on a previously obtained expression where the equalized output probability density function is calculated via the approximated input probability density function which itself is approximated with the maximum entropy density approximation technique. This newly proposed expression has a reduced computational burden compared with the previously obtained expressions for the conditional expectation based on the maximum entropy approximation technique. The simulation results indicate that the newly proposed algorithm with the newly proposed Lagrange multipliers is suitable for signal-to-noise ratio values down to 0 dB and has an improved equalization performance from the residual inter-symbol-interference point of view compared to the previously obtained algorithms based on the conditional expectation obtained via the maximum entropy technique.

On the use of local maximum entropy approximants for Cahn–Hilliard phase-field models in 2D domains and on surfaces

We apply a local maximum entropy (LME) approximation scheme to the fourth order phase-field model for the traditional Cahn–Hilliard theory. The discretization of the Cahn–Hilliard equation by Galerkin method requires at least C1-continuous basis functions. This requirement can be fulfilled by using LME shape functions which are C∞-continuous. In this case, the primal variational formulations of the fourth-order partial differential equation are well defined and integrable. Hence, there is no need to split the fourth-order partial differential equation into two second-order partial differential equations; this splitting scheme is a common practice in mixed finite element formulations with C0-continuous Lagrange shape functions. Furthermore, we use a general and simple numerical method such as statistical manifold learning technique that allows dealing with general point set surfaces avoiding a global parameterization, which can be applied to tackle surfaces of complex geometry and topology, and to solve Cahn–Hilliard equation on general surfaces. Finally, the flexibility and robustness of the presented methodology is demonstrated for several representative numerical examples.

Enhanced local maximum-entropy approximation for stable meshfree simulations

We introduce an improved meshfree approximation scheme which is based on the local maximum-entropy strategy as a compromise between shape function locality and entropy in an information-theoretical sense. The improved version is specifically designed for severe, finite deformation and offers significantly enhanced stability as opposed to the original formulation. This is achieved by (i) formulating the quasistatic mechanical boundary value problem in a suitable updated-Lagrangian setting, (ii) introducing anisotropy in the shape function support to accommodate directional variations in nodal spacing with increasing deformation and eliminate tensile instability, (iii) spatially bounding and evolving shape function support to restrict the domain of influence and increase efficiency, (iv) truncating shape functions at interfaces in order to stably represent multi-component systems like composites or polycrystals. The new scheme is applied to benchmark problems of severe elastic and elastoplastic deformation that demonstrate its performance both in terms of accuracy (as compared to exact solutions and, where applicable, finite element simulations) and efficiency. Importantly, the presented formulation overcomes the classical tensile instability found in most meshfree interpolation schemes, as shown for stable simulations of, e.g., the inhomogeneous extension of a hyperelastic block up to 100% or the torsion of a hyperelastic cube by 200° — both in an updated Lagrangian setting and without the need for remeshing.