Distribution For Modeling Data Research Articles

Task-Aware Compressed Sensing With Generative Adversarial Networks

In recent years, neural network approaches have been widely adopted for machine learning tasks, with applications in computer vision. More recently, unsupervised generative models based on neural networks have been successfully applied to model data distributions via low-dimensional latent spaces. In this paper, we use Generative Adversarial Networks (GANs) to impose structure in compressed sensing problems, replacing the usual sparsity constraint. We propose to train the GANs in a task-aware fashion, specifically for reconstruction tasks. We also show that it is possible to train our model without using any (or much) non-compressed data. Finally, we show that the latent space of the GAN carries discriminative information and can further be regularized to generate input features for general inference tasks. We demonstrate the effectiveness of our method on a variety of reconstruction and classification problems.

Bit-wise Pseudo-Bayes genetic algorithms to model data distributions

This work introduces a method to generate implicit models from data. The algorithm is based on Bayesian networks, discrete codification and genetic algorithms. The concept of bit-wise Pseudo-Bayes networks is introduced in this work. It refers to Bayesian networks generated from discretized data. The network describes the model in function of the correlations between bits. The model is consider implicit in the sense the meaning of the original variables is lost during discretization, but it can provide random samples with a distribution that is similar to the one of the original data. These samples can be the input of other algorithms that rely on samples of data in a transparent fashion. Moreover, this approach alleviates the problem of storing and handling of larges volumes of data, a common occurrence in modern data science, and circumvent the problems of identification process. The algorithm to generate bit-wise Pseudo-Bayes models is described in detail, and introduces innovations to representation of Bayesian networks based on extended chain structures. Also, it introduces new discretization methods and compares them to others reported in the literature, which have been mainly used to evolutionary continuous optimization. The performance of the proposed algorithm is studied using two data sets: prices data from the stock of the Dow Jones industrial average, and prices data from the stocks of the Mexican Índice de precios y cotizaciones. The proposed method is compared against other discrete modeling techniques reported in the literature, attaining a higher performance. The results indicate direct discretization methods were effective when they are coupled with Bayesian networks, but further research is needed to guarantee scalability. The study indicated the Dow Jones data set was more difficult than the Mexican index data set, but this was attributed to 2008 American crisis.

IMPLEMENTASI ALGORITMA EXPECTATION-MAXIMIZATION UNTUK ESTIMASI PARAMETER MODEL DISTRIBUSI CAMPURAN

Mixture distribution is a very flexible distribution for modeling data. If the mixture distribution fitted to the data, the parameters are generally not known. This paper examines the estimation problem of the distribution mixture parameter. The method used to estimate the parameters of a mixture distribution is the maximum likelihood method. However, the maximum likelihood estimator can not be found analytically. To overcome these problems, the EM algorithm proposed. EM algorithm consists of two phases: expectation and maximization stage. EM algorithm converges to the maximum likelihood estimator. Performance of the EM algorithm is tested using simulated data. The results show that the EM algorithm can estimate the mixture distribution parameter. Further EM algorithm is implemented on real data encountered in everyday life.

Comparison of individual-based model output to data using a model of walleye pollock early life history in the Gulf of Alaska

Biophysical individual-based models (IBMs) have been used to study aspects of early life history of marine fishes such as recruitment, connectivity of spawning and nursery areas, and marine reserve design. However, there is no consistent approach to validating the spatial outputs of these models. In this study, we hope to rectify this gap. We document additions to an existing individual-based biophysical model for Alaska walleye pollock (Gadus chalcogrammus), some simulations made with this model and methods that were used to describe and compare spatial output of the model versus field data derived from ichthyoplankton surveys in the Gulf of Alaska. We used visual methods (e.g. distributional centroids with directional ellipses), several indices (such as a Normalized Difference Index (NDI), and an Overlap Coefficient (OC), and several statistical methods: the Syrjala method, the Getis-Ord Gi* statistic, and a geostatistical method for comparing spatial indices. We assess the utility of these different methods in analyzing spatial output and comparing model output to data, and give recommendations for their appropriate use. Visual methods are useful for initial comparisons of model and data distributions. Metrics such as the NDI and OC give useful measures of co-location and overlap, but care must be taken in discretizing the fields into bins. The Getis-Ord Gi* statistic is useful to determine the patchiness of the fields. The Syrjala method is an easily implemented statistical measure of the difference between the fields, but does not give information on the details of the distributions. Finally, the geostatistical comparison of spatial indices gives good information of details of the distributions and whether they differ significantly between the model and the data. We conclude that each technique gives quite different information about the model-data distribution comparison, and that some are easy to apply and some more complex. We also give recommendations for a multistep process to validate spatial output from IBMs.

Transmuted Rayleigh Distribution

In this article, we generalize the Rayleigh distribution using the quadratic rank transmutation map studied by Shaw et al. (2009) to develop a transmuted Rayleigh distribution. We provide a comprehensive description of the mathematical properties of the subject distribution along with its reliabilitybehavior. The usefulness of the transmuted Rayleigh distribution for modeling data is illustrated using real data.

A Bimodal Extension of the Generalized Gamma Distribution

A bimodal extension of the generalized gamma distribution is proposed by using a mixing approach. Some distributional properties of the new distribution are investigated. The maximum likelihood (ML) estimators for the parameters of the new distribution are obtained. Real data examples are given to show the strength of the new distribution for modeling data.

Digital model data distribution in civil engineering contracts

Purpose – The use of digital-models to communicate civil-engineering design continues to generate debate; this pilot-work reviews technology uptake towards data repurposing and assesses digital (vs traditional) design-preparation timelines and fees for infrastructure. The paper aims to discuss these issues. Design/methodology/approach – Extending (building-information-modelling) literature, distribution-impact is investigated across: quality-management, technical-applications and contractual-liability. Project case-study scenarios were developed and validated with resultant modelling-application timeline/fees examined, in conjunction with qualitative semi-structured interviews with 11 prominent stakeholder companies. Findings – Results generated to explore digital-model data-distribution/usage identify: an 8 per cent time/efficiency improvement at the design-phase, and a noteworthy cost-saving of 0.7 per cent overall. Fragmented opinion regarding modelling utilisation exists across supply-chains, with concerns over liability, quality-management and, the lack of Australian-Standard contract-clause(s) dealing directly with digital-model document hierarchy/clarification/reuse. Research limitations/implications – Representing a small-scale/snapshot industrial-study, findings suggest that (model-distribution) must emphasise checking-procedures within quality-systems and, seek precedence clarification for dimensioned documentation. Similarly, training in specific file-formatting (digital-model-addenda) techniques, CAD-file/hard-copy continuity, and digital-visualisation software, can better regulate model dissemination/reuse. Time/cost savings through digital-model data-distribution in civil-engineering contracts are available to enhance provision of society’s infrastructure. Originality/value – This work extends knowledge of 3D-model distribution for roads/earthworks/drainage, and presents empirical evidence that (alongside appropriate consideration of general-conditions-of-contract and specific training to address revision-document continuity), industry may achieve tangible benefits from digital-model data as a means to communicate civil-engineering design.

Transmuted Generalized Rayleigh Distribution

In this article, we generalize the generalized Rayleigh distribution using the qu adratic rank transmutation map studied by Shaw et al. (9) to develop a transmuted generalized Rayleigh distribution. We provide a comprehensive description of the mathematical properties of the subject distribution along with its reliability behav ior. The usefulness of the transmuted generalized Rayleigh distribution for modeling data is illustrated using real data.

Modeling Data with Flat Densities

In this article, a simple probability distribution for modeling data with flat densities is introduced and used to model real world assessment data. The new distribution is a mixture of three distributions, two truncated normals, and a uniform. The parameters are estimated by using the sample percentiles because the likelihood and the method of moment approaches result in complicated forms. The proposed method is mainly based on the shape of the empirical density. The proposed method looks promising for modeling flat densities that are similar to the one used in the study.

CHANGE POINT DETECTION IN TIME SERIES DATA USING SUPPORT VECTORS

Change Point Detection in time series data is of interest in various research areas including data mining, pattern recognition, statistics, etc. Even though there are several effective methods in the literature for detecting changes in mean, and an increase in variance, there are none for decrease in variance. Effective detection of decreased variance has been reported as future work in earlier papers. In addition, most, if not all, methods require some model like AR to fit into the time series data in order to extract noise information, which is assumed to be independent and identically distributed (i.i.d.) and follow standard normal distribution (white noise). Thus, effectiveness of the methods is tied to the fitness degree of the AR model to the time series data. This paper presents a change point detection method based on support vectors that targets changes in mean and variance (including variance decrease) without any assumption of model fitting or data distribution. The data is represented by a hyper-sphere in a higher dimensional space using kernel trick. The change is identified by the change in the radius of the hyper-sphere. A comparison of this method with other methods is presented in the paper.

A Comparison of Four Estimators of a Population Measure of Model Fit in Covariance Structure Analysis

A major issue in the utilization of covariance structure analysis is model fit evaluation. Recent years have witnessed increasing interest in various test statistics and so-called fit indexes, most of which are actually based on or closely related to F 0, a measure of model fit in the population. This study aims to provide a systematic investigation about the performance of 4 available estimators of F 0. [Fcirc]01 is the conventional estimator and is based on noncentral chi-square approximation. [Fcirc]02 is newly proposed and does not assume noncentral chi-square approximation. [Fcirc]03 and [Fcirc]04 are variations of [Fcirc]02. A Monte Carlo simulation study is conducted to examine how these four estimators of F 0 perform across varying model misspecifications, data distributions, model sizes, and sample sizes. The results show that under normality all 4 quantities estimate F 0 equally well, and under nonnormality [Fcirc]02, [Fcirc]03, and [Fcirc]04 outperform [Fcirc]01. Issues related to these findings are discussed.

GS-distributions: A new family of distributions for continuous unimodal variables

The choice of the best-suited statistical distribution for modeling data is not a trivial issue. Unless a sound theoretical background exists for selecting a particular distribution, one will usually resort to testing various candidates and select a distribution based on its fit to the observed data. While this is a legitimate strategy, it is more objective and efficient to define a sufficiently general family that can be used for this purpose. This approach has a long tradition in statistics, and resulted in various families of distributions, most notably Pearson's. Given such a family, modeling a data set requires estimating the appropriate parameters within this family and assessing the resulting fit. As a contribution to this methodology, the Generalized S-distribution is introduced here as a new family of distributions that can serve as statistical models for unimodal continuous distributions. The article begins with a description of the rationale for defining this family. It then discusses its basic properties and introduces a numerical procedure for determining appropriate parameters using maximum likelihood estimation. Finally, the paper illustrates the distribution and methods with several examples.

Using The Generalized Lambda Distribution (GLD) To Improve Physical Fitness Testing Assessment

Exercise scientists routinely use statistical methods considered outmoded (e.g., dating from ∼1805 to 1933) or otherwise inappropriate (e.g., invalid, imprecise, or heavily biased) by the statistical science community. PURPOSE Introduce ACSM members to the Generalized Lambda Distribution (GLD); a relatively new, very precise, and extremely flexible statistical distribution for modeling data. METHODS Data consisted of “Physical Fitness Norms” presented in ACSM Guidelines for Exercise Testing and Prescription (e.g., percent bodyfat, aerobic power, & upper body strength). Rho statistics (median, inter-decile range, left-right tail-weight ratio, & tail-weight factor) were obtained from the sample data; the two Normal parameters (mean and standard deviation) and four GLD parameters (lambda1, lambda2, lambda3, & lambda4) were estimated via numerical methods from the rhos (typical error ≤ 0.000001). Parameter estimates were used to construct probability density functions to assess the chances of occurrence for various values. RESULTS For all variables considered, the GLD provided a very different view of the data than the N (an example is provided below). These differences were evident in all aspects of data description (e.g., centrality, variability, skewness, and kurtosis) and have important implications for population inference. CONCLUSION GLD fitting methods are useful for exercise scientists seeking additional information and/or greater precision not obtainable from the N.Figure

The use of kernel principal component analysis to model data distributions

We describe the use of kernel principal component analysis (KPCA) to model data distributions in high-dimensional spaces. We show that a previous approach to representing non-linear data constraints using KPCA is not generally valid, and introduce a new ‘proximity to data’ measure that behaves correctly. We investigate the relation between this measure and the actual density for various low-dimensional data distributions. We demonstrate the effectiveness of the method by applying it to the higher-dimensional case of modelling an ensemble of images of handwritten digits, showing how it can be used to extract the digit information from noisy input images.