scholarly journals On the S-instability and degeneracy of discrete deep learning models

2019 ◽  
Vol 9 (3) ◽  
pp. 627-655 ◽  
Author(s):  
Andee Kaplan ◽  
Daniel J Nordman ◽  
Stephen B Vardeman
Keyword(s):  
Probability Model ◽  
Correlated Data ◽  
Data Sequence ◽  
Probability Models ◽  
Large Classes ◽  
Learning Contexts ◽  
Probability Structure ◽  
Model Probability ◽  
Parameter Sequence ◽  
Outcome Result

Abstract A probability model exhibits instability if small changes in a data outcome result in large and, often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a given configuration of parameters. For correlated data structures found in several application areas, there is increasing interest in identifying such sensitivity in model probability structure. We consider the problem of quantifying instability for general probability models defined on sequences of observations, where each sequence of length $N$ has a finite number of possible values that can be taken at each point. A sequence of probability models, indexed by $N$, and an associated parameter sequence result to accommodate data of expanding dimension. Model instability is formally shown to occur when a certain log probability ratio under such models grows faster than $N$. In this case, a one component change in the data sequence can shift probability by orders of magnitude. Also, as instability becomes more extreme, the resulting probability models are shown to tend to degeneracy, placing all their probability on potentially small portions of the sample space. These results on instability apply to large classes of models commonly used in random graphs, network analysis and machine learning contexts.

Study on Hazard Analysis Method of Earthquake Secondary Fire Disaster in Urban Area Based on GIS

2012 ◽  
Vol 204-208 ◽  
pp. 3457-3461
Author(s):  
Tian Qi Li ◽  
Fei Geng
Keyword(s):  
Urban Areas ◽  
Hazard Analysis ◽  
Probability Model ◽  
Probability Models ◽  
Housing Density ◽  
Earthquake Excitation ◽  
Fire Disaster ◽  
High Hazard ◽  
The City ◽  
And Diffusion

In order to study the probability of occurrence of secondary fire after the earthquake in urban areas, the probability model of the hazard analysis that the fire occurred and the spread is established and applied. Probability models need to consider the destruction level of buildings under earthquake excitation as well as the probability of the leakage and diffusion of combustible material in the buildings in the corresponding destruction level, combination of weather, season, housing density and other factors to determine the probability of the single building earthquake secondary fire. On this basis , the natural administrative areas in the city as a unit , considering the factors of regional hazard analysis such as population density , property distribution and density within a region , to calculate the hazard indicator and determine the high hazard areas of secondary fire in the city. The Geographic Information System was used as the platform, to division of urban earthquake secondary fire high-hazard areas.

scholarly journals Bell Could Become the Copernicus of Probability

2016 ◽  
Vol 23 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Probability Model ◽  
Quantum Probability ◽  
Bell’S Inequality ◽  
Probability Models ◽  
Bell's Inequality ◽  
Mathematical Probability ◽  
Model Interpretation ◽  
Born’S Rule ◽  
Quantum Phenomena

Our aim is to emphasize the role of mathematical models in physics, especially models of geometry and probability. We briefly compare developments of geometry and probability by pointing to similarities and differences: from Euclid to Lobachevsky and from Kolmogorov to Bell. In probability, Bell could play the same role as Lobachevsky in geometry. In fact, violation of Bell’s inequality can be treated as implying the impossibility to apply the classical probability model of Kolmogorov (1933) to quantum phenomena. Thus the quantum probabilistic model (based on Born’s rule) can be considered as the concrete example of the non-Kolmogorovian model of probability, similarly to the Lobachevskian model — the first example of the non-Euclidean model of geometry. This is the “probability model” interpretation of the violation of Bell’s inequality. We also criticize the standard interpretation—an attempt to add to rigorous mathematical probability models additional elements such as (non)locality and (un)realism. Finally, we compare embeddings of non-Euclidean geometries into the Euclidean space with embeddings of the non-Kolmogorovian probabilities (in particular, quantum probability) into the Kolmogorov probability space. As an example, we consider the CHSH-test.

scholarly journals A new approach for modeling covid-19 death data

2021 ◽  
pp. 1-9
Author(s):  
Muhammad Farooq ◽  
Qamar-uz-zaman ◽  
Muhammad Ijaz
Keyword(s):  
Probability Model ◽  
Developed Countries ◽  
Likelihood Method ◽  
Data Sets ◽  
Probability Models ◽  
New Approach ◽  
Proposed Model ◽  
Rate Functions ◽  
Day By Day ◽  
Death Data

The Covid-19 infections outbreak is increasing day by day and the mortality rate is increasing exponentially both in underdeveloped and developed countries. It becomes inevitable for mathematicians to develop some models that could define the rate of infections and deaths in a population. Although there exist a lot of probability models but they fail to model different structures (non-monotonic) of the hazard rate functions and also do not provide an adequate fit to lifetime data. In this paper, a new probability model (FEW) is suggested which is designed to evaluate the death rates in a Population. Various statistical properties of FEW have been screened out in addition to the parameter estimation by using the maximum likelihood method (MLE). Furthermore, to delineate the significance of the parameters, a simulation study is conducted. Using death data from Pakistan due to Covid-19 outbreak, the proposed model applications is studied and compared to that of other existing probability models such as Ex-W, W, Ex, AIFW, and GAPW. The results show that the proposed model FEW provides a much better fit while modeling these data sets rather than Ex-W, W, Ex, AIFW, and GAPW.

scholarly journals Factors Influencing the Performance of Regression-Based Statistical Postprocessing Models for Short-Term Precipitation Forecasts

2019 ◽  
Vol 34 (6) ◽  
pp. 2067-2084
Author(s):  
Wentao Li ◽  
Qingyun Duan ◽  
Quan J. Wang
Keyword(s):  
Prediction Models ◽  
Probability Model ◽  
Weather Prediction ◽  
Joint Probability ◽  
Ensemble Spread ◽  
Probability Models ◽  
Short Term ◽  
Huai River ◽  
Censored Regression Model ◽  
Distributional Regression

Abstract Statistical postprocessing models can be used to correct bias and dispersion errors in raw precipitation forecasts from numerical weather prediction models. In this study, we conducted experiments to investigate four factors that influence the performance of regression-based postprocessing models with normalization transformations for short-term precipitation forecasts. The factors are 1) normalization transformations, 2) incorporation of ensemble spread as a predictor in the model, 3) objective function for parameter inference, and 4) two postprocessing schemes, including distributional regression and joint probability models. The experiments on the first three factors are based on variants of a censored regression model with conditional heteroscedasticity (CRCH). For the fourth factor, we compared CRCH as an example of the distributional regression with a joint probability model. The results show that the CRCH with normal quantile transformation (NQT) or power transformation performs better than the CRCH with log–sinh transformation for most of the subbasins in Huai River basin with a subhumid climate. The incorporation of ensemble spread as a predictor in CRCH models can improve forecast skill in our research region at short lead times. The influence of different objective functions (minimum continuous ranked probability score or maximum likelihood) on postprocessed results is limited to a few relatively dry subbasins in the research region. Both the distributional regression and the joint probability models have their advantages, and they are both able to achieve reliable and skillful forecasts.

scholarly journals Spatial probability modelling of eelgrass (Zostera marina) distribution on the west coast of Norway

2008 ◽  
Vol 65 (7) ◽  
pp. 1093-1101 ◽  
Author(s):  
Trine Bekkby ◽  
Eli Rinde ◽  
Lars Erikstad ◽  
Vegar Bakkestuen ◽  
Oddvar Longva ◽  
...  
Keyword(s):  
West Coast ◽  
Zostera Marina ◽  
Probability Model ◽  
Probability Models ◽  
The West ◽  
Spatial Probability ◽  
Marine Habitats ◽  
Predictive Probability ◽  
Field Samples ◽  
Probability Modelling

Abstract Bekkby, T., Rinde, E., Erikstad, L., Bakkestuen, V., Longva, O., Christensen, O., Isæus, M., and Isachsen, P. E. 2008. Spatial probability modelling of eelgrass (Zostera marina) distribution on the west coast of Norway. – ICES Journal of Marine Science, 65: 1093–1101. Based on modelled and measured geophysical variables and presence/absence data of eelgrass Zostera marina, we developed a spatial predictive probability model for Z. marina. Our analyses confirm previous reports and show that the probability of finding Z. marina is at its highest in shallow, gently sloping, and sheltered areas. We integrated the empirical knowledge from field samples in GIS and developed a model-based map of the probability of finding Z. marina using the model-selection approach Akaike Information Criterion (AIC) and the spatial probability modelling extension GRASP in S-Plus. Spatial predictive probability models contribute to a better understanding of the factors and processes structuring the distribution of marine habitats. Additionally, such models provide a useful tool for management and research, because they are quantitative and defined objectively, extrapolate knowledge from sampled to unsurveyed areas, and result in a probability map that is easy to understand and disseminate to stakeholders.

scholarly journals EROL GELENBE: A CAREER IN MULTI-DISCIPLINARY PROBABILITY MODELS

2016 ◽  
Vol 30 (3) ◽  
pp. 308-325
Author(s):  
M. Ufuk Çag̃layan
Keyword(s):  
Communication Systems ◽  
Regulatory Networks ◽  
Applied Mathematics ◽  
Probability Model ◽  
Electrical Energy ◽  
Analytical Models ◽  
Probability Models ◽  
Trade Offs ◽  
Random Neural Network ◽  
Innovative Work

We focus on Erol Gelenbe's scientific and technical contributions to probability models in the computer and information sciences, but limit our survey to the last fifteen years. We start with a brief overview of his work as a single author, as well as his work in collaboration with over 200 co-authors. We discuss some of his recent and innovative work regarding a new probability model that represents Intermittent Energy Sources for Computing and Communications, introducingEnergy Packet Networkswhich are a probabilistic representation of the flow, storage and consumption of electrical energy at the microscopic level (in electronic chips), and at the macroscopic level (e.g. in buildings or data centers) and for its routing and dynamic usage by consuming units (such as computer elements, chips or machines). We next discuss his work on designing computer and communication systems that parsimoniously use energy in order to achieve a satisfactory level of quality of service (QoS). Trade-offs between system QoS and energy consumption are also considered. Then we turn to Prof. Gelenbe's pioneering work on Autonomic Communications and the design and implementation of CPN, the Cognitive Packet Network, and we also briefly review his spiking random neural network that was used in CPN. This is followed by a brief review of work that he conducted since 1999 on human evacuation from dangerous or catastrophic environments, and the design of technology driven Emergency Management Systems. His research since the late 2000s on Gene Regulatory Networks is then covered together with its application to the detecting possible disease from microarray data. Finally, we briefly discuss some novel analytical models that he developed in this period with publications appearing in journals of physics and applied mathematics.

Drift and Scaling in Estimation of Distribution Algorithms

2005 ◽  
Vol 13 (1) ◽  
pp. 99-123 ◽  
Author(s):  
J. L. Shapiro
Keyword(s):  
Population Size ◽  
Probability Model ◽  
Search Space ◽  
System Size ◽  
Estimation Of Distribution Algorithms ◽  
Square Root ◽  
Problem Size ◽  
Probability Models ◽  
Estimation Of Distribution ◽  
Distribution Algorithms

This paper considers a phenomenon in Estimation of Distribution Algorithms (EDA) analogous to drift in population genetic dynamics. Finite population sampling in selection results in fluctuations which get reinforced when the probability model is updated. As a consequence, any probability model which can generate only a single set of values with probability 1 can be an attractive fixed point of the algorithm. To avoid this, parameters of the algorithm must scale with the system size in strongly problem-dependent ways, or the algorithm must be modified. This phenomenon is shown to hold for general EDAs as a consequence of the lack of ergodicity and irreducibility of the Markov chain on the state of probability models. It is illustrated in the case of UMDA, in which it is shown that the global optimum is only found if the population size is sufficiently large. For the needle-in-a haystack problem, the population size must scale as the square-root of the size of the search space. For the one-max problem, the population size must scale as the square-root of the problem size.

scholarly journals Ultralogics and probability models

2001 ◽  
Vol 27 (5) ◽  
pp. 321-325 ◽  
Author(s):  
Robert A. Herrmann
Keyword(s):  
Probability Model ◽  
Informational Content ◽  
Single Event ◽  
Probability Models ◽  
Specific Distribution ◽  
Consequence Operators

We show how nonstandard consequence operators, ultralogics, can generate the general informational content displayed by probability models. In particular, a probability model that predicts that a specific single event will occur and those models that predict that a specific distribution of events will occur.

scholarly journals Quadrature as applied to computer models for robust design: theoretical and empirical assessment

2021 ◽  
Vol 7 ◽  
Author(s):  
Daniel D. Frey ◽  
Yiben Lin ◽  
Petra Heijnen
Keyword(s):  
Case Studies ◽  
Robust Design ◽  
Probability Model ◽  
Computer Experiments ◽  
Engineering Systems ◽  
Probability Models ◽  
Model Based ◽  
Mean And Variance ◽  
Gauss Hermite Quadrature

Abstract This paper develops theoretical foundations for extending Gauss–Hermite quadrature to robust design with computer experiments. When the proposed method is applied with m noise variables, the method requires 4m + 1 function evaluations. For situations in which the polynomial response is separable, this paper proves that the method gives exact transmitted variance if the response is a fourth-order separable polynomial response. It is also proven that the relative error mean and variance of the method decrease with the dimensionality m if the response is separable. To further assess the proposed method, a probability model based on the effect hierarchy principle is used to generate sets of polynomial response functions. For typical populations of problems, it is shown that the proposed method has less than 5% error in 90% of cases. Simulations of five engineering systems were developed and, given parametric alternatives within each case study, a total of 12 case studies were conducted. A comparison is made between the cumulative density function for the hierarchical probability models and a corresponding distribution function for case studies. The data from the case-based evaluations are generally consistent with the results from the model-based evaluation.

Proposed Heavy Vehicle Encroachment Adjustment Factor

2015 ◽  
Vol 2521 (1) ◽  
pp. 103-110
Author(s):  
Christine E. Carrigan ◽  
Malcolm H. Ray
Keyword(s):  
Probability Model ◽  
Large Data ◽  
Segment Length ◽  
Heavy Vehicle ◽  
Heavy Vehicles ◽  
Adjustment Factor ◽  
Probability Models ◽  
Data Set ◽  
Vehicle Type ◽  
Passenger Vehicles

Encroachment probability models such as the Roadside Safety Analysis Program (RSAP) have traditionally assumed that heavy vehicles and passenger vehicles share the same encroachment characteristics. This assumption was reviewed in developing bridge railing selection guidelines in NCHRP 22-12(03), where an examination of a specific highway and a national sample of data indicated that trucks encroached at a different rate than passenger vehicles. This paper describes the development of a new vehicle-type encroachment adjustment factor (EAF). The results confirmed previous findings, but this analysis controlled for traffic volumes, highway type, percentage of heavy vehicles [i.e., percentage of trucks (PT)], and segment length. The result was a more robust model that was valid over a wider range of average annual daily traffic and PTs. The large data set included 635,464 segments of data from the states of Ohio and Washington. The proposed EAF was recommended for inclusion in RSAPv3. Ideally, encroachment data would be collected for heavy vehicles to determine the frequency of heavy vehicles encroaching onto the roadside and the trajectories heavy vehicles took during encroachment, but this process proved to be financially challenging. The study used crash data to carry out a comprehensive analysis of traffic volume, heavy vehicle mix, highway type, and segment length. A vehicle-type EAF was developed for divided and undivided roadways. The results provided some indication of how best to incorporate heavy vehicles in the encroachment probability model used in RSAP.

Sign in / Sign up

Export Citation Format

Share Document