Neural Networks for Estimating Probability Distributions for Survival Analysis

2021 ◽  
Vol 9 (2) ◽  
pp. T585-T598
Author(s):  
Abidin B. Caf ◽  
John D. Pigott

Extensive dolomitization is prevalent in the platform and periplatform carbonates in the Lower-Middle Permian strata in the Midland and greater Permian Basin. Early workers have found that the platform and shelf-top carbonates were dolomitized, whereas slope and basinal carbonates remained calcitic, proposing a reflux dolomitization model as the possible diagenetic mechanism. More importantly, they underline that this dolomitization pattern controls the porosity and forms an updip seal. These studies are predominately conducted using well logs, cores, and outcrop analogs, and although exhibiting high resolution vertically, such determinations are laterally sparse. We have used supervised Bayesian classification and probabilistic neural networks (PNN) on a 3D seismic volume to create an estimation of the most probable distribution of dolomite and limestone within a subsurface 3D volume petrophysically constrained. Combining this lithologic information with porosity, we then illuminate the diagenetic effects on a seismic scale. We started our workflow by deriving lithology classifications from well-log crossplots of neutron porosity and acoustic impedance to determine the a priori proportions of the lithology and the probability density functions calculation for each lithology type. Then, we applied these probability distributions and a priori proportions to 3D seismic volumes of the acoustic impedance and predicted neutron porosity volume to create a lithology volume and probability volumes for each lithology type. The acoustic impedance volume was obtained by model-based poststack inversion, and the neutron porosity volume was obtained by the PNN. Our results best supported a regional reflux dolomitization model, in which the porosity is increasing from shelf to slope while the dolomitization is decreasing, but with sea-level forcing. With this study, we determined that diagenesis and the corresponding reservoir quality in these platforms and periplatform strata can be directly imaged and mapped on a seismic scale by quantitative seismic interpretation and supervised classification methods.


Author(s):  
Thomas R. Shultz

Computational modeling implements developmental theory in a precise manner, allowing generation, explanation, integration, and prediction. Several modeling techniques are applied to development: symbolic rules, neural networks, dynamic systems, Bayesian processing of probability distributions, developmental robotics, and mathematical analysis. The relative strengths and weaknesses of each approach are identified and examples of each technique are described. Ways in which computational modeling contributes to developmental issues are documented. A probabilistic model of the vocabulary spurt shows that various psychological explanations for it are unnecessary. Constructive neural networks clarify the distinction between learning and development and show how it is possible to escape Fodor’s paradox. Connectionist modeling reveals different versions of innateness and how learning and evolution might interact. Agent-based models analyze the basic principles of evolution in a testable, experimental fashion that generates complete evolutionary records. Challenges posed by stimulus poverty and lack of negative examples are explored in neural-network models that learn morphology or syntax probabilistically from indirect negative evidence.


Author(s):  
Chunyuan Li ◽  
Changyou Chen ◽  
Yunchen Pu ◽  
Ricardo Henao ◽  
Lawrence Carin

Learning probability distributions on the weights of neural networks has recently proven beneficial in many applications. Bayesian methods such as Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) offer an elegant framework to reason about model uncertainty in neural networks. However, these advantages usually come with a high computational cost. We propose accelerating SG-MCMC under the masterworker framework: workers asynchronously and in parallel share responsibility for gradient computations, while the master collects the final samples. To reduce communication overhead, two protocols (downpour and elastic) are developed to allow periodic interaction between the master and workers. We provide a theoretical analysis on the finite-time estimation consistency of posterior expectations, and establish connections to sample thinning. Our experiments on various neural networks demonstrate that the proposed algorithms can greatly reduce training time while achieving comparable (or better) test accuracy/log-likelihood levels, relative to traditional SG-MCMC. When applied to reinforcement learning, it naturally provides exploration for asynchronous policy optimization, with encouraging performance improvement.


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