Recognition on Finite Set of Events: Bayesian Analysis of Generalization Ability and Classification Tree Pruning

The problem of recognition on finite set of events is considered. The generalization ability of classifiers for this problem is studied within the Bayesian approach. The method for non-uniform prior distribution specification on recognition tasks is suggested. It takes into account the assumed degree of intersection between classes. The results of the analysis are applied for pruning of classification trees.

A world full of surprises:Bayesian theory of surprise to quantify degrees of uncertainty

In the specific area of software engineering (SE) for self-adaptive systems (SASs) there is a growing research awareness about the synergy between SE and artificial intelligence (AI). However, just few significant results have been published so far. In this paper, we propose a novel and formal Bayesian definition of surprise as the basis for quantitative analysis to measure degrees of uncertainty and deviations of self-adaptive systems from normal behavior. A surprise measures how observed data affects the models or assumptions of the world during runtime. The key idea is that a "surprising" event can be defined as one that causes a large divergence between the belief distributions prior to and posterior to the event occurring. In such a case the system may decide either to adapt accordingly or to flag that an abnormal situation is happening. In this paper, we discuss possible applications of Bayesian theory of surprise for the case of self-adaptive systems using Bayesian dynamic decision networks. Copyright © 2014 ACM.

Bayesian neural network approach for determining the risk of re-intervention after endovascular aortic aneurysm repair

This article proposes a Bayesian neural network approach to determine the risk of re-intervention after endovascular aortic aneurysm repair surgery. The target of proposed technique is to determine which patients have high chance to re-intervention (high-risk patients) and which are not (low-risk patients) after 5 years of the surgery. Two censored datasets relating to the clinical conditions of aortic aneurysms have been collected from two different vascular centers in the United Kingdom. A Bayesian network was first employed to solve the censoring issue in the datasets. Then, a back propagation neural network model was built using the uncensored data of the first center to predict re-intervention on the second center and classify the patients into high-risk and low-risk groups. Kaplan-Meier curves were plotted for each group of patients separately to show whether there is a significant difference between the two risk groups. Finally, the logrank test was applied to determine whether the neural network model was capable of predicting and distinguishing between the two risk groups. The results show that the Bayesian network used for uncensoring the data has improved the performance of the neural networks that were built for the two centers separately. More importantly, the neural network that was trained with uncensored data of the first center was able to predict and discriminate between groups of low risk and high risk of re-intervention after 5 years of endovascular aortic aneurysm surgery at center 2 (p = 0.0037 in the logrank test).

Distribution modeling of nonlinear inverse controllers under a Bayesian framework

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems and is demonstrated on nonlinear single-input-single-output (SISO) and multiple-input-multiple-output (MIMO) examples. © 2006 IEEE.

A Bayesian approach to modeling the conditional density of the inverse controller

The inverse controller is traditionally assumed to be a deterministic function. This paper presents a pedagogical methodology for estimating the stochastic model of the inverse controller. The proposed method is based on Bayes' theorem. Using Bayes' rule to obtain the stochastic model of the inverse controller allows the use of knowledge of uncertainty from both the inverse and the forward model in estimating the optimal control signal. The paper presents the methodology for general nonlinear systems. For illustration purposes, the proposed methodology is applied to linear Gaussian systems. © 2004 IEEE.

A Bayesian Spatial Mixture Model for FMRI Analysis

We develop, implement and study a new Bayesian spatial mixture model (BSMM). The proposed BSMM allows for spatial structure in the binary activation indicators through a latent thresholded Gaussian Markov random field. We develop a Gibbs (MCMC) sampler to perform posterior inference on the model parameters, which then allows us to assess the posterior probabilities of activation for each voxel. One purpose of this article is to compare the HJ model and the BSMM in terms of receiver operating characteristics (ROC) curves. Also we consider the accuracy of the spatial mixture model and the BSMM for estimation of the size of the activation region in terms of bias, variance and mean squared error. We perform a simulation study to examine the aforementioned characteristics under a variety of configurations of spatial mixture model and BSMM both as the size of the region changes and as the magnitude of activation changes.

Application of MARS for the Construction of Nonparametric Models

2000 Mathematics Subject Classification: 62G08, 62P30.

A Note on Bayesian Estimation for the Negative-Binomial Model

2000 Mathematics Subject Classification: 62F15.

Suboptimal Multistage Nonparametric Hypotheses Test

2000 Mathematics Subject Classification: 62L10, 62L15.

Suboptimal Nonparametric Hypotheses Discriminating from Small Dependent Observations

2000 Mathematics Subject Classification: 62L10.

Nonparametric versus Parametric Statistical Approaches for Genetic Anticipation: The Pancreatic Cancer Case

2000 Mathematics Subject Classi cation: 62N01, 62N05, 62P10, 92D10, 92D30.

Nonparametric Estimation in the Class of Bisexual Processes with Population-Size Dependent Mating

2000 Mathematics Subject Classification: 60J80, 62M05

Seeking Relationships in Big Data: A Bayesian Perspective

The real purpose of collecting big data is to identify causality in the hope that this will facilitate credible predictivity . But the search for causality can trap one into infinite regress, and thus one takes refuge in seeking associations between variables in data sets. Regrettably, the mere knowledge of associations does not enable predictivity. Associations need to be embedded within the framework of probability calculus to make coherent predictions. This is so because associations are a feature of probability models, and hence they do not exist outside the framework of a model. Measures of association, like correlation, regression, and mutual information merely refute a preconceived model. Estimated measures of associations do not lead to a probability model; a model is the product of pure thought. This paper discusses these and other fundamentals that are germane to seeking associations in particular, and machine learning in general. ACM Computing Classification System (1998): H.1.2, H.2.4., G.3.

A Bayesian Model for Learning Using Flashcards

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015

On Supra-Bayesian Weighted Combination of Available Data Determined by Kerridge Inaccuracy and Entropy

2010 Mathematics Subject Classification: 94A17.