84,198 research outputs found
icet - A Python library for constructing and sampling alloy cluster expansions
Alloy cluster expansions (CEs) provide an accurate and computationally
efficient mapping of the potential energy surface of multi-component systems
that enables comprehensive sampling of the many-dimensional configuration
space. Here, we introduce \textsc{icet}, a flexible, extensible, and
computationally efficient software package for the construction and sampling of
CEs. \textsc{icet} is largely written in Python for easy integration in
comprehensive workflows, including first-principles calculations for the
generation of reference data and machine learning libraries for training and
validation. The package enables training using a variety of linear regression
algorithms with and without regularization, Bayesian regression, feature
selection, and cross-validation. It also provides complementary functionality
for structure enumeration and mapping as well as data management and analysis.
Potential applications are illustrated by two examples, including the
computation of the phase diagram of a prototypical metallic alloy and the
analysis of chemical ordering in an inorganic semiconductor.Comment: 10 page
Classification of newborn EEG maturity with Bayesian averaging over decision trees
EEG experts can assess a newborn’s brain maturity by visual analysis of age-related patterns in sleep EEG. It is highly desirable to make the results of assessment most accurate and reliable. However, the expert analysis is limited in capability to provide the estimate of uncertainty in assessments. Bayesian inference has been shown providing the most accurate estimates of uncertainty by using Markov Chain Monte Carlo (MCMC) integration over the posterior distribution. The use of MCMC enables to approximate the desired distribution by sampling the areas of interests in which the density of distribution is high. In practice, the posterior distribution can be multimodal, and so that the existing MCMC techniques cannot provide the proportional sampling from the areas of interest. The lack of prior information makes MCMC integration more difficult when a model parameter space is large and cannot be explored in detail within a reasonable time. In particular, the lack of information about EEG feature importance can affect the results of Bayesian assessment of EEG maturity. In this paper we explore how the posterior information about EEG feature importance can be used to reduce a negative influence of disproportional sampling on the results of Bayesian assessment. We found that the MCMC integration tends to oversample the areas in which a model parameter space includes one or more features, the importance of which counted in terms of their posterior use is low. Using this finding, we proposed to cure the results of MCMC integration and then described the results of testing the proposed method on a set of sleep EEG recordings
Bayesian Cluster Enumeration Criterion for Unsupervised Learning
We derive a new Bayesian Information Criterion (BIC) by formulating the
problem of estimating the number of clusters in an observed data set as
maximization of the posterior probability of the candidate models. Given that
some mild assumptions are satisfied, we provide a general BIC expression for a
broad class of data distributions. This serves as a starting point when
deriving the BIC for specific distributions. Along this line, we provide a
closed-form BIC expression for multivariate Gaussian distributed variables. We
show that incorporating the data structure of the clustering problem into the
derivation of the BIC results in an expression whose penalty term is different
from that of the original BIC. We propose a two-step cluster enumeration
algorithm. First, a model-based unsupervised learning algorithm partitions the
data according to a given set of candidate models. Subsequently, the number of
clusters is determined as the one associated with the model for which the
proposed BIC is maximal. The performance of the proposed two-step algorithm is
tested using synthetic and real data sets.Comment: 14 pages, 7 figure
Neural Models of Motion Integration, Segmentation, and Probablistic Decision-Making
When brain mechanism carry out motion integration and segmentation processes that compute unambiguous global motion percepts from ambiguous local motion signals? Consider, for example, a deer running at variable speeds behind forest cover. The forest cover is an occluder that creates apertures through which fragments of the deer's motion signals are intermittently experienced. The brain coherently groups these fragments into a trackable percept of the deer in its trajectory. Form and motion processes are needed to accomplish this using feedforward and feedback interactions both within and across cortical processing streams. All the cortical areas V1, V2, MT, and MST are involved in these interactions. Figure-ground processes in the form stream through V2, such as the seperation of occluding boundaries of the forest cover from the boundaries of the deer, select the motion signals which determine global object motion percepts in the motion stream through MT. Sparse, but unambiguous, feauture tracking signals are amplified before they propogate across position and are intergrated with far more numerous ambiguous motion signals. Figure-ground and integration processes together determine the global percept. A neural model predicts the processing stages that embody these form and motion interactions. Model concepts and data are summarized about motion grouping across apertures in response to a wide variety of displays, and probabilistic decision making in parietal cortex in response to random dot displays.National Science Foundation (SBE-0354378); Office of Naval Research (N00014-01-1-0624
Bayesian Model Selection in Complex Linear Systems, as Illustrated in Genetic Association Studies
Motivated by examples from genetic association studies, this paper considers
the model selection problem in a general complex linear model system and in a
Bayesian framework. We discuss formulating model selection problems and
incorporating context-dependent {\it a priori} information through different
levels of prior specifications. We also derive analytic Bayes factors and their
approximations to facilitate model selection and discuss their theoretical and
computational properties. We demonstrate our Bayesian approach based on an
implemented Markov Chain Monte Carlo (MCMC) algorithm in simulations and a real
data application of mapping tissue-specific eQTLs. Our novel results on Bayes
factors provide a general framework to perform efficient model comparisons in
complex linear model systems
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