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Exploring physics of ferroelectric domain walls via Bayesian analysis of atomically resolved STEM data

Christopher T. Nelson, Rama K. Vasudevan, Xiaohang Zhang, Maxim Ziatdinov, Eugene A. Eliseev, Ichiro Takeuchi, Anna N. Morozovska, Sergei V. Kalinin
2020 Nature Communications  
The preexisting materials knowledge naturally folds in the Bayesian framework in the form of prior distributions, with the different order parameters forming competing (or hierarchical) models.  ...  ., c, d, e) are clearly marginalizable, whereas the parameters L c -η (f) show that probability density is not marginalizable.  ...  Fig . 3 109°Domain wall: LGD models and posterior probability densities. a The 90% highest posterior density interval for the Bayesian analysis (red band) overlaid on experimental mean values (data points  ... 
doi:10.1038/s41467-020-19907-2 pmid:33311492 fatcat:fpocqhlxe5aqnhmieffvuwndaq

Exploring physics of ferroelectric domain walls via Bayesian analysis of atomically resolved STEM data [article]

Christopher T. Nelson, Rama K. Vasudevan, Xiaohang Zhang, Maxim Ziatdinov, Eugene A. Eliseev, Ichiro Takeuchi, Anna N. Morozovska, Sergei V. Kalinin
2020 arXiv   pre-print
The preexisting materials knowledge naturally folds in the Bayesian framework in the form of prior distributions, with the different order parameters forming competing (or hierarchical) models.  ...  Some parameters (e.g. c,d,e) are clearly marginalizable, whereas the parameters Lc-show that probability density is not marginalizable.  ...  Figure 3 . 3 109° Domain wall: GLD models and posterior probability densities.  ... 
arXiv:2004.09814v1 fatcat:v3k7d2yevjbudd3m2aegfzglpq

Marginalizable conditional model for clustered ordinal data [article]

Rui Zhang, Kwun Chuen Gary Chan
2014 arXiv   pre-print
likelihood estimation under a correct model specification.  ...  This leads to a robust estimation equation with an optimal weighting matrix being the inverse of a genuine model-based covariance matrix.  ...  Due to model identifiability and condition C.3, E(B) is a negative definite matrix and thus continuously invertible. Therefore, P.5 is also satisfied.  ... 
arXiv:1403.7812v1 fatcat:3lnxgpg7mffilloibrjcvs3anq

MAP Estimation, Linear Programming and Belief Propagation with Convex Free Energies [article]

Yair Weiss, Chen Yanover, Talya Meltzer
2012 arXiv   pre-print
In experiments, we show that our theorems allow us to find the MAP in many real-world instances of graphical models where exact inference using junction-tree is impossible.  ...  Finding the most probable assignment (MAP) in a general graphical model is known to be NP hard but good approximations have been attained with max-product belief propagation (BP) and its variants.  ...  If the sharpened max-product beliefs are sum-marginalizable then they are a solution to the LP problem.  ... 
arXiv:1206.5286v1 fatcat:gg26bodlqrbznf4cebgmbzunka

A marginalizable frailty model for correlated right-censored data [article]

Rui Zhang Kwun Chuen Gary Chan
2014 arXiv   pre-print
We introduce a flexible individual frailty model for clustered right-censored data, in which covariate effects can be marginally interpreted as log failure odds ratios.  ...  Marginalizable property of our model remains yet η merges with the intercept λ 0 and thus is non-identifiable.  ...  CONCLUDING REMARKS In this paper we introduce a marginalizable individual frailty model for analysing clustered rightcensored data.  ... 
arXiv:1403.6744v1 fatcat:homn3elujjaizjzbp4kxvt22ji

Perturb-and-max-product: Sampling and learning in discrete energy-based models [article]

Miguel Lazaro-Gredilla, Antoine Dedieu, Dileep George
2021 arXiv   pre-print
Perturb-and-MAP offers an elegant approach to approximately sample from a energy-based model (EBM) by computing the maximum-a-posteriori (MAP) configuration of a perturbed version of the model.  ...  Models can be arbitrary as long as they are built using tractable factors.  ...  A NN that is broken into max-marginalizable pieces, however, can be used.  ... 
arXiv:2111.02458v2 fatcat:i3diri6xd5c5daeocuilvr5ofi

Probabilistic Models for Unified Collaborative and Content-Based Recommendation in Sparse-Data Environments [article]

Alexandrin Popescul, Lyle H. Ungar, David M Pennock, Steve Lawrence
2013 arXiv   pre-print
Global probabilistic models also allow more general inferences than local methods like k-NN.  ...  We extend Hofmann's [1999] aspect model to incorporate three-way co-occurrence data among users, items, and item content.  ...  Marginaliz ing out z, we obtain z ization. TEM makes use of an inverse computational tem perature /3.  ... 
arXiv:1301.2303v1 fatcat:rrjeeumykfhcfbzh2y7kye3nte

Random networks, graphical models and exchangeability

Steffen Lauritzen, Alessandro Rinaldo, Kayvan Sadeghi
2018 Journal of The Royal Statistical Society Series B-statistical Methodology  
We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts.  ...  Finally we study those exchangeable models that are also summarized in the sense that the probability of a network only depends on the degree distribution, and identify a class of models that is dual to  ...  In that sense, the ERGMs are not marginalizable; see also Snijders (2010) as well as Shalizi and Rinaldo (2013) . The Erdös-Rényi models and the beta models are marginalizable in this sense.  ... 
doi:10.1111/rssb.12266 fatcat:5izskhdqwrh5zca25opgm4ohtq

DISCOVERY OF TIDAL TAILS AROUND THE DISTANT GLOBULAR CLUSTER PALOMAR 14

A. Sollima, D. Martínez-Delgado, D. Valls-Gabaud, J. Peñarrubia
2010 Astrophysical Journal  
The density map constructed with the optimal matched filter technique shows a nearly symmetrical and elongated distribution of stars on both sides of the cluster, forming a S-shape characteristic of mass  ...  They found that the observed density profiles deviate from the prediction of a best-fit King model at the outermost radii and extend beyond the conventional limiting radius set by this model.  ...  Our best fit King 6 In the model fitting a constant background of density log ρ = −1.37 stars arcmin −2 has been assumed from the MS star counts in the most external region of our image (at r >25').  ... 
doi:10.1088/0004-637x/726/1/47 fatcat:vtw33gpxlfeyxahocjrnmgp2pa

Random Networks, Graphical Models, and Exchangeability [article]

Steffen Lauritzen and Alessandro Rinaldo and Kayvan Sadeghi
2017 arXiv   pre-print
We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their theoretical counterparts.  ...  Finally we study those exchangeable models that are also summarized in the sense that the probability of a network only depends onthe degree distribution, and identify a class of models that is dual to  ...  In that sense, the ERGMs are not marginalizable; see also Snijders (2010) as well as Shalizi and Rinaldo (2013) . The Erdös-Rényi models and the beta models are marginalizable in this sense.  ... 
arXiv:1701.08420v2 fatcat:dywirpkvunfptpcjg72pm5t5he

Exploring particle dynamics during self-organization processes via rotationally invariant latent representations [article]

Sergei V. Kalinin, Shuai Zhang, Mani Valleti, Harley Pyles, David Baker, James J. De Yoreo, Maxim Ziatdinov
2020 arXiv   pre-print
Note that the L1distribution is almost marginalizable, with clear 6-fold maxima associated with angle distribution.  ...  Here, we visualize both the individual data points and the superimposed kernel density estimates.  ... 
arXiv:2009.00783v1 fatcat:fgdbshantrgddbudsdwso67i3i

Ancestor Sampling for Particle Gibbs [article]

Fredrik Lindsten, Michael I. Jordan, Thomas B. Schön
2012 arXiv   pre-print
We apply the PG-AS framework to the challenging class of non-Markovian state-space models.  ...  Several application examples are discussed, including Rao-Blackwellized particle smoothing and inference in degenerate state-space models.  ...  In fact, this is nothing but another application of Rao-Blackwellization as discussed in Section 5.1, where the z t -state is conditionally deterministic and thus trivially marginalizable.  ... 
arXiv:1210.6911v1 fatcat:s7mmrrnz5rdijnjx6e4f75txxq

Naive Bayesian Learning in Social Networks [article]

Jerry Anunrojwong, Nat Sothanaphan
2018 arXiv   pre-print
Our proposed model captures aspects of both Bayesian and naive learning.  ...  We propose a model that captures this aspect of communication by incorporating signal informativeness into the naive social learning scenario.  ...  We make the following marginalizability assumption, which is important in order to reason consistently about marginal densities.  ... 
arXiv:1805.05878v2 fatcat:yrtq7viguvhixhmup4p7ipc5d4

A General Algorithm for Approximate Inference and its Application to Hybrid Bayes Nets [article]

Daphne Koller, Uri Lerner, Dragomir Anguelov
2013 arXiv   pre-print
The algorithm essentially does clique tree propagation, using approximate inference to estimate the densities in each clique.  ...  Each clique executes local computations over the variables in the clique, which corre spond to multiplying messages and CPDs, and marginaliz ing the result over some of the variables in the clique (by  ...  Until now, most of the Bayesian network models designed have admitted inference using one of the existing algorithms.  ... 
arXiv:1301.6709v1 fatcat:dqzgpf7gujbelkvgwgfmg5k3g4

Analytic marginalization of absorption line continua [article]

Kirill Tchernyshyov
2019 arXiv   pre-print
Simultaneous probabilistic modeling of absorption features and continuum shape is a promising approach for automating this analysis.  ...  In addition to speeding up probabilistic modeling, analytic marginalization makes it trivial to marginalize over continuum parameterizations and to combine continuum description marginalization with optimization  ...  Marginalizable linear models can still be useful even in this case as a way of introducing small corrections for pseudo-continuum features that are not perfectly described by the non-linear model.  ... 
arXiv:1901.06416v1 fatcat:s2i7naqv7vdbvkuhcs7caphqlm
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