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Variational Inference with Holder Bounds [article]

Junya Chen, Danni Lu, Zidi Xiu, Ke Bai, Lawrence Carin, Chenyang Tao
2021 arXiv   pre-print
The recent introduction of thermodynamic integration techniques has provided a new framework for understanding and improving variational inference (VI).  ...  This motivates our new VI objectives, named the Holder bounds, which flatten the thermodynamic curves and promise to achieve a one-step approximation of the exact marginal log-likelihood.  ...  Flattening the curve with Hölder bounds In order to generalize the integration path, we consider the more general Hölder averaging operation. wrt Hölder paths, with the following statement directly generalizing  ... 
arXiv:2111.02947v2 fatcat:cms2wta3z5fxja3mpubwgnioeq

Approximate Inference with the Variational Holder Bound [article]

Guillaume Bouchard, Balaji Lakshminarayanan
2015 arXiv   pre-print
We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference.  ...  with respect to the variational parameters.  ...  Variational Bayes Variational Hölder vs.  ... 
arXiv:1506.06100v1 fatcat:4szmyce6cjd77bmvvndress5xa

Gauged Mini-Bucket Elimination for Approximate Inference [article]

Sungsoo Ahn, Michael Chertkov, Jinwoo Shin, Adrian Weller
2018 arXiv   pre-print
WMBE-G can provide both upper and lower bounds on Z, and is easier to optimize than the prior gauge-variational algorithm.  ...  Since this is computationally intractable, variational approximations are often used in practice. Recently, so-called gauge transformations were used to improve variational lower bounds on Z.  ...  Variational approaches frame the inference task as an opti- mization problem, which is typically solved approximately.  ... 
arXiv:1801.01649v2 fatcat:yfblfpxqobbbziehfr7jwycsqu

Variational Infinite Heterogeneous Mixture Model for Semi-supervised Clustering of Heart Enhancers [article]

Tahmid F Mehdi, Gurdeep Singh, Jennifer A Mitchell, Alan M Moses
2018 bioRxiv   pre-print
We derived a novel variational inference algorithm to handle semi-supervised learning tasks where certain observations are forced to cluster together.  ...  Results: We implemented a Dirichlet Process Heterogeneous Mixture model that infers Gaussian, Bernoulli and Poisson distributions over features.  ...  Variational inference approximates the true posterior of the latent variables with a variational distribution q by maximizing the evidence lower bound (ELBO): ( ) = [ln ( , µ, , , , , )] − [ln (µ, , ,  ... 
doi:10.1101/442392 fatcat:rl2xdyj64fegpp2fu7dgjyijki

Convergence Rates of Variational Inference in Sparse Deep Learning [article]

Badr-Eddine Chérief-Abdellatif
2019 arXiv   pre-print
In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference.  ...  Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning.  ...  Assume that f 0 is β-Hölder smooth with 0 < β < d.  ... 
arXiv:1908.04847v2 fatcat:smw4kc2eqfgrxhfrl2riw6rqke

Partial regularity for minimizers of variational integrals with discontinuous integrands

Christoph Hamburger
1996 Annales de l'Institut Henri Poincare. Analyse non linéar  
HAMBURGER such that but We set Then (2.1) and (2.2) become 263 VARIATIONAL INTEGRALS From (2.7) we immediately have Since 0 as m -~ oo, and a ~ 8, it follows from (2.9) that We infer  ...  By virtue of the higher integrability theorem, we then deduce from a Caccioppoli inequality a reverse Holder inequality for Du -Po, for constant Po E This leads to a uniform bound of ~Dwm ~ in for some  ... 
doi:10.1016/s0294-1449(16)30104-4 fatcat:3bypjwzwpvbphn6xoaqktno7rq

Coarse-grained modeling of mitochondrial metabolism enables subcellular flux inference from fluorescence lifetime imaging microscopy [article]

Xingbo Yang, Daniel J Needleman
2020 bioRxiv   pre-print
We showed that this subcellular variation in mitochondrial flux correlates with a corresponding subcellular variation in mitochondrial membrane potential.  ...  Mitochondria are central to metabolism and their dysfunctions are associated with many diseases.  ...  flux correlates with a corresponding subcellular variation in mitochondrial membrane potential.  ... 
doi:10.1101/2020.11.20.392225 fatcat:brq7h5wxsjbpzm3w65zytirqn4

Variational Inference of Population Structure in Large SNP Datasets [article]

Anil Raj, Matthew Stephens, Jonathan K Pritchard
2013 bioRxiv   pre-print
Here, we develop efficient algorithms for approximate inference of the model underlying the STRUCTURE program using a variational Bayesian framework.  ...  Variational methods pose the problem of computing relevant posterior distributions as an optimization problem, allowing us to build on recent advances in optimization theory to develop fast inference tools  ...  Accelerated variational inference: Similar to the EM algorithm, the convergence of the iterative algorithm for variational inference can be quite slow.  ... 
doi:10.1101/001073 fatcat:2mkaddnylfdpxbhj244z6nwayy

Stochastic Variational Inference for Bayesian Phylogenetics: A Case of CAT Model [article]

Tung Dang, Hirohisa Kishino
2018 bioRxiv   pre-print
Here, we have developed a variational Bayesian procedure to speed up the widely used PhyloBayes MPI program, which deals with the heterogeneity of amino acid propensity.  ...  By taking into account the complex heterogeneity of evolutionary processes among sites in a genome, Bayesian infinite mixture models of genomic evolution enable robust phylogenetic inference.  ...  To estimate each global variational parameter in the CAT-Poisson model, we use the stochastic variational inference (SVI) algorithm to optimize the lower bound in Equation (2) (Hoffman et al. 2013)  ... 
doi:10.1101/358747 fatcat:if2nh5zf5bbaxjjiavdy423kxq

Generalised free energy and active inference: can the future cause the past? [article]

Thomas Parr, Karl J Friston
2018 bioRxiv   pre-print
We compare two free energy functionals for active inference under Markov decision processes.  ...  When using the free energy function, which is blind to counterfactual (i.e., future) observations, we equip the generative model with a prior over policies that ensure preferred (i.e., priors over) outcomes  ...  When this maximisation uses approximate Bayesian inference, this is equivalent to minimising variational free energy (Friston et al. 2006 ) -a form of bounded rational behaviour that minimises a variational  ... 
doi:10.1101/304782 fatcat:3hnq2wj5fzewxchksu53mwgepa

Reverse engineering neural networks to characterise their cost functions [article]

Takuya Isomura, Karl J. Friston
2019 bioRxiv   pre-print
In brief, we show that such cost functions can be cast as a variational bound on model evidence, or marginal likelihood, under an implicit generative model.  ...  This insight is potentially important because it suggests that any free parameter of a neural network's cost function can itself be optimised - by minimisation with respect to variational free energy.  ...  However, this evaluation 55 can be converted into an optimisation problem by inducing a variational bound on surprise. 56 In machine learning, this is known as an evidence lower bound (ELBO), while the  ... 
doi:10.1101/654467 fatcat:djxpbyn5x5ag7mv7ysdq5vp42m

Scaling probabilistic models of genetic variation to millions of humans

Prem Gopalan, Wei Hao, David M Blei, John D Storey
2016 Nature Genetics  
It is a principled approach to Bayesian inference that iterates between subsampling locations of the genome and updating an estimate of the latent population structure of the individuals.  ...  One of the major goals of population genetics is to quantitatively understand variation of genetic polymorphisms among individuals.  ...  The key idea in TeraStructure is to solve this optimization problem with stochastic variational inference [7] , a way of doing variational inference that scales to large data.  ... 
doi:10.1038/ng.3710 pmid:27819665 pmcid:PMC5127768 fatcat:xh6w5ipdmjfc5ic33j72tath3u

Scaling probabilistic models of genetic variation to millions of humans [article]

Prem Gopalan, Wei Hao, David M. Blei, John D. Storey
2014 bioRxiv   pre-print
It is a principled approach to Bayesian inference that iterates between subsampling locations of the genome and updating an estimate of the latent population structure of the individuals.  ...  One of the major goals of population genetics is to quantitatively understand variation of genetic polymorphisms among individuals.  ...  The key idea in TeraStructure is to solve this optimization problem with stochastic variational inference [7] , a way of doing variational inference that scales to large data.  ... 
doi:10.1101/013227 fatcat:q5lb57hrfbgltgec4drtbl3lbi

Root-n consistent density estimators of convolutions in weighted -norms

Anton Schick, Wolfgang Wefelmeyer
2007 Journal of Statistical Planning and Inference  
We show that this remains true even for discontinuous densities as long as they are of bounded variation. The assumption of bounded variation can be relaxed.  ...  It is known that the convolution of a smooth density with itself can be estimated at the root-n rate by a convolution of an appropriate density estimator with itself.  ...  If g is of bounded variation, then g is L 1 -Hölder with exponent γ = 1; see Corollary 2 in Section 4.  ... 
doi:10.1016/j.jspi.2006.06.041 fatcat:52b7s4jusrbdxbnf7bpe6zhz5m

msCentipede: Modeling heterogeneity across genomic sites improves accuracy in the inference of transcription factor binding [article]

Anil Raj, Heejung Shim, Yoav Gilad, Jonathan K Pritchard, Matthew Stephens
2014 bioRxiv   pre-print
Results: In this work, we adapt a multi-scale modeling framework for inhomogeneous Poisson processes to better model the underlying variation in DNase I cleavage patterns across genomic locations bound  ...  However, the model for the spatial profile in this framework underestimates the substantial variation in the DNase I cleavage profiles across factor-bound genomic locations and across replicate measurements  ...  vs unbound), and infers the probability that each site is bound.  ... 
doi:10.1101/012013 fatcat:mdwyolnwhrd3namlxyckwi3w7m
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