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Refined α-Divergence Variational Inference via Rejection Sampling
[article]
2019
arXiv
pre-print
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We present an approximate inference method, based on a synergistic combination of Rényi α-divergence variational inference (RDVI) and rejection sampling (RS). ...
RDVI is based on minimization of Rényi α-divergence D_α(p||q) between the true distribution p(x) and a variational approximation q(x); RS draws samples from a distribution p(x) = p̃(x)/Z_p using a proposal ...
Introduction We present an approximate inference method, based on a synergistic combination of Rényi αdivergence variational inference (RDVI) and rejection sampling (RS). ...
arXiv:1909.07627v3
fatcat:czubmsuss5ekxiupyvvv4qdwgm
alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction
[article]
2022
arXiv
pre-print
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2022 pre-print arXiv:2201.08506v1 fatcat:klrkoocc6vbphfvhhm4fdfmcdu
Traditional approaches for posterior estimation include sampling-based methods and variational inference. ...
In this paper, we propose alpha-DPI, a deep learning framework that first learns an approximate posterior using alpha-divergence variational inference paired with a generative neural network, and then ...
α-divergence Variational Inference (α-VI) with Normalizing Flow VI is an approach that solves an optimization problem to estimate a posterior distribution. ...
arXiv:2201.08506v2
fatcat:5t6cchz7ffdmrk3tq5aruk7jxi
Automated Variational Inference in Probabilistic Programming
[article]
2013
arXiv
pre-print
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We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. ...
We show how to automatically derive mean-field probabilistic programs and optimize them, and demonstrate that our perspective improves inference efficiency over other algorithms. ...
While they do highlight the need for optimizing the parameters of the variational program, they do not offer a general algorithm for doing so, instead suggesting rejection sampling or importance sampling ...
arXiv:1301.1299v1
fatcat:jchutrnmkfeqbob27lk5oz3hy4
A Contrastive Divergence for Combining Variational Inference and MCMC
[article]
2019
arXiv
pre-print
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2019 pre-print arXiv:1905.04062v1 fatcat:fz6wwzuisbfirbhznlrlc4qzx4
To make inference tractable, we introduce the variational contrastive divergence (VCD), a new divergence that replaces the standard Kullback-Leibler (KL) divergence used in VI. ...
The VCD objective can be optimized efficiently with respect to the variational parameters via stochastic optimization. ...
Method Description Here we formally describe the method for refining the variational distribution with Markov chain Monte Carlo (MCMC) sampling, as well as the variational contrastive divergence (VCD) ...
arXiv:1905.04062v2
fatcat:ofmqcqgrgrepdj2bp553yfd7zu
Parallelizing MCMC via Weierstrass Sampler
[article]
2014
arXiv
pre-print
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The new sampler approximates the full data posterior samples via combining the posterior draws from independent subset MCMC chains, and thus enjoys a higher computational efficiency. ...
The algorithm is referred to as a Weierstrass refinement sampler, because samples from an initial rough approximation to the posterior (obtained via Laplace, variational approximations or other methods ...
Since the model is multidimensional, we drew 2000 samples via the sequential rejection sampling described in Weierstrass (sequential) rejection sampling correctly recognized the posterior modes. ...
arXiv:1312.4605v2
fatcat:kay5rt5kgjdoxeacrff4m2fj54
Cooperative Training of Fast Thinking Initializer and Slow Thinking Solver for Conditional Learning
[article]
2021
arXiv
pre-print
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We propose to learn the two models jointly, where the fast thinking initializer serves to initialize the sampling of the slow thinking solver, and the solver refines the initial output by an iterative ...
The solver learns from the difference between the refined output and the observed output, while the initializer learns from how the solver refines its initial output. ...
Those baselines include GAN-based, flow-based, and variational inference methods. ...
arXiv:1902.02812v3
fatcat:yb5aq6rzlvho3mc3p7yfznndja
MCMC-Interactive Variational Inference
[article]
2020
arXiv
pre-print
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Constructing a variational distribution followed by a short Markov chain that has parameters to learn, MIVI takes advantage of the complementary properties of variational inference and MCMC to encourage ...
On one hand, with the variational distribution locating high posterior density regions, the Markov chain is optimized within the variational inference framework to efficiently target the posterior despite ...
Variational inference (VI) approximates posterior p(z | x) with variational distribution q(z) by minimizing KL(q(z) || p(z | x)), the Kullback-Leibler (KL) divergence from p(z | x) to q(z) (Jordan et ...
arXiv:2010.02029v1
fatcat:kbq3obwkfrdrtj3fyktwe3gdkq
Quantum Inspired Training for Boltzmann Machines
[article]
2015
arXiv
pre-print
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We present an efficient classical algorithm for training deep Boltzmann machines (DBMs) that uses rejection sampling in concert with variational approximations to estimate the gradients of the training ...
Our rejection sampling approach can yield more accurate gradients than low-order contrastive divergence training and the costs incurred in finding increasingly accurate gradients can be easily parallelized ...
Instrumental Rejection Sampling The main insight behind our result, and stemming from [1] , is that variational approximations to the Gibbs state can be used to make training with rejection sampling much ...
arXiv:1507.02642v1
fatcat:wl3lgye55jdyplefpngpewiymu
Advances in Variational Inference
[article]
2018
arXiv
pre-print
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2018 pre-print arXiv:1711.05597v2 fatcat:k67k6x2hh5crlgirvgk2kvwhl4Other Versions
with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. ...
In this review, we give an overview of recent trends in variational inference. ...
For α → 1, we recover standard VI (involving the KL divergence). α-divergences have recently been used in variational inference [103] , [104] . ...
arXiv:1711.05597v3
fatcat:st53lmyx5ndpvezmw6vhw4fnhy
Advances in Variational Inference
2018
IEEE Transactions on Pattern Analysis and Machine Intelligence
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with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. ...
In this review, we give an overview of recent trends in variational inference. ...
For α → 1, we recover standard VI (involving the KL divergence). α-divergences have recently been used in variational inference [103] , [104] . ...
doi:10.1109/tpami.2018.2889774
fatcat:xffyfbw5w5c4dklgs3uvwynp3u
Latent Space Refinement for Deep Generative Models
[article]
2021
arXiv
pre-print
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We extend this idea to all types of generative models and show how latent space refinement via iterated generative modeling can circumvent topological obstructions and improve precision. ...
Recent proposals have suggested using classifier weights to refine the learned density of deep generative models. ...
This can be for instance done directly using the following methods: • Rejection sampling: We can use the weights w(z) to perform rejection sampling on the latent space. ...
arXiv:2106.00792v2
fatcat:otqmjkryurhebhmxlpj2kf2wo4
Measuring Uncertainty through Bayesian Learning of Deep Neural Network Structure
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:1911.09804v2 fatcat:ey5eeghdaza6hfszac6okvpusyOther Versions
We then develop an efficient stochastic variational inference approach which unifies the learning of both network structure and weights. ...
This paper investigates a new line of Bayesian deep learning by performing Bayesian inference on network structure. ...
Similar as the "cold posterior" trick [55] , we propose to sharpen the variational posterior of the structure via two refinements. ...
arXiv:1911.09804v3
fatcat:p7tvfrpnpfawhnmcuawp2mh62i
Energy-Inspired Models: Learning with Sampler-Induced Distributions
[article]
2020
arXiv
pre-print
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Moreover, EIMs allow us to generalize a recent connection between multi-sample variational lower bounds and auxiliary variable variational inference. ...
As a result, inference in EBMs relies on approximate sampling algorithms, leading to a mismatch between the model and inference. ...
As a result, semi-implicit variational inference is simply auxiliary variable variational inference by another name. ...
arXiv:1910.14265v2
fatcat:z72wzvq6areh7kw5q4rm56cpsy
Dating Primate Divergences through an Integrated Analysis of Palaeontological and Molecular Data
2010
Systematic Biology
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Estimation of divergence times is usually done using either the fossil record or sequence data from modern species. ...
[Approximate Bayesian computation; molecular phylogeny; palaeontological data; primate divergence.] ...
A rejection-based ABC algorithm for inference would be: Optimal Subtree Selection (OSS) 1. Draw parameters θ = (τ, α, ψ, p, λ) from π(•). 2. Simulate a tree and fossil finds using parameter θ. ...
doi:10.1093/sysbio/syq054
pmid:21051775
pmcid:PMC2997628
fatcat:3baaawb64ra4xmd2bq5jfzrf3q
ParaDRAM: A Cross-Language Toolbox for Parallel High-Performance Delayed-Rejection Adaptive Metropolis Markov Chain Monte Carlo Simulations
[article]
2020
arXiv
pre-print
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We present ParaDRAM, a high-performance Parallel Delayed-Rejection Adaptive Metropolis Markov Chain Monte Carlo software for optimization, sampling, and integration of mathematical objective functions ...
encountered in scientific inference. ...
The numerical computation of the IAC, however, poses another challenge to decorrelating MCMC samples since the variance of its estimator in (18) diverges to infinity. ...
arXiv:2008.09589v1
fatcat:kjxkj63syjb67it4bdm6f5q6rq
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