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Validated Variational Inference via Practical Posterior Error Bounds [article]

Jonathan H. Huggins, Mikołaj Kasprzak, Trevor Campbell, Tamara Broderick
<span title="2020-02-29">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we provide rigorous bounds on the error of posterior mean and uncertainty estimates that arise from full-distribution approximations, as in variational inference.  ...  Our bounds are also computationally efficient for variational inference because they require only standard values from variational objectives, straightforward analytic calculations, and simple Monte Carlo  ...  Acknowledgements The authors thank Sushrutha Reddy for pointing out some improvements to our Wasserstein bounds on the standard deviation and variance, and also Daniel Simpson, Lester Mackey, Arthur Gretton  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.04102v4">arXiv:1910.04102v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wwq4xlhfdzeajhhyijyxdbli5e">fatcat:wwq4xlhfdzeajhhyijyxdbli5e</a> </span>
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Gaussian Mean Field Regularizes by Limiting Learned Information

Julius Kunze, Louis Kirsch, Hippolyt Ritter, David Barber
<span title="2019-08-03">2019</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4d3elkqvznfzho6ki7a35bt47u" style="color: black;">Entropy</a> </i> &nbsp;
We quantify a maximum capacity when the posterior variance is either fixed or learned and connect it to generalization error, even when the KL-divergence in the objective is scaled by a constant.  ...  Variational inference with a factorized Gaussian posterior estimate is a widely-used approach for learning parameters and hidden variables.  ...  Flexible Variational Distributions The objective function for variational inference is maximized when the approximate posterior is equal to the true one.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/e21080758">doi:10.3390/e21080758</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/33267472">pmid:33267472</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC7515287/">pmcid:PMC7515287</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oj7kzldvxbe3zimh3m32yqdpry">fatcat:oj7kzldvxbe3zimh3m32yqdpry</a> </span>
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Gaussian Mean Field Regularizes by Limiting Learned Information [article]

Julius Kunze, Louis Kirsch, Hippolyt Ritter, David Barber
<span title="2019-02-12">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We quantify a maximum capacity when the posterior variance is either fixed or learned and connect it to generalization error, even when the KL-divergence in the objective is rescaled.  ...  Variational inference with a factorized Gaussian posterior estimate is a widely used approach for learning parameters and hidden variables.  ...  Flexible Variational Distributions The objective function for variational inference is maximized when the approximate posterior is equal to the true one.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.04340v1">arXiv:1902.04340v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nn3phevt25gktiognm46ckzkt4">fatcat:nn3phevt25gktiognm46ckzkt4</a> </span>
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Variational Inference with Holder Bounds [article]

Junya Chen, Danni Lu, Zidi Xiu, Ke Bai, Lawrence Carin, Chenyang Tao
<span title="2021-11-13">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In particular, we elucidate how the TVO naturally connects the three key variational schemes, namely the importance-weighted VI, Renyi-VI, and MCMC-VI, which subsumes most VI objectives employed in practice  ...  In this work, we present a careful analysis of the thermodynamic variational objective (TVO), bridging the gap between existing variational objectives and shedding new insights to advance the field.  ...  Figure S10 : S10 Figure S10: Comparison of posterior estimates from different variational objectives, overlaid on ground-truth contours.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2111.02947v2">arXiv:2111.02947v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cms2wta3z5fxja3mpubwgnioeq">fatcat:cms2wta3z5fxja3mpubwgnioeq</a> </span>
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Boosting Black Box Variational Inference [article]

Francesco Locatello, Gideon Dresdner, Rajiv Khanna, Isabel Valera, and Gunnar Rätsch
<span title="2018-11-28">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational family.  ...  Borrowing ideas from the classic boosting framework, recent approaches attempt to boost VI by replacing the selection of a single density with a greedily constructed mixture of densities.  ...  To sample from R t , we sample U, V from the boosted posterior (U, V) t and then sample from N (U V, I).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1806.02185v5">arXiv:1806.02185v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/upsqt5t3wjfijewd5763tlnrr4">fatcat:upsqt5t3wjfijewd5763tlnrr4</a> </span>
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Mixed Variational Inference [article]

Nikolaos Gianniotis
<span title="2019-06-04">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies.  ...  Variational approaches avoid this issue by explicitly minimising the Kullback-Leibler divergence DKL between a postulated posterior and the true (unnormalised) logarithmic posterior.  ...  The main idea is to take the Gaussian posterior obtained from the Laplace approximation, plug it into the variational lower bound and adapt it by optimising the lower bound.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.04791v3">arXiv:1901.04791v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6w6jliicqfao5n7vnmtsba7e2u">fatcat:6w6jliicqfao5n7vnmtsba7e2u</a> </span>
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Variational Inference via χ-Upper Bound Minimization [article]

Adji B. Dieng, Dustin Tran, Rajesh Ranganath, John Paisley, David M. Blei
<span title="2017-11-12">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we propose CHIVI, a black-box variational inference algorithm that minimizes D_χ(p || q), the χ-divergence from p to q.  ...  When compared to expectation propagation and classical VI, CHIVI produces better error rates and more accurate estimates of posterior variance.  ...  The objective is not guaranteed to be an upper bound if S is not chosen appropriately from the beginning.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1611.00328v4">arXiv:1611.00328v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u2ibwbhmdbccplzh4rjwytddbu">fatcat:u2ibwbhmdbccplzh4rjwytddbu</a> </span>
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Decision-Making with Auto-Encoding Variational Bayes [article]

Romain Lopez, Pierre Boyeau, Nir Yosef, Michael I. Jordan, Jeffrey Regier
<span title="2020-10-21">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Our theoretical results suggest that a posterior approximation distinct from the variational distribution should be used for making decisions.  ...  Second, the variational distribution may not equal the posterior distribution under the fitted model.  ...  NY and RL were supported by grant U19 AI090023 from NIH-NIAID.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2002.07217v3">arXiv:2002.07217v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6cmn2vnltfb2zb3pythxwlesre">fatcat:6cmn2vnltfb2zb3pythxwlesre</a> </span>
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Variational Dropout via Empirical Bayes [article]

Valery Kharitonov, Dmitry Molchanov, Dmitry Vetrov
<span title="2018-11-28">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that ARD applied to Bayesian DNNs with Gaussian approximate posterior distributions leads to a variational bound similar to that of variational dropout, and in the case of a fixed dropout rate,  ...  objectives are exactly the same.  ...  It is also easy to show that Sparse VD objective is actually a lower bound on the ARD objective. Furthermore, when α j → ∞, L SV DO (µ, α) approaches L ARD (µ, α) from below.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.00596v2">arXiv:1811.00596v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ctfo4hvlnjdkzcpd3yk7slou5m">fatcat:ctfo4hvlnjdkzcpd3yk7slou5m</a> </span>
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Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory [article]

Ron Amit, Ron Meir
<span title="2019-05-20">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We develop a gradient-based algorithm which minimizes an objective function derived from the bounds and demonstrate its effectiveness numerically with deep neural networks.  ...  We present a framework for meta-learning that is based on generalization error bounds, allowing us to extend various PAC-Bayes bounds to meta-learning.  ...  MLAP-VB: In this method the learning objective is derived from a Hierarchal Bayesian framework using variational Bayes tools 13 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1711.01244v8">arXiv:1711.01244v8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uvbegjw6erezjebbinjrrejzpe">fatcat:uvbegjw6erezjebbinjrrejzpe</a> </span>
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Robust One-Bit Bayesian Compressed Sensing with Sign-Flip Errors

Fuwei Li, Jun Fang, Hongbin Li, Lei Huang
<span title="">2015</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/msfmoh6v7bdk7lrsmtbklto74i" style="color: black;">IEEE Signal Processing Letters</a> </i> &nbsp;
Index Terms-One-bit Bayesian compressed sensing, sign-flip errors, variational expectation-maximization.  ...  We consider the problem of sparse signal recovery from one-bit measurements.  ...  In practice, however, due to the noise in signal acquisition and transmission, some of the signs may be flipped to their opposite states, in which case the above algorithms may suffer from considerable  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lsp.2014.2373380">doi:10.1109/lsp.2014.2373380</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7e35xcq3ebgtlcolabysv2yvoy">fatcat:7e35xcq3ebgtlcolabysv2yvoy</a> </span>
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There and Back Again: Unraveling the Variational Auto-Encoder [article]

Graham Fyffe
<span title="2021-05-26">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The penalty incurred from using a constant posterior variance is small under mild conditions, and otherwise discourages large variations in the decoder Hessian.  ...  We prove that the evidence lower bound (ELBO) employed by variational auto-encoders (VAEs) admits non-trivial solutions having constant posterior variances under certain mild conditions, removing the need  ...  optimal variational lower bound, in the case of Gaussian prior and posterior.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1912.10309v3">arXiv:1912.10309v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lq52zlsh4zgpfgyvgvmpq4fo4u">fatcat:lq52zlsh4zgpfgyvgvmpq4fo4u</a> </span>
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Universal Boosting Variational Inference [article]

Trevor Campbell, Xinglong Li
<span title="2019-10-27">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Finally, we discuss statistical benefits of the Hellinger distance as a variational objective through bounds on posterior probability, moment, and importance sampling errors.  ...  Boosting variational inference (BVI) approximates an intractable probability density by iteratively building up a mixture of simple component distributions one at a time, using techniques from sparse convex  ...  Finally, we discuss other statistical benefits of the Hellinger distance as a variational objective through bounds on posterior probability, moment, and importance sampling errors.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1906.01235v2">arXiv:1906.01235v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f666sfmr7rfbhhppxydhex6wjm">fatcat:f666sfmr7rfbhhppxydhex6wjm</a> </span>
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Alpha-Divergences in Variational Dropout [article]

Bogdan Mazoure, Riashat Islam
<span title="2017-11-12">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
the lowest training error, and optimizes a good lower bound for the evidence lower bound (ELBO) among all values of the parameter α∈ [0,∞).  ...  Stochastic gradient variational Bayes (SGVB) aevb is a general framework for estimating the evidence lower bound (ELBO) in Variational Bayes.  ...  Figure 2a presents a rearrangement of the test set errors from variational A dropout.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1711.04345v1">arXiv:1711.04345v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5rgnvbraejccfk6nnggogpmpty">fatcat:5rgnvbraejccfk6nnggogpmpty</a> </span>
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Early Stopping is Nonparametric Variational Inference [article]

Dougal Maclaurin, David Duvenaud, Ryan P. Adams
<span title="2015-04-06">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that unconverged stochastic gradient descent can be interpreted as a procedure that samples from a nonparametric variational approximate posterior distribution.  ...  By tracking the change in entropy over this sequence of transformations during optimization, we form a scalable, unbiased estimate of the variational lower bound on the log marginal likelihood.  ...  from q to the true posterior, giving the closest approximation available within the variational family.  ... 
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