Sharad Vikram
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Automatic Differentiation Variational Inference (ADVI) is a useful tool for efficiently learning probabilistic models in machine learning. Generally approximate posteriors learned by ADVI are forced to be unimodal in order to facilitate use of the reparameterization trick. In this paper, we show how stratified sampling may be used to enable mixture distributions as the approximate posterior, and derive a new lower bound on the evidence analogous to the importance weighted autoencoder (IWAE). We show that this "SIWAE" is a tighter bound than both IWAE and the traditional ELBO, both of which are special instances of this bound. We verify empirically that the traditional ELBO objective disfavors the presence of multimodal posterior distributions and may therefore not be able to fully capture structure in the latent space. Our experiments show that using the SIWAE objective allows the encoder to learn more complex distributions which regularly contain multimodality, resulting in higher accuracy and better calibration in the presence of incomplete, limited, or corrupted data.
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Automatic Structured Variational Inference
Luca Ambrogioni
Max Hinne
Dave Moore
Marcel van Gerven
AISTATS (2021)
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Probabilistic programming is concerned with the symbolic specification of probabilistic models for which inference can be performed automatically. Gradient-based automatic differentiation stochastic variational inference offers an attractive option as the default method for (differentiable) probabilistic programming. However, the performance of any (parametric) variational approach depends on the choice of an appropriate variational family. Here, we introduce automated structured variational inference (ASVI), a fully automated method for constructing structured variational families, inspired by the closed-form update in conjugate Bayesian models. These pseudo-conjugate families incorporate the forward pass of the input probabilistic program and can therefore capture complex statistical dependencies. Pseudo-conjugate families have the same space and time complexity of the input probabilistic program and are therefore tractable for a very large family of models including both continuous and discrete variables. We provide a fully automatic implementation in TensorFlow Probability. We validate our automatic variational method on a wide range of both low- and high-dimensional inference problems including deep learning components.
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Estimating the Changing Infection Rate of COVID-19 Using Bayesian Models of Mobility
Xue Ben
Shawn O'Banion
medRxiv, vol. https://www.medrxiv.org/content/10.1101/2020.08.06.20169664v1.full (2020)
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In order to prepare for and control the continued spread of the COVID-19 pandemic while minimizing its economic impact, the world needs to be able to estimate and predict COVID-19’s spread.
Unfortunately, we cannot directly observe the prevalence or growth rate of COVID-19; these must be inferred using some kind of model.
We propose a hierarchical Bayesian extension to the classic susceptible-exposed-infected-removed (SEIR) compartmental model that adds compartments to account for isolation and death and allows the infection rate to vary as a function of both mobility data collected from mobile phones and a latent time-varying factor that accounts for changes in behavior not captured by mobility data. Since confirmed-case data is unreliable, we infer the model’s parameters conditioned on deaths data. We replace the exponential-waiting-time assumption of classic compartmental models with Erlang distributions, which allows for a more realistic model of the long lag between exposure and death. The mobility data gives us a leading indicator that can quickly detect changes in the pandemic’s local growth rate and forecast changes in death rates weeks ahead of time. This is an analysis of observational data, so any causal interpretations of the model's inferences should be treated as suggestive at best; nonetheless, the model’s inferred relationship between different kinds of trips and the infection rate do suggest some possible hypotheses about what kinds of activities might contribute most to COVID-19’s spread.
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