back to shrinkage!
Our Warwick PhD student Shreya Sinha-Roy—who is now looking for a postdoctoral position next semester!—, along with Sherman Khoo, Ritabrata Dutta and myself, has now completed a paper on shrinkage priors for implicit generative models. That is, models based on deep neural networks and hence associated with intractable likelihoods. The work centres on developing and assessing an efficient training mechanism for these models, leveraging on tools from Bayesian model averaging using shrinkage (yay!) priors inspired from Lasso (rather than from my PhD years!) and generalized Bayes. In this large p (dimension of parameters) and small n (sample size of data) scenario, those sparsity inducing priors have been successfully used for linear regression when p is much larger than n, but have not been applied to implicit generative models due to the intractability of the likelihood function of the parameters of the model given observed data. Adapting a scoring rule posterior based on a strictly proper scoring rule as in generalized Bayes, we propose a block SGMCMC within Gibbs sampling mechanism to handle high dimensional parameter space for learning a sparse Bayesian model averaged neural implicit generative model in a sample efficient way. We illustrate excellent performance of our proposed method for p (much larger than n) linear regressions and three applications of neural generative models in tasks relevant to weather forecasting to reinforcement learning
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