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UBC Theses and Dissertations

Advancing variational inference via thermodynamic integration Masrani, Vaden


Variational inference (VI) is a popular method used within statistics and machine learning to approximate intractable probability distributions via optimization. Central to VI is the Evidence Lower Bound (ELBO), a variational objective function which lower bounds the log marginal likelihood, and can be used to jointly perform maximum likelihood parameter estimation and approximate posterior inference using stochastic gradient ascent. The core contribution of this thesis is the Thermodynamic Variational Objective (TVO), a novel variational objective derived from a key connection we make between variational inference and thermodynamic integration. The TVO both tightens and generalizes the ubiquitous ELBO, and empirically leads to improvements in model and inference network learning in both discrete and continuous deep generative models. Using a novel exponential family interpretation of the geometric mixture curve underlying the TVO, we characterize the divergence bound gap left by the TVO as a sum of KL divergences between adjacent distributions, with the forward and reverse KL’s corresponding to the lower and upper-bound TVO variants. To enable the TVO to be used in gradient- based optimization algorithms, we provide two computationally efficient score-function and doubly-reparameterized based gradient estimators, as well as two adaptive “schedulers” which choose the discretization locations of a one- dimensional Riemann integral approximation, a key hyperparameter in the TVO. Additionally, we show that the objective functions used in Variational Inference, Variational AutoEncoders, Wake-Sleep, Inference Compilation, and Rényi Divergence Variational Inference are all special cases of the TVO. Finally, we evaluate the TVO in two real-world settings - a stochastic control flow models with discrete latent variables, and multi-agent trajectory prediction with continuous latent variables built on top of a differentiable driving simulator - and find the TVO improves upon baseline objectives in both cases.

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