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Using Reinforcement Learning for Variational Inference
This blog post details how we can use ideas from Reinforcement Learning (RL) to efficiently perform variational inference in sequential settings.
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publications
A Gradient Based Strategy for Hamiltonian Monte Carlo Hyperparameter Optimization Permalink
Hamiltonian Monte Carlo (HMC) is one of the most successful sampling methods in machine learning. However, its performance is significantly affected by the choice of hyperparameter values. Existing approaches for optimizing the HMC hyperparameters either optimize a proxy for mixing speed or consider the HMC chain as an implicit variational distribution and optimize a tractable lower bound that can be very loose in practice. Instead, we propose to optimize an objective that quantifies directly the speed of convergence to the target distribution. Our objective can be easily optimized using stochastic gradient descent. We evaluate our proposed method and compare to baselines on a variety of problems including sampling from synthetic 2D distributions, reconstructing sparse signals, learning deep latent variable models and sampling molecular configurations from the Boltzmann distribution of a 22 atom molecule. We find that our method is competitive with or improves upon alternative baselines in all these experiments.
Trans-Dimensional Generative Modeling via Jump Diffusion Models Permalink
We propose a new class of generative models that naturally handle data of varying dimensionality by jointly modeling the state and dimension of each datapoint. The generative process is formulated as a jump diffusion process that makes jumps between different dimensional spaces. We first define a dimension destroying forward noising process, before deriving the dimension creating time-reversed generative process along with a novel evidence lower bound training objective for learning to approximate it. Simulating our learned approximation to the time-reversed generative process then provides an effective way of sampling data of varying dimensionality by jointly generating state values and dimensions. We demonstrate our approach on molecular and video datasets of varying dimensionality, reporting better compatibility with test-time diffusion guidance imputation tasks and improved interpolation capabilities versus fixed dimensional models that generate state values and dimensions separately.
A Continuous Time Framework for Discrete Denoising Models Permalink
We provide the first complete continuous time framework for denoising diffusion models of discrete data. This is achieved by formulating the forward noising process and corresponding reverse time generative process as Continuous Time Markov Chains (CTMCs). The model can be efficiently trained using a continuous time version of the ELBO. We simulate the high dimensional CTMC using techniques developed in chemical physics and exploit our continuous time framework to derive high performance samplers that we show can outperform discrete time methods for discrete data. The continuous time treatment also enables us to derive a novel theoretical result bounding the error between the generated sample distribution and the true data distribution.
Online Variational Filtering and Parameter Learning Permalink
We present a variational method for online state estimation and parameter learning in state-space models (SSMs), a ubiquitous class of latent variable models for sequential data. As per standard batch variational techniques, we use stochastic gradients to simultaneously optimize a lower bound on the log evidence with respect to both model parameters and a variational approximation of the states’ posterior distribution. However, unlike existing approaches, our method is able to operate in an entirely online manner, such that historic observations do not require revisitation after being incorporated and the cost of updates at each time step remains constant, despite the growing dimensionality of the joint posterior distribution of the states. This is achieved by utilizing backward decompositions of this joint posterior distribution and of its variational approximation, combined with Bellman-type recursions for the evidence lower bound and its gradients. We demonstrate the performance of this methodology across several examples, including high-dimensional SSMs and sequential Variational Auto-Encoders.
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