A Filtering Approach to Stochastic Variational Inference
Stochastic variational inference (SVI) uses stochastic optimization to scale up Bayesian computation to massive data. We present an alternative perspective on SVI as approximate parallel coordinate ascent. SVI trades-off bias and variance to step close to the unknown true coordinate optimum given by batch variational Bayes (VB). We define a model to automate this process. The model infers the location of the next VB optimum from a sequence of noisy realizations. As a consequence of this construction, we update the variational parameters using Bayes rule, rather than a hand-crafted optimization schedule. When our model is a Kalman filter this procedure can recover the original SVI algorithm and SVI with adaptive steps. We may also encode additional assumptions in the model, such as heavytailed noise. By doing so, our algorithm outperforms the original SVI schedule and a state-of-the-art adaptive SVI algorithm in two diverse domains.
Stochastic variational inference (SVI) requires careful selection of a step size. This paper proposes a Kalman filter to set the step size automatically. The authors show that standard Gaussian KF does not satisfy the Robbins Munro criteria (and performs badly). They propose to apply a KF based on T-distributions, and show that this gives better results than standard SVI.The problem addressed in this paper is relevant. The solutions proposed are also quite interesting and seem useful. I have few theoretical and computational concerns which I have discussed below. The paper is clearly written. The work is original and significant. The numerical experiments shown are satisfactory.Below are some of my comments to help improve the quality of this paper.Eq. 7 and 8 involve inverting a matrix at every iteration of the algorithm. Since Q and R change every time, we cannot precompute the step sizes. Does this increase the computation significantly? I would expect that there is some increase due to inversion of the matrices who size depends on size of lambda. Will you please discuss the extent of computation increase you notice in your experiments?Doing filtering and parameter estimation at the same time for Kalman filter should be problematic, at least initially. I don't see that in the Fig. 4. Why is that? Do you use some method to compensate for this? In any case, it will be good to include a discussion about the consequences of this approach. When is it going to work and when is it going to be troublesome? Does the size of lambda play a role in this too? etc.You mention that for fixed Q and R Robbins-Munro criteria do not hold. When they are varying, does it holds for sure? can you prove it? Is it the same for T-distribution KF? Is this the reason why in Fig. 4 Gaussian KF doesn't reach the true maximum? There are small typos here and there. There is a mistake in Eq. 5. The first equation works for t, while the second equation works with t+1.