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Register a new userLearning Patterns in Sample Distributions for Monte Carlo Variance Reduction
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Oskar Elek
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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This paper investigates a novel a-posteriori variance reduction approach in Monte Carlo image synthesis. Unlike most established methods based on lateral filtering in the image space, our proposition is to produce the best possible estimate for each pixel separately, from all the samples drawn for it. To enable this, we systematically study the per-pixel sample distributions for diverse scene configurations. Noting that these are too complex to be characterized by standard statistical distributions (e.g. Gaussians), we identify patterns recurring in them and exploit those for training a variance-reduction model based on neural nets. In result, we obtain numerically better estimates compared to simple averaging of samples. This method is compatible with existing image-space denoising methods, as the improved estimates of our model can be used for further processing. We conclude by discussing how the proposed model could in future be extended for fully progressive rendering with constant memory footprint and scene-sensitive output.
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Sampling from a log-concave distribution function is one core problem that has wide applications in Bayesian statistics and machine learning. While most gradient free methods have slow convergence rate, the Langevin Monte Carlo (LMC) that provides fast convergence requires the computation of gradients. In practice one uses finite-differencing approximations as surrogates, and the method is expensive in high-dimensions. A natural strategy to reduce computational cost in each iteration is to utilize random gradient approximations, such as random coordinate descent (RCD) or simultaneous perturbation stochastic approximation (SPSA). We show by a counter-example that blindly applying RCD does not achieve the goal in the most general setting. The high variance induced by the randomness means a larger number of iterations are needed, and this balances out the saving in each iteration. We then introduce a new variance reduction approach, termed Randomized Coordinates Averaging Descent (RCAD), and incorporate it with both overdamped and underdamped LMC. The methods are termed RCAD-O-LMC and RCAD-U-LMC respectively. The methods still sit in the random gradient approximation framework, and thus the computational cost in each iteration is low. However, by employing RCAD, the variance is reduced, so the methods converge within the same number of iterations as the classical overdamped and underdamped LMC. This leads to a computational saving overall.
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