[Paper Review] Conditioning by adaptive sampling for robust design

David H. Brookes, Hahnbeom Park+1 more|arXiv (Cornell University)|Jan 29, 2019

Machine Learning and Algorithms5 references47 citations

TL;DR

CbAS presents a model-based, non-differentiable approach to design problems by conditioning a prior on desired properties using adaptive sampling; it combats oracle pathologies by focusing on rare-event conditioning.

ABSTRACT

We present a new method for design problems wherein the goal is to maximize or specify the value of one or more properties of interest. For example, in protein design, one may wish to find the protein sequence that maximizes fluorescence. We assume access to one or more, potentially black box, stochastic "oracle" predictive functions, each of which maps from input (e.g., protein sequences) design space to a distribution over a property of interest (e.g. protein fluorescence). At first glance, this problem can be framed as one of optimizing the oracle(s) with respect to the input. However, many state-of-the-art predictive models, such as neural networks, are known to suffer from pathologies, especially for data far from the training distribution. Thus we need to modulate the optimization of the oracle inputs with prior knowledge about what makes `realistic' inputs (e.g., proteins that stably fold). Herein, we propose a new method to solve this problem, Conditioning by Adaptive Sampling, which yields state-of-the-art results on a protein fluorescence problem, as compared to other recently published approaches. Formally, our method achieves its success by using model-based adaptive sampling to estimate the conditional distribution of the input sequences given the desired properties.

Motivation & Objective

• Motivate design problems where the goal is to maximize or specify a property of interest using a black-box predictor.
• Address pathologies of predictive models far from training data by conditioning on realistic input regions.
• Develop a principled, prior-informed method to sample designs that are likely to meet the property desiderata.

Proposed method

• Model the input prior p(x) with a generative model trained on realistic examples.
• Define the conditioning event S on property values and compute p(x|S) via Bayes rule.
• Introduce an adaptive, importance-sampling scheme to estimate the conditional density p(x|S) when S is rare.
• Iteratively update a search model q(x|φ) to approximate p(x|S) by minimizing KL divergence.
• Use a sequence of relaxed events S(t) with corresponding proposals r(t)(x) to obtain non-vanishing expectations and stable optimization.
• Extend the approach to latent-variable priors and joint densities when needed.

Experimental results

Research questions

• RQ1 How can one condition a generative prior on desired property values when the property oracle is a black box and possibly non-differentiable?
• RQ2 Can adaptive sampling and KL-based updates reliably approximate the conditional distribution p(x|S) for rare-event design targets?
• RQ3 How does CbAS compare to existing AM, GAN/VAE-based, and cross-entropy methods in handling oracle pathologies and keeping designs within realistic regions?
• RQ4 Can the method be extended to latent variable models while maintaining exactness or tractable approximations?
• RQ5 Is the approach robust to different oracle uncertainty models (e.g., ensembles) in protein design applications?

Key findings

• CbAS yields a close approximation to the target conditional distribution as shown by decreasing KL divergence across iterations.
• The method effectively avoids oracle pathologies by focusing on high-probability regions under the prior and the conditioning event.
• CbAS is applicable with non-differentiable oracles and discrete design spaces, avoiding back-propagation through the oracle.
• Experiments on protein fluorescence demonstrate favorable performance against multiple baselines, including AM and DbAS variants.
• The approach can be extended to latent-variable priors with exact-density formulations when joint densities are tractable.
• CbAS maintains proximity to the prior through density-ratio weights, balancing objective maximization with prior adherence.