REMBO : Bayesian Optimization in a Billion Dimensions via Random Embeddings - implementation -

I am a little late on this one, but here is a Random Features approach used to enable large scale bayesian computations:

Bayesian Optimization in a Billion Dimensions via Random Embeddings by Ziyu Wang, Masrour Zoghi, Frank Hutter, David Matheson, Nando de Freitas

Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high-dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple, has important invariance properties, and applies to domains with both categorical and continuous variables. We present a thorough theoretical analysis of REMBO, including regret bounds that only depend on the problem's intrinsic dimensionality. Empirical results confirm that REMBO can effectively solve problems with billions of dimensions, provided the intrinsic dimensionality is low. They also show that REMBO achieves state-of-the-art performance in optimizing the 47 discrete parameters of a popular mixed integer linear programming solver.

Bayesian Optimization in High Dimensions via Random Embeddings by Ziyu Wang, Masrour Zoghi, Frank Hutter, David Matheson, Nando de Freitas

Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple and applies to domains with both categorical and continuous variables. The experiments demonstrate that REMBO can effectively solve high-dimensional problems, including automatic parameter configuration of a popular mixedinteger linear programming solver.

An implementation of REMBO can be found at: https://github.com/ziyuw/rembo

Let us note the potential use of this technique for synthetic gene design

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