Developing Efficient Numerical Algorithms Using Fast Bayesian Random Forests

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Is working with Random Forests a key interest of yours? Would you like to become adept at using Sequential Monte Carlo Samplers and parallel computing techniques? GCHQ and the CDT is looking for a keen PhD candidate who is conversant in Random Forest algorithms to assist them in developing new divide-and-conquer approaches that can help generate more accurate predictions. Does this sound like the challenging project you are looking for?Random Forests (e.g. in sk-learn) are in pervasive use in data science and machine learning. In such algorithms, each tree describes succinct rules that relate the inputs to the outputs (which can be both continuous values, in the context of regression, and discrete labels, in the context of classification). Random Forests then use the diversity of the set of trees to convey uncertainty about which rules apply to any datum. This combination of succinctness and diversity is perhaps why the training algorithms for random forests are both fast and often (remarkably) effective.When seen through the lens of statistics, the training algorithms for Random Forests are ad-hoc. The belief that a more principled approach could lead to improved performance has motivated historic attempts to use numerical Bayesian techniques to estimate the parameters of tree-based data science algorithms. The resulting approaches, e.g. Bayesian Additive Regression Trees (BART) and Classification Additive Regression Trees (CART), despite using models that are arguably less sophisticated than those used in Random Forests, are typically slow. This lack of speed comes about because algorithms like BART and CART use a specific numerical Bayesian technique, Markov Chain Monte Carlo (MCMC). While efficient general-purpose variants of MCMC (e.g. the No-U-Turn-Sampler (NUTS)) exist and can applied to many problems, these MCMC variants are not applicable in contexts where the number of parameters is unknown. Since trees can have different numbers of nodes and so different numbers of parameters, algorithms like NUTS can't be used to improve the run-time for tree-based algorithms like BART and CART.NUTS achieves its efficiency by using gradient information to identify the directions in which to move to optimise the parameters of the model. While one cannot calculate gradients in the context of trees, one can emulate the calculation of gradients in such settings using a hierarchy of what is known as mini-batches in the neural network literature. An algorithm that exploits this idea, Hierarchical Importance with Nested Training Samples (HINTS), was developed in 2004, but it is now obscure and its potential largely untapped. Furthermore, there is potential to use more recent advances in the context of Sequential Monte Carlo (SMC) samplers, a family of algorithms that can be exploit parallel processing resources (e.g. GPUs) and that can remove the need for the sequential burn-in phase that is often responsible for MCMC algorithms' slow run-time.This PhD will seek to develop efficient numerical Bayesian algorithms (likely to be based on a combination of HINTS and SMC samplers) that can be used to develop a variant of a Random Forest algorithms. The intent is that the new algorithms would be drop-in replacements to the Random Forest algorithms used in sk-learn that offer the same interfaces, but can use parallel computational resources to use a given training dataset to provide GCHQ more accurate predictions in the same elapsed time.