Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data. Bayesian methods represent one important class of statistic methods for machine learning, with substantial recent developments on adaptive, flexible and scalable Bayesian learning. This article provides a survey of the recent advances in Big learning with Bayesian methods, termed Big Bayesian Learning, including nonparametric Bayesian methods for adaptively inferring model complexity, regularized Bayesian inference for improving the flexibility via posterior regularization, and scalable algorithms and systems based on stochastic subsampling and distributed computing for dealing with large-scale applications.
Bayesian optimization (BO) @cite_54 aims to optimize some objective, which may be expensive to evaluate or do not have easily available derivatives, with successful applications in robotics, planning, recommendation, advertising, and automatic algorithm configuration. In Big data era, the learning models are becoming incredibly huge @cite_43 and the learning algorithms often have tuning parameters (e.g., the learning rates of SGD algorithms). Manually tuning such hyper-parameters is often prohibitive. Recent progress has been made on practical BO methods to automatically select good parameters based on Gaussian process using a multi-core parallel Monte Carlo algorithm @cite_111 or a stochastic variational inference method @cite_120 . To deal with the challenge of learning in high dimensional spaces, the work @cite_40 presents a random embedding BO algorithm.
@cite_54 @cite_120 @cite_43 @cite_40 @cite_111
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Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function @math which is only accessible via point evaluations. It is typically used in settings where @math is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, only permits tuning scalar hyper-parameters of machine learning algorithms. However, with the surge of interest in deep learning, there is an increasing demand to tune neural network . In this work, we develop NASBOT, a Gaussian process based BO framework for neural architecture search. To accomplish this, we develop a distance metric in the space of neural network architectures which can be computed efficiently via an optimal transport program. This distance might be of independent interest to the deep learning community as it may find applications outside of BO. We demonstrate that NASBOT outperforms other alternatives for architecture search in several cross validation based model selection tasks on multi-layer perceptrons and convolutional neural networks. We introduce a means of automating machine learning (ML) for big data tasks, by performing scalable stochastic Bayesian optimisation of ML algorithm parameters and hyper-parameters. More often than not, the critical tuning of ML algorithm parameters has relied on domain expertise from experts, along with laborious hand-tuning, brute search or lengthy sampling runs. Against this background, Bayesian optimisation is finding increasing use in automating parameter tuning, making ML algorithms accessible even to non-experts. However, the state of the art in Bayesian optimisation is incapable of scaling to the large number of evaluations of algorithm performance required to fit realistic models to complex, big data. We here describe a stochastic, sparse, Bayesian optimisation strategy to solve this problem, using many thousands of noisy evaluations of algorithm performance on subsets of data in order to effectively train algorithms for big data. We provide a comprehensive benchmarking of possible sparsification strategies for Bayesian optimisation, concluding that a Nystrom approximation offers the best scaling and performance for real tasks. Our proposed algorithm demonstrates substantial improvement over the state of the art in tuning the parameters of a Gaussian Process time series prediction task on real, big data. Bayesian optimization is a powerful tool for fine-tuning the hyper-parameters of a wide variety of machine learning models. The success of machine learning has led practitioners in diverse real-world settings to learn classifiers for practical problems. As machine learning becomes commonplace, Bayesian optimization becomes an attractive method for practitioners to automate the process of classifier hyper-parameter tuning. A key observation is that the data used for tuning models in these settings is often sensitive. Certain data such as genetic predisposition, personal email statistics, and car accident history, if not properly private, may be at risk of being inferred from Bayesian optimization outputs. To address this, we introduce methods for releasing the best hyper-parameters and classifier accuracy privately. Leveraging the strong theoretical guarantees of differential privacy and known Bayesian optimization convergence bounds, we prove that under a GP assumption these private quantities are also near-optimal. Finally, even if this assumption is not satisfied, we can use different smoothness guarantees to protect privacy. Recently, Bayesian Optimization (BO) has been used to successfully optimize parametric policies in several challenging Reinforcement Learning (RL) applications. BO is attractive for this problem because it exploits Bayesian prior information about the expected return and exploits this knowledge to select new policies to execute. Effectively, the BO framework for policy search addresses the exploration-exploitation tradeoff. In this work, we show how to more effectively apply BO to RL by exploiting the sequential trajectory information generated by RL agents. Our contributions can be broken into two distinct, but mutually beneficial, parts. The first is a new Gaussian process (GP) kernel for measuring the similarity between policies using trajectory data generated from policy executions. This kernel can be used in order to improve posterior estimates of the expected return thereby improving the quality of exploration. The second contribution, is a new GP mean function which uses learned transition and reward functions to approximate the surface of the objective. We show that the model-based approach we develop can recover from model inaccuracies when good transition and reward models cannot be learned. We give empirical results in a standard set of RL benchmarks showing that both our model-based and model-free approaches can speed up learning compared to competing methods. Further, we show that our contributions can be combined to yield synergistic improvement in some domains.