Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets

Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration often takes hours, days, or even weeks, which limits the achievable performance. To accelerate hyperparameter optimization, we propose a generative model for the validation error as a function of training set size, which is learned during the optimization process and allows exploration of preliminary configurations on small subsets, by extrapolating to the full dataset. We construct a Bayesian optimization procedure, dubbed Fabolas, which models loss and training time as a function of dataset size and automatically trades off high information gain about the global optimum against computational cost. Experiments optimizing support vector machines and deep neural networks show that Fabolas often finds high-quality solutions 10 to 100 times faster than other state-of-the-art Bayesian optimization methods or the recently proposed bandit strategy Hyperband

Hyperparameter Importance Across Datasets

With the advent of automated machine learning, automated hyperparameter optimization methods are by now routinely used in data mining. However, this progress is not yet matched by equal progress on automatic analyses that yield information beyond performance-optimizing hyperparameter settings. In this work, we aim to answer the following two questions: Given an algorithm, what are generally its most important hyperparameters, and what are typically good values for these? We present methodology and a framework to answer these questions based on meta-learning across many datasets. We apply this methodology using the experimental meta-data available on OpenML to determine the most important hyperparameters of support vector machines, random forests and Adaboost, and to infer priors for all their hyperparameters. The results, obtained fully automatically, provide a quantitative basis to focus efforts in both manual algorithm design and in automated hyperparameter optimization. The conducted experiments confirm that the hyperparameters selected by the proposed method are indeed the most important ones and that the obtained priors also lead to statistically significant improvements in hyperparameter optimization.Comment: \c{opyright} 2018. Copyright is held by the owner/author(s). Publication rights licensed to ACM. This is the author's version of the work. It is posted here for your personal use, not for redistribution. The definitive Version of Record was published in Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Minin

Learning Multiple Defaults for Machine Learning Algorithms

The performance of modern machine learning methods highly depends on their hyperparameter configurations. One simple way of selecting a configuration is to use default settings, often proposed along with the publication and implementation of a new algorithm. Those default values are usually chosen in an ad-hoc manner to work good enough on a wide variety of datasets. To address this problem, different automatic hyperparameter configuration algorithms have been proposed, which select an optimal configuration per dataset. This principled approach usually improves performance, but adds additional algorithmic complexity and computational costs to the training procedure. As an alternative to this, we propose learning a set of complementary default values from a large database of prior empirical results. Selecting an appropriate configuration on a new dataset then requires only a simple, efficient and embarrassingly parallel search over this set. We demonstrate the effectiveness and efficiency of the approach we propose in comparison to random search and Bayesian Optimization

OBOE: Collaborative Filtering for AutoML Model Selection

Algorithm selection and hyperparameter tuning remain two of the most challenging tasks in machine learning. Automated machine learning (AutoML) seeks to automate these tasks to enable widespread use of machine learning by non-experts. This paper introduces OBOE, a collaborative filtering method for time-constrained model selection and hyperparameter tuning. OBOE forms a matrix of the cross-validated errors of a large number of supervised learning models (algorithms together with hyperparameters) on a large number of datasets, and fits a low rank model to learn the low-dimensional feature vectors for the models and datasets that best predict the cross-validated errors. To find promising models for a new dataset, OBOE runs a set of fast but informative algorithms on the new dataset and uses their cross-validated errors to infer the feature vector for the new dataset. OBOE can find good models under constraints on the number of models fit or the total time budget. To this end, this paper develops a new heuristic for active learning in time-constrained matrix completion based on optimal experiment design. Our experiments demonstrate that OBOE delivers state-of-the-art performance faster than competing approaches on a test bed of supervised learning problems. Moreover, the success of the bilinear model used by OBOE suggests that AutoML may be simpler than was previously understood

A Noise-Robust Fast Sparse Bayesian Learning Model

This paper utilizes the hierarchical model structure from the Bayesian Lasso in the Sparse Bayesian Learning process to develop a new type of probabilistic supervised learning approach. The hierarchical model structure in this Bayesian framework is designed such that the priors do not only penalize the unnecessary complexity of the model but will also be conditioned on the variance of the random noise in the data. The hyperparameters in the model are estimated by the Fast Marginal Likelihood Maximization algorithm which can achieve sparsity, low computational cost and faster learning process. We compare our methodology with two other popular learning models; the Relevance Vector Machine and the Bayesian Lasso. We test our model on examples involving both simulated and empirical data, and the results show that this approach has several performance advantages, such as being fast, sparse and also robust to the variance in random noise. In addition, our method can give out a more stable estimation of variance of random error, compared with the other methods in the study.Comment: 15 page

Hyperparameter Learning via Distributional Transfer

Bayesian optimisation is a popular technique for hyperparameter learning but typically requires initial exploration even in cases where similar prior tasks have been solved. We propose to transfer information across tasks using learnt representations of training datasets used in those tasks. This results in a joint Gaussian process model on hyperparameters and data representations. Representations make use of the framework of distribution embeddings into reproducing kernel Hilbert spaces. The developed method has a faster convergence compared to existing baselines, in some cases requiring only a few evaluations of the target objective

Understanding and Comparing Scalable Gaussian Process Regression for Big Data

As a non-parametric Bayesian model which produces informative predictive distribution, Gaussian process (GP) has been widely used in various fields, like regression, classification and optimization. The cubic complexity of standard GP however leads to poor scalability, which poses challenges in the era of big data. Hence, various scalable GPs have been developed in the literature in order to improve the scalability while retaining desirable prediction accuracy. This paper devotes to investigating the methodological characteristics and performance of representative global and local scalable GPs including sparse approximations and local aggregations from four main perspectives: scalability, capability, controllability and robustness. The numerical experiments on two toy examples and five real-world datasets with up to 250K points offer the following findings. In terms of scalability, most of the scalable GPs own a time complexity that is linear to the training size. In terms of capability, the sparse approximations capture the long-term spatial correlations, the local aggregations capture the local patterns but suffer from over-fitting in some scenarios. In terms of controllability, we could improve the performance of sparse approximations by simply increasing the inducing size. But this is not the case for local aggregations. In terms of robustness, local aggregations are robust to various initializations of hyperparameters due to the local attention mechanism. Finally, we highlight that the proper hybrid of global and local scalable GPs may be a promising way to improve both the model capability and scalability for big data.Comment: 25 pages, 15 figures, preprint submitted to KB