Machines learning techniques plays a preponderant role in dealing with massive amount of data and are employed in almost every possible domain. Building a high quality machine learning model to be deployed in production is a challenging task, from both, the subject matter experts and the machine learning practitioners. For a broader adoption and scalability of machine learning systems, the construction and configuration of machine learning workflow need to gain in automation. In the last few years, several techniques have been developed in this direction, known as autoML. In this paper, we present a two-stage optimization process to build data pipelines and configure machine learning algorithms. First, we study the impact of data pipelines compared to algorithm configuration in order to show the importance of data preprocessing over hyperparameter tuning. The second part presents policies to efficiently allocate search time between data pipeline construction and algorithm configuration. Those policies are agnostic from the metaoptimizer. Last, we present a metric to determine if a data pipeline is specific or independent from the algorithm, enabling fine-grain pipeline pruning and meta-learning for the coldstart problem.
The intrinsic difficulty of building a machine learning pipeline lies in the nature of the search space: the objective is non-separable i.e., the marginal performance of an operator @math depends on all the operators in all the paths leading to @math from the source, within the configuration space of a specific operator @math , there might be some dependencies between the hyperparameters (e.g. for Neural Networks, the coefficients @math , @math and @math make sense only for Adam solver @cite_10 ). Therefore, building a machine learning pipeline is a mix between selecting a proper sequence of operations and, for each operation, selecting the proper configuration in a structured and conditional space. On the contrary, most systems handle the problem by aggregating the whole search space, losing the sequential aspect of it. A notable exception is @cite_26 , inspired by , that explores the search space in terms of actions on operators (insertion, deletion, etc.).
@cite_26 @cite_10
2304209433 2770298516 2616602896 2133027741 2598232788 2131241448 2143161696 2099119623 2117763124 2012619263 2210969396 2950182411 2408019865 2084323233 2963815651 1530941242 2309832917 2953359974 2951127468 1595276678
Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While current methods offer efficiencies by adaptively choosing new configurations to train, an alternative strategy is to adaptively allocate resources across the selected configurations. We formulate hyperparameter optimization as a pure-exploration non-stochastic infinitely many armed bandit problem where allocation of additional resources to an arm corresponds to training a configuration on larger subsets of the data. We introduce Hyperband for this framework and analyze its theoretical properties, providing several desirable guarantees. We compare Hyperband with state-of-the-art Bayesian optimization methods and a random search baseline on a comprehensive benchmark including 117 datasets. Our results on this benchmark demonstrate that while Bayesian optimization methods do not outperform random search trained for twice as long, Hyperband in favorable settings offers valuable speedups. Neural networks dominate the modern machine learning landscape, but their training and success still suffer from sensitivity to empirical choices of hyperparameters such as model architecture, loss function, and optimisation algorithm. In this work we present , a simple asynchronous optimisation algorithm which effectively utilises a fixed computational budget to jointly optimise a population of models and their hyperparameters to maximise performance. Importantly, PBT discovers a schedule of hyperparameter settings rather than following the generally sub-optimal strategy of trying to find a single fixed set to use for the whole course of training. With just a small modification to a typical distributed hyperparameter training framework, our method allows robust and reliable training of models. We demonstrate the effectiveness of PBT on deep reinforcement learning problems, showing faster wall-clock convergence and higher final performance of agents by optimising over a suite of hyperparameters. In addition, we show the same method can be applied to supervised learning for machine translation, where PBT is used to maximise the BLEU score directly, and also to training of Generative Adversarial Networks to maximise the Inception score of generated images. In all cases PBT results in the automatic discovery of hyperparameter schedules and model selection which results in stable training and better final performance. In order to achieve state-of-the-art performance, modern machine learning techniques require careful data pre-processing and hyperparameter tuning. Moreover, given the ever increasing number of machine learning models being developed, model selection is becoming increasingly important. Automating the selection and tuning of machine learning pipelines, which can include different data pre-processing methods and machine learning models, has long been one of the goals of the machine learning community. In this paper, we propose to solve this meta-learning task by combining ideas from collaborative filtering and Bayesian optimization. Specifically, we use a probabilistic matrix factorization model to transfer knowledge across experiments performed in hundreds of different datasets and use an acquisition function to guide the exploration of the space of possible ML pipelines. In our experiments, we show that our approach quickly identifies high-performing pipelines across a wide range of datasets, significantly outperforming the current state-of-the-art. These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification of uncertainty within applications in volving the blending of mathematical models with data. The finite dimensional situation is described first, along with some motivational examples. Then the development of probability measures on separable Banach space is undertaken, using a random series over an infinite set of functions to construct draws; these probability measures are used as priors in the Bayesian approach to inverse problems. Regularity of draws from the priors is studied in the natural Sobolev or Besov spaces implied by the choice of functions in the random series construction, and the Kolmogorov continuity theorem is used to extend regularity considerations to the space of Holder continuous functions. Bayes’ theorem is de rived in this prior setting, and here interpreted as finding conditions under which the posterior is absolutely continuous with respect to the prior, and determining a formula for the Radon-Nikodym derivative in terms of the likelihood of the data. Having established the form of the posterior, we then describe various properties common to it in the infinite dimensional setting. These properties include well-posedness, approximation theory, and the existence of maximum a posteriori estimators. We then describe measure-preserving dynamics, again on the infinite dimensional space, including Markov chain-Monte C arlo and sequential Monte Carlo methods, and measure-preserving reversible stochastic differential equations. By formulating the theory and algorithms on the underlying infinite dimensional space, we obtain a framework suitable for rigorous analysis of the accuracy of reconstructions, of computational complexity, as well as naturally constructing algorithms which perform well under mesh refinement, since they are inherently well-defined in infinite dimensions. The performance of many machine learning algorithms depends crucially on the hyperparameter settings, especially in Deep Learning. Manually tuning the hyperparameters is laborious and time consuming. To address this issue, Bayesian optimization (BO) methods and their extensions have been proposed to optimize the hyperparameters automatically. However, they still suffer from highly computational expense when applying to deep generative models (DGMs) due to their strategy of the black-box function optimization. This paper provides a new hyperparameter optimization procedure at the pre-training phase of the DGMs, where we avoid combining all layers as one black-box function by taking advantage of the layer-by-layer learning strategy. Following this procedure, we are able to optimize multiple hyperparameters in an adaptive way by using Gaussian process. In contrast to the traditional BO methods, which mainly focus on the supervised models, the pre-training procedure is unsupervised where there is no validation error can be used. To alleviate this problem, this paper proposes a new holdout loss, the free energy gap, which takes into account both factors of the model fitting and over-fitting. The empirical evaluations demonstrate that our method not only speeds up the process of hyperparameter optimization, but also improves the performances of DGMs significantly in both the supervised and unsupervised learning tasks. The use of machine learning algorithms frequently involves careful tuning of learning parameters and model hyperparameters. Unfortunately, this tuning is often a "black art" requiring expert experience, rules of thumb, or sometimes brute-force search. There is therefore great appeal for automatic approaches that can optimize the performance of any given learning algorithm to the problem at hand. In this work, we consider this problem through the framework of Bayesian optimization, in which a learning algorithm's generalization performance is modeled as a sample from a Gaussian process (GP). We show that certain choices for the nature of the GP, such as the type of kernel and the treatment of its hyperparameters, can play a crucial role in obtaining a good optimizer that can achieve expertlevel performance. We describe new algorithms that take into account the variable cost (duration) of learning algorithm experiments and that can leverage the presence of multiple cores for parallel experimentation. We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization for many algorithms including latent Dirichlet allocation, structured SVMs and convolutional neural networks. Recent work has shown that machine learning can automate and in some cases outperform hand crafted compiler optimizations. Central to such an approach is that machine learning techniques typically rely upon summaries or features of the program. The quality of these features is critical to the accuracy of the resulting machine learned algorithm; no machine learning method will work well with poorly chosen features. However, due to the size and complexity of programs, theoretically there are an infinite number of potential features to choose from. The compiler writer now has to expend effort in choosing the best features from this space. This paper develops a novel mechanism to automatically find those features which most improve the quality of the machine learned heuristic. The feature space is described by a grammar and is then searched with genetic programming and predictive modeling. We apply this technique to loop unrolling in GCC 4.3.1 and evaluate our approach on a Pentium 6. On a benchmark suite of 57 programs, GCC's hard-coded heuristic achieves only 3 of the maximum performance available, while a state of the art machine learning approach with hand-coded features obtains 59 . Our feature generation technique is able to achieve 76 of the maximum available speedup, outperforming existing approaches. In discriminative machine learning one is interested in training a system to optimize a certain desired measure of performance, or loss. In binary classification one typically tries to minimizes the error rate. But in structured prediction each task often has its own measure of performance such as the BLEU score in machine translation or the intersection-over-union score in PASCAL segmentation. The most common approaches to structured prediction, structural SVMs and CRFs, do not minimize the task loss: the former minimizes a surrogate loss with no guarantees for task loss and the latter minimizes log loss independent of task loss. The main contribution of this paper is a theorem stating that a certain perceptron-like learning rule, involving features vectors derived from loss-adjusted inference, directly corresponds to the gradient of task loss. We give empirical results on phonetic alignment of a standard test set from the TIMIT corpus, which surpasses all previously reported results on this problem. A common obstacle preventing the rapid deployment of supervised machine learning algorithms is the lack of labeled training data. This is particularly expensive to obtain for structured prediction tasks, where each training instance may have multiple, interacting labels, all of which must be correctly annotated for the instance to be of use to the learner. Traditional active learning addresses this problem by optimizing the order in which the examples are labeled to increase learning efficiency. However, this approach does not consider the difficulty of labeling each example, which can vary widely in structured prediction tasks. For example, the labeling predicted by a partially trained system may be easier to correct for some instances than for others. We propose a new active learning paradigm which reduces not only how many instances the annotator must label, but also how difficult each instance is to annotate. The system also leverages information from partially correct predictions to efficiently solicit annotations from the user. We validate this active learning framework in an interactive information extraction system, reducing the total number of annotation actions by 22 . We propose an automatic approximation of the intrinsic manifold for general semi-supervised learning problems. Unfortunately, it is not trivial to define an optimization function to obtain optimal hyperparameters. Usually, pure cross-validation is considered but it does not necessarily scale up. A second problem derives from the suboptimality incurred by discrete grid search and overfitting problems. As a consequence, we developed an ensemble manifold regularization (EMR) framework to approximate the intrinsic manifold by combining several initial guesses. Algorithmically, we designed EMR very carefully so that it (a) learns both the composite manifold and the semi-supervised classifier jointly; (b) is fully automatic for learning the intrinsic manifold hyperparameters implicitly; (c) is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption; and (d) is scalable for a large number of candidate manifold hyperparameters, from both time and space perspectives. Extensive experiments over both synthetic and real datasets show the effectiveness of the proposed framework. The success of hand-crafted machine learning systems in many applications raises the question of making machine learning algorithms more autonomous, i.e., to reduce the requirement of expert input to a minimum. We discuss two strategies towards this goal: (1) automated optimization of hyperparameters (including mechanisms for feature selection, preprocessing, model selection, etc) and (2) the development of algorithms with reduced sets of hyperparameters. Since many research directions (e.g., deep learning), show a tendency towards increasingly complex algorithms with more and more hyperparamters, the demand for both of these strategies continuously increases. We review recent hyperparameter optimization methods and discuss data-driven approaches to avoid the introduction of hyperparameters using unsupervised learning. We end in discussing how these complementary strategies can work hand-in-hand, representing a very promising approach towards autonomous machine learning. Machine learning algorithms frequently require careful tuning of model hyperparameters, regularization terms, and optimization parameters. Unfortunately, this tuning is often a "black art" that requires expert experience, unwritten rules of thumb, or sometimes brute-force search. Much more appealing is the idea of developing automatic approaches which can optimize the performance of a given learning algorithm to the task at hand. In this work, we consider the automatic tuning problem within the framework of Bayesian optimization, in which a learning algorithm's generalization performance is modeled as a sample from a Gaussian process (GP). The tractable posterior distribution induced by the GP leads to efficient use of the information gathered by previous experiments, enabling optimal choices about what parameters to try next. Here we show how the effects of the Gaussian process prior and the associated inference procedure can have a large impact on the success or failure of Bayesian optimization. We show that thoughtful choices can lead to results that exceed expert-level performance in tuning machine learning algorithms. We also describe new algorithms that take into account the variable cost (duration) of learning experiments and that can leverage the presence of multiple cores for parallel experimentation. We show that these proposed algorithms improve on previous automatic procedures and can reach or surpass human expert-level optimization on a diverse set of contemporary algorithms including latent Dirichlet allocation, structured SVMs and convolutional neural networks. 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. Abstract Many neural net learning algorithms aim at finding “simple” nets to explain training data. The expectation is that the “simpler” the networks, the better the generalization on test data (→ Occam's razor). Previous implementations, however, use measures for “simplicity” that lack the power, universality and elegance of those based on Kolmogorov complexity and Solomonoff's algorithmic probability. Likewise, most previous approaches (especially those of the “Bayesian” kind) suffer from the problem of choosing appropriate priors. This paper addresses both issues. It first reviews some basic concepts of algorithmic complexity theory relevant to machine learing, and how the Solomonoff-Levin distribution (or universal prior) deals with the prior problem. The universal prior leads to a probabilistic method for finding “algorithmically simple” problem solutions with high generalization capability. The method is based on Levin complexity (a time-bounded generalization of Kolmogorov complexity) and inspired by Levin's optimal universal search algorithm. For a given problem, solution candidates are computed by efficient “self-sizing” programs that influence their own runtime and storage size. The probabilistic search algorithm finds the “good” programs (the ones quickly computing algorithmically probable solutions fitting the training data). Simulations focus on the task of discovering “algorithmically simple” neural networks with low Kolmogorov complexity and high generalization capability. It is demonstrated that the method, at least with certain toy problems where it is computationally feasible, can lead to generalization results unmatchable by previous neural network algorithms. Much remains to be done, however, to make large scale applications and “incremental learning” feasible. © 1997 Elsevier Science Ltd. Performance of machine learning algorithms depends critically on identifying a good set of hyperparameters. While recent approaches use Bayesian optimization to adaptively select configurations, we focus on speeding up random search through adaptive resource allocation and early-stopping. We formulate hyperparameter optimization as a pure-exploration nonstochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations. We introduce a novel algorithm, Hyperband, for this framework and analyze its theoretical properties, providing several desirable guarantees. Furthermore, we compare Hyperband with popular Bayesian optimization methods on a suite of hyperparameter optimization problems. We observe that Hyperband can provide over an order-of-magnitude speedup over our competitor set on a variety of deep-learning and kernel-based learning problems. Many machine learning algorithms aim at finding “simple” rules to explain training data. The expectation is: the “simpler” the rules, the better the generalization on test data (→ Occam's razor). Most practical implementations, however, use measures for “simplicity” that lack the power, universality and elegance of those based on Kolmogorov complexity and Solomonoff's algorithmic probability. Likewise, most previous approaches (especially those of the “Bayesian” kind) suffer from the problem of choosing appropriate priors. This paper addresses both issues. It first reviews some basic concepts of algorithmic complexity theory relevant to machine learning, and how the Solomonoff-Levin distribution (or universal prior) deals with the prior problem. The universal prior leads to a probabilistic method for finding “algorithmically simple” problem solutions with high generalization capability. The method is based on Levin complexity (a time-bounded extension of Kolmogorov complexity) and inspired by Levin's optimal universal search algorithm. With a given problem, solution candidates are computed by efficient “self-sizing” programs that influence their own runtime and storage size. The probabilistic search algorithm finds the “good” programs (the ones quickly computing algorithmically probable solutions fitting the training data). Experiments focus on the task of discovering “algorithmically simple” neural networks with low Kolmogorov complexity and high generalization capability. These experiments demonstrate that the method, at least with certain toy problems where it is computationally feasible, can lead to generalization results unmatchable by previous neural net algorithms. As the field of data science continues to grow, there will be an ever-increasing demand for tools that make machine learning accessible to non-experts. In this paper, we introduce the concept of tree-based pipeline optimization for automating one of the most tedious parts of machine learning--pipeline design. We implement an open source Tree-based Pipeline Optimization Tool (TPOT) in Python and demonstrate its effectiveness on a series of simulated and real-world benchmark data sets. In particular, we show that TPOT can design machine learning pipelines that provide a significant improvement over a basic machine learning analysis while requiring little to no input nor prior knowledge from the user. We also address the tendency for TPOT to design overly complex pipelines by integrating Pareto optimization, which produces compact pipelines without sacrificing classification accuracy. As such, this work represents an important step toward fully automating machine learning pipeline design. As the field of data science continues to grow, there will be an ever-increasing demand for tools that make machine learning accessible to non-experts. In this paper, we introduce the concept of tree-based pipeline optimization for automating one of the most tedious parts of machine learning---pipeline design. We implement an open source Tree-based Pipeline Optimization Tool (TPOT) in Python and demonstrate its effectiveness on a series of simulated and real-world benchmark data sets. In particular, we show that TPOT can design machine learning pipelines that provide a significant improvement over a basic machine learning analysis while requiring little to no input nor prior knowledge from the user. We also address the tendency for TPOT to design overly complex pipelines by integrating Pareto optimization, which produces compact pipelines without sacrificing classification accuracy. As such, this work represents an important step toward fully automating machine learning pipeline design. Over the past decade, data science and machine learning has grown from a mysterious art form to a staple tool across a variety of fields in academia, business, and government. In this paper, we introduce the concept of tree-based pipeline optimization for automating one of the most tedious parts of machine learning---pipeline design. We implement a Tree-based Pipeline Optimization Tool (TPOT) and demonstrate its effectiveness on a series of simulated and real-world genetic data sets. In particular, we show that TPOT can build machine learning pipelines that achieve competitive classification accuracy and discover novel pipeline operators---such as synthetic feature constructors---that significantly improve classification accuracy on these data sets. We also highlight the current challenges to pipeline optimization, such as the tendency to produce pipelines that overfit the data, and suggest future research paths to overcome these challenges. As such, this work represents an early step toward fully automating machine learning pipeline design. Data mining and knowledge discovery aim at producing useful and reliable models from the data. Unfortunately some databases contain noisy data which perturb the generalization of the models. An important source of noise consists of mislabelled training instances. We offer a new approach which deals with improving classification accuracies by using a preliminary filtering procedure. An example is suspect when in its neighbourhood defined by a geometrical graph the proportion of examples of the same class is not significantly greater than in the database itself. Such suspect examples in the training data can be removed or relabelled. The filtered training set is then provided as input to learning algorithms. Our experiments on ten benchmarks of UCI Machine Learning Repository using 1-NN as the final algorithm show that removal gives better results than relabelling. Removing allows maintaining the generalization error rate when we introduce from 0 to 20 of noise on the class, especially when classes are well separable. The filtering method proposed is finally compared to the relaxation relabelling schema.