In the context of deep learning, the costliest phase from a computational point of view is the full training of the learning algorithm. However, this process is to be used a significant number of times during the design of a new artificial neural network, leading therefore to extremely expensive operations. Here, we propose a low-cost strategy to predict the accuracy of the algorithm, based only on its initial behaviour. To do so, we train the network of interest up to convergence several times, modifying its characteristics at each training. The initial and final accuracies observed during this beforehand process are stored in a database. We then make use of both curve fitting and Support Vector Machines techniques, the latter being trained on the created database, to predict the accuracy of the network, given its accuracy on the primary iterations of its learning. This approach can be of particular interest when the space of the characteristics of the network is notably large or when its full training is highly time-consuming. The results we obtained are promising and encouraged us to apply this strategy to a topical issue: hyper-parameter optimisation (HO). In particular, we focused on the HO of a convolutional neural network for the classification of the databases MNIST and CIFAR-10. By using our method of prediction, and an algorithm implemented by us for a probabilistic exploration of the hyper-parameter space, we were able to find the hyper-parameter settings corresponding to the optimal accuracies already known in literature, at a quite low-cost.
Two of the most intuitive and widely spread methods are the grid search and the random search @cite_1 . These techniques however are not well-suited in applications where a given set of hyper-parameters is costly to evaluate. As a result, Sequential Model-Based Optimisation (SMBO) @cite_8 algorithms have been employed in many settings when the performance evaluation of a model is expensive. They approximate the black-box objective function @math that is to be maximised by a surrogate function, cheaper to evaluate. At each iteration of the algorithm, the new point where the surrogate is to be evaluated is chosen by maximising a chosen criterion. Several SMBO algorithms have been proposed in the literature, and differ in the criteria by which they optimise the surrogate, and in the way they model the surrogate given the observation history. Two of the most famous SMBO approaches are the Bayesian Optimisation approach @cite_9 @cite_10 and the Tree-structured Parzen Estimator strategy @cite_2 .
@cite_8 @cite_9 @cite_1 @cite_2 @cite_10
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Algorithm selection as well as hyperparameter optimization are tedious task that have to be dealt with when applying machine learning to real-world problems. Sequential model-based optimization (SMBO), based on so-called “surrogate models”, has been employed to allow for faster and more direct hyperparameter optimization. A surrogate model is a machine learning regression model which is trained on the meta-level instances in order to predict the performance of an algorithm on a specific data set given the hyperparameter settings and data set descriptors. Gaussian processes, for example, make good surrogate models as they provide probability distributions over labels. Recent work on SMBO also includes meta-data, i.e. observed hyperparameter performances on other data sets, into the process of hyperparameter optimization. This can, for example, be accomplished by learning transfer surrogate models on all available instances of meta-knowledge; however, the increasing amount of meta-information can make Gaussian processes infeasible, as they require the inversion of a large covariance matrix which grows with the number of instances. Consequently, instead of learning a joint surrogate model on all of the meta-data, we propose to learn individual surrogate models on the observations of each data set and then combine all surrogates to a joint one using ensembling techniques. The final surrogate is a weighted sum of all data set specific surrogates plus an additional surrogate that is solely learned on the target observations. Within our framework, any surrogate model can be used and explore Gaussian processes in this scenario. We present two different strategies for finding the weights used in the ensemble: the first is based on a probabilistic product of experts approach, and the second is based on kernel regression. Additionally, we extend the framework to directly estimate the acquisition function in the same setting, using a novel technique which we name the “transfer acquisition function”. In an empirical evaluation including comparisons to the current state-of-the-art on two publicly available meta-data sets, we are able to demonstrate that our proposed approach does not only scale to large meta-data, but also finds the stronger prediction models. This paper addresses the difficult problem of finding an optimal neural architecture design for a given image classification task. We propose a method that aggregates two main results of the previous state-of-the-art in neural architecture search. These are, appealing to the strong sampling efficiency of a search scheme based on sequential model-based optimization (SMBO), and increasing training efficiency by sharing weights among sampled architectures. Sequential search has previously demonstrated its capabilities to find state-of-the-art neural architectures for image classification. However, its computational cost remains high, even unreachable under modest computational settings. Affording SMBO with weight-sharing alleviates this problem. On the other hand, progressive search with SMBO is inherently greedy, as it leverages a learned surrogate function to predict the validation error of neural architectures. This prediction is directly used to rank the sampled neural architectures. We propose to attenuate the greediness of the original SMBO method by relaxing the role of the surrogate function so it predicts architecture sampling probability instead. We demonstrate with experiments on the CIFAR-10 dataset that our method, denominated Efficient progressive neural architecture search (EPNAS), leads to increased search efficiency, while retaining competitiveness of found architectures. A novel algorithm based on random forests with surrogate splits is proposed to address the classification problem of incomplete data without imputation.The algorithm allows each tree to cast a vote even the voting process is interrupted by missing attributes.Experimental results on various acknowledged datasets show that the proposed method is robust and efficient. Random forests (RF) is known as an efficient algorithm in classification, however it depends on the integrity of datasets. Conventional methods in dealing with missing values usually employ estimation and imputation approaches whose efficiency is tied to the assumptions of data features. Recently, algorithm of surrogate decisions in RF was developed and this paper proposes a random forests algorithm with modified surrogate splits (Adjusted Weight Voting Random Forest, AWVRF) which is able to address the incomplete data without imputation.Differing from the present surrogate method, in AWVRF algorithm, when the primary splitting attribute and the surrogate attributes of an internal node are all missing, the undergoing instance is allowed to exit at the current node with a vote. Then the weight of the vote is adjusted by the strength of the involved attributes and the final decision is made by weighted voting. AWVRF does not comprise imputation step, thus it is independent of data features.AWVRF is compared with the methods of mean imputation, LeoFill, knnimpute, BPCAfill and conventional RF with surrogate decisions (surrRF) using 50 times repeated 5-fold cross validation on 10 acknowledged datasets. In a total of 22 experiment settings, the method of AWVRF harvests the highest accuracy in 14 settings and the largest AUC in 7 settings, exhibiting its superiority over other methods. Compared with surrRF, AWVRF is significantly more efficient and remain good discrimination of prediction. Experimental results show that the present AWVRF algorithm can successfully handle the classification task for incomplete data. We propose a new method for learning the structure of convolutional neural networks (CNNs) that is more efficient than recent state-of-the-art methods based on reinforcement learning and evolutionary algorithms. Our approach uses a sequential model-based optimization (SMBO) strategy, in which we search for structures in order of increasing complexity, while simultaneously learning a surrogate model to guide the search through structure space. Direct comparison under the same search space shows that our method is up to 5 times more efficient than the RL method of (2018) in terms of number of models evaluated, and 8 times faster in terms of total compute. The structures we discover in this way achieve state of the art classification accuracies on CIFAR-10 and ImageNet.