Active Learning And Its Applications

In some machine learning tasks,collecting training samples is costly and resources are limited,so collecting high quality samples with limited resources is crucial.Randomly selected samples usually are assumed to be independent and identically distributed.However,active learning selects the next sample based on the samples that have been queried,and active learning considers the correlation between samples,so the samples collected by active learning are of higher quality.Landmarks are data representatives and have important applications in mani-fold learning,spectral clustering and other fields.When the size of dataset is large,the time cost of the current landmarks selection algorithm on manifold is high.In order to apply active learning to the landmarks selection on manifold,we pro-pose the algorithm,Landmarks Selection based on Active Learning and Gaussian Processes(LS-ALGP).The landmarks selected by LS-ALGP can characterize the manifold geometry and preserve the characteristics of the dataset itself.(1)We introduce a new objective:maximizing the change of the overall variance of the Gaussian process over the dataset.Because evaluating the objective on whole dataset is computationally prohibitive as the size of dataset increases,the objec-tive is approximated by maximizing the change of the variance over the k nearest neighbors of the landmarks.In the Gaussian process,landmarks have a greater influence on the variance of neighboring data points and have a smaller effect on data points that are further away.(2)We propose a strategy to determine the number of landmarks.When the number of landmarks increases,if the change of the objective function within a certain number of steps is less than a given threshold,the algorithm can be stopped.(3)We select landmarks for each class individually.In order to effectively use these landmarks,we combine Orthogonal Matching Pursuit(OMP)and neural network to design a classification algorithm framework.Given the landmarks for each class,we use OMP to get the ap-proximate sparse coefficients of a data point,and we concatenate all the sparse coefficients as training data for neural networks.LS-ALGP is compared with other landmarks selection algorithms on different datasets and different classifiers.The specific plan is to use the landmarks to reduce the dimension of the original data firstly,then train the classifier on the reduced dimension data,and finally evaluate the selection of the landmarks according to the effect of the classifiers.We per-formed experiments on MNIST and LetterRec datasets using logistic regression and support vector machine,respectively.And results have shown that LS-ALGP is more competitive than ML.Covariance Matrix Adaptation Evolutionary Strategy(CMA-ES)can handle continuous optimization of non-linear,non-convex functions and achieve com-petitive performance on ill-conditioned,ruggedness,high dimension and/or non-separable problems.To achieve better performance,the hyper-parameters of CMA-ES should be preset or adjusted appropriately.Hyper-parameter config-uration is a black box optimization problem with hyper-parameters,and it is very expensive to evaluate hyper-parameters in some algorithms.Therefore,it is critical to obtain high-quality hyper-parameters.We use active learning to find the best hyper-parameters of CMA-ES.(1)We tune the hyper-parameters cc,c1 and cμ of CMA-ES.Our experiments show that cc,c1 and cμ have a crucial impact on the performance of CMA-ES.(2)In order to describe the relationship between solution quality and hyper-parameters,based on Tree-structured Parzen Estimators(TPE),we get the distribution of solution quality and the conditional distribution of configuration given solution quality.Based on the two distribu-tions,Expected Improvement(EI)guides active learning to search in the hyper-parameter space.El is the possible improvement in the solution quality corre-sponding to the hyper-parameter compared to the best solution quality that has been found.Experimental results show that our approach improves the solution quality over the default CMA-ES and the state-of-the-art algorithm self-CMA-ES on the Black-Box Optimization Benchmarking(BBOB)noiseless problems.