Robust Adaptive Machine Learning Methods And Their Application

Recently,due to the rapid development of computer technology,big data and cloud computing can be commonly seen in our daily life,and massive data have changed the way we live today.However,since realistic data are inevitably corrupted by complicated and heterogeneous noise,or the sample size is so large that data must become available in a real time manner.Therefore,in the field of traditional data analysis and statistic model,two main challenges need to be addressed.The first one is to adjust the model in order to adapt the complicated data structures.The other challenge is to absorb new information from the incoming data flow and incrementally update the predictive model.Therefore,robust online learning has become a hot topic in machine learning and has attracted the attention of many researchers.In this paper,we introduce the optimal control theory into the machine learning research and build a novel state feedback control framework.Using this framework,we propose a series of robust adaptive algorithms to solve the problems of regression and classification in linear and nonlinear forms.Moreover,the algorithm is extended into deep learning model and plays the role of optimizer,image recognition and text classification tasks can be addressed by this novel optimizer.In addition,we solve sample selection problem from the perspective of machine learning with the help of the proposed algorithm.Therefore,robust online learning has become a hot topic in machine learning and has attracted the attention of many researchers.The main research work of this thesis is as follows:Firstly,we develop a novel robust online learning framework based on optimal control theory,linear regression,binary classification and multi-class classification problems are considered in this framework.By a carefully designed scheme,the online learning task is first formulated as a state feedback control problem;Then,the linear quadratic regulator(LQR)is used to obtain the optimal parameter updating.For the case with few unknown parameters,Riccati equation is solved with iterative approach,the corresponding algorithm is named as online linear quadratic regulator(OLQR).For more common high-dimensional cases,we reduce the corresponding computational complexity via an efficient polar decomposition,and name the algorithm as online high dimensional learning algorithm(ROHDL).Comparing with conventional methods,both two algorithms can achieve more robust and accurate performance with faster convergence,especially for the data streams with complex noise disturbances.Numerical results on benchmark datasets and practical applications confirm the advantages of our new method.Secondly,we consider the online nonlinear learning problem in reproducing kernel Hilbert space(RHKS).With the help of kernel trick,nonlinear learning task can be essentially regarded as a series of finite-dimensional feedback control problems.Therefore,using Gaussian kernel with fixed bandwidth,we propose a control based kernel regression algorithm,named online kernel linear quadratic regulator(OKLQR).However,the manually selected bandwidth may make the learning model rigid and inappropriate for complex data streams.For this reason,we set kernel bandwidth as an unknown parameter,then by employing optimal control techniques,two effective algorithms named online adaptive kernel learning(OKAL)and control-based adaptive online kernel classification(CAOKC)are developed for regression and classification tasks respectively,and the parameters in the learning model including kernel bandwidth can be efficiently updated in a real-time manner.A large quantity of numerical results supports our theory and illustrate the efficiency,accuracy and robustness of our algorithm.Thirdly,we present a new optimizer for deep learning named control-based stochastic gradient compression(CSGC).Deep learning generally needs numerous samples to complete the training,and each time of updating only involves a mini-batch of samples,which is essentially an online learning approach.Following a carefully designed alternating optimization scheme,we reinterpret the learning process as an optimal feedback control problem for a series of linear,controllable systems.Network parameters are divided into blocks according to their connection with the next layer,then parameters in each block are updated through the subsystems.Also,polar decomposition is employed to reduce computational complexity.Compared with the existing benchmark methods,the proposed optimizer can obtain faster and more robust convergence and relief the issue of vanishing gradient in some tasks.The results presented in this paper demonstrate how optimal control can provide fresh ideas and be an effective approach for training networks.Numerical results on benchmark synthetic and realistic datasets are provided to illustrate our new method.Fourthly,based on the concept of deep learning,we propose a novel deep learningbased sample selection model named deep sample selection network(DSSN).We use some particular techniques in residual neural and long short-term memory networks to implement the sample selection mechanism and reinterpret the benchmark sample selection models(Tobit-I model and Tobit-II model)as two carefully designed deep neural networks named deep Tobit-I and deep Tobit-II networks,respectively.CSGC plays the role of optimizer in this model.Compared with traditional sample selection models,the proposed networks can provide robust and satisfying econometric analysis with minimal random assumptions on the model and successfully describe the underlying highly nonlinear relationships to achieve considerable improvements in fitting and prediction accuracy,especially in the cases of large datasets.Numerical experiments on benchmark synthetic and realistic datasets are provided to illustrate our new model.The innovation of this paper can be listed as follows:(1)We propose a comprehensive control based online learning framework using linear quadratic regulator,in which the predicting error can achieve exponential convergence.With the help of efficient polar decomposition,it solves the problem of computational complexity in control based algorithms and can be applied to high-dimensional cases.(2)In the filed of deep learning optimizer,few optimizer can balance convergence speed and computational accuracy,but our proposed control based optimizer takes advantage of robustness,fast convergent speed and better predicting accuracy,which provides some ideas for the design of new deep learning algorithms.(3)Some special architecture and techniques are introduced to build two different deep sample selection network thus makes full use of the unique advantages of neural networks in micro econometric modeling.On the one hand,any assumptions about the distribution of random disturbance are not needed in network model,which greatly ensures the flexibility and generalization ability of the model.On the other hand,there is no strong restriction on model structure,so that the proposed model can achieve better performance from large sample and nonlinear relationship.(4)To the best of our knowledge,for the first time,we consider the econometric concept and interpretability in sample selection models from the perspective of machine learning.The results presented in this paper demonstrate some fresh ideas and a novel approach to deploy machine learning techniques for traditional micro econometric problems.In conclusion,this thesis provides a new framework for online learning methods based on optimal feedback control.In the context of this framework,classification,regression and even deep neural network can obtain more stable learning performance,which offers new perspectives for future research.Besides,the results presented in this paper demonstrate some fresh ideas and a novel approach to deploy machine learning techniques for traditional micro econometric problems.