The standard Gaussian process (GP) regression is often intractable when a data set is large or spatially nonstationary. In this paper, we address these challenging data properties by designing a novel K nearest neighbor based Kalman filter Gaussian process (KNN-KFGP) regression. Based on a state space model established by the KNN driven data grouping, our KNN-KFGP recursively filters out the latent function values in a computationally efficient and accurate Kalman filtering framework. Moreover, KNN allows each test point to find its strongly correlated local training subset, so our KNN-KFGP provides a suitable way to deal with spatial nonstationary problems. We evaluate the performance of our KNN-KFGP on several synthetic and real data sets to show its validity.

Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in its stronger robustness. To solve the model, we devise a majorization-minimization augmented Lagrange multiplier (MM-ALM) algorithm which finds the local optimal solutions of the proposed nonconvex model. We also provide an efficient strategy to speedup MM-ALM, which makes the running time comparable with the state-of-the-art algorithm of solving RPCA. Finally, empirical results demonstrate the superiority of our nonconvex approach over RPCA in terms of matrix recovery accuracy.

Online feature selection with dynamic features has become an active research area in recent years. However, in some real-world applications such as image analysis and email spam filtering, features may arrive by groups. Existing online feature selection methods evaluate features individually, while existing group feature selection methods cannot handle online processing. Motivated by this, we formulate the online group feature selection problem, and propose a novel selection approach for this problem. Our proposed approach consists of two stages: online intra-group selection and online inter-group selection. In the intra-group selection, we use spectral analysis to select discriminative features in each group when it arrives. In the inter-group selection, we use Lasso to select a globally optimal subset of features. This 2-stage procedure continues until there are no more features to come or some predefined stopping conditions are met. Extensive experiments conducted on benchmarkand real-world data sets demonstrate that our proposed approach outperforms other state-of-the-art online feature selection methods.

In this work, we present a new framework for large scale online kernel classification, making kernel methods efficient and scalable for large-scale online learning tasks. Unlike the regular budget kernel online learning scheme that usually uses different strategies to bound the number of support vectors, our framework explores a functional approximation approach to approximating a kernel function/matrix in order to make the subsequent online learning task efficient and scalable. Specifically, we present two different online kernel machine learning algorithms: (i) the Fourier Online Gradient Descent (FOGD) algorithm that applies the random Fourier features for approximating kernel functions; and (ii) the Nystrom Online Gradient Descent (NOGD) algorithm that applies the Nystrom method to approximate large kernel matrices. We offer theoretical analysis of the proposed algorithms, and conduct experiments for large-scale online classification tasks with some data set of over 1 million instances. Our encouraging results validate the effectiveness and efficiency of the proposed algorithms, making them potentially more practical than the family of existing budget kernel online learning approaches.

This paper proposes a novel algorithm for manifold alignment preserving global geometry. This approach constructs mapping functions that project data instances from different input domains to a new lower-dimensional space, simultaneously matching the instances in correspondence and preserving global distances between instances within the original domains. In contrast to previous approaches, which are largely based on preserving local geometry, the proposed approach is suited to applications where the global manifold geometry needs to be respected. We evaluate the effectiveness of our algorithm for transfer learning in two real-world cross-lingual information retrieval tasks.

The usual representation of quantitative data is to formalize it as an information table, which assumes the independence of attributes. In real-world data, attributes are more or less interacted and coupled via explicit or implicit relationships. Limited research has been conducted on analyzing such attribute interactions, which only describe a local picture of attribute couplings in an implicit way. This paper proposes a framework of the coupled attribute analysis to capture the global dependency of continuous attributes. Such global couplings integrate the intra-coupled interaction within an attribute (i.e. the correlations between attributes and their own powers) and inter-coupled interaction among different attributes (i.e. the correlations between attributes and the powers of others) to form a coupled representation for numerical objects by the Taylor-like expansion. This work makes one step forward towards explicitly addressing the global interactions of continuous attributes, verified by the applications in data structure analysis, data clustering, and data classification. Substantial experiments on 13 UCI data sets demonstrate that the coupled representation can effectively capture the global couplings of attributes and outperforms the traditional way, supported by statistical analysis.

This paper proposes a simple linear Bayesian approach to reinforcement learning. We show that with an appropriate basis, a Bayesian linear Gaussian model is sufficient for accurately estimating the system dynamics, and in particular when we allow for correlated noise. Policies are estimated by first sampling a transition model from the current posterior, and then performing approximate dynamic programming on the sampled model. This form of approximate Thompson sampling results in good exploration in unknown environments. The approach can also be seen as a Bayesian generalisation of least-squares policy iteration, where the empirical transition matrix is replaced with a sample from the posterior.

Non-negative Matrix Factorization (NMF) is a traditional unsupervised machine learning technique for decomposing a matrix into a set of bases and coefficients under the non-negative constraint. NMF with sparse constraints is also known for extracting reasonable components from noisy data. However, NMF tends to give undesired results in the case of highly sparse data, because the information included in the data is insufficient to decompose. Our key idea is that we can ease this problem if complementary data are available that we could integrate into the estimation of the bases and coefficients. In this paper, we propose a novel matrix factorization method called Non-negative Multiple Matrix Factorization (NMMF), which utilizes complementary data as auxiliary matrices that share the row or column indices of the target matrix. The data sparse- ness is improved by decomposing the target and auxiliary matrices simultaneously, since auxiliary matrices provide information about the bases and coefficients. We formulate NMMF as a generalization of NMF, and then present a parameter estimation procedure derived from the multiplicative up- date rule. We examined NMMF in both synthetic and real data experiments. The effect of the auxiliary matrices appeared in the improved NMMF performance. We also confirmed that the bases that NMMF obtained from the real data were intuitive and reasonable thanks to the non-negative constraint.

Maximum entropy discrimination (MED) is a general framework for discriminative estimation based on the well known maximum entropy principle, which embodies the Bayesian integration of prior information with large margin constraints on observations. It is a successful combination of maximum entropy learning and maximum margin learning, and can subsume support vector machines (SVMs) as a special case. In this paper, we present a multi-view maximum entropy discrimination framework that is an extension of MED to the scenario of learning with multiple feature sets. Different from existing approaches to exploiting multiple views, such as co-training style algorithms and co-regularization style algorithms, we propose a new method to make use of the distinct views where classification margins from these views are required to be identical. We give the general form of the solution to the multi-view maximum entropy discrimination, and provide an instantiation under a specific prior formulation which is analogical to a multi-view version of SVMs. Experimental results on real-world data sets show the effectiveness of the proposed multi-view maximum entropy discrimination approach.

When doing learning from demonstration, it is often the case that the demonstrator provides corrective examples to fix errant behavior by the agent or robot. We present a set of algorithms which use this corrective data to identify and remove noisy examples in datasets which caused errant classifications, and ultimately errant behavior. The objective is to actually modify the source datasets rather than solely rely on the noise-insensitivity of the classification algorithm. This is particularly useful in the sparse datasets often found in learning from demonstration experiments. Our approach tries to distinguish between noisy misclassification and mere undersampling of the learning space. If errors are a result of misclassification, we potentially remove the responsible points and update the classifier. We demonstrate our method on UCI Machine Learning datasets at different levels of sparsity and noise, using decision trees, K-Nearest-Neighbor, and support vector machines.