Canonical Correlation Analysis (CCA) is a classical technique for two-view correlation analysis, while Probabilistic CCA (PCCA) provides a generative and more general viewpoint for this task. Recently, PCCA has been extended to bilinear cases for dealing with two-view matrices in order to preserve and exploit the matrix structures in PCCA. However, existing bilinear PCCAs impose restrictive model assumptions for matrix structure preservation, sacrificing generative correctness or model flexibility. To overcome these drawbacks, we propose BPCCA, a new bilinear extension of PCCA, by introducing a hybrid joint model. Our new model preserves matrix structures indirectly via hybrid vector-based and matrix-based concatenations. This enables BPCCA to gain more model flexibility in capturing two-view correlations and obtain close-form solutions in parameter estimation. Experimental results on two real-world applications demonstrate the superior performance of BPCCA over competing methods.

Stochastic gradient descent (SGD) and its variants have attracted much attention in machine learning due to their efficiency and effectiveness for optimization. To handle large-scale problems, researchers have recently proposed several lock-free strategy based parallel SGD (LF-PSGD) methods for multi-core systems. However, existing works have only proved the convergence of these LF-PSGD methods for convex problems. To the best of our knowledge, no work has proved the convergence of the LF-PSGD methods for non-convex problems. In this paper, we provide the theoretical proof about the convergence of two representative LF-PSGD methods, Hogwild! and AsySVRG, for non-convex problems. Empirical results also show that both Hogwild! and AsySVRG are convergent on non-convex problems, which successfully verifies our theoretical results.

In multi-task learning, when the number of tasks is large, pairwise task relations exhibit sparse patterns since usually a task cannot be helpful to all of the other tasks and moreover, sparse task relations can reduce the risk of overfitting compared with the dense ones. In this paper, we focus on learning sparse task relations. Based on a regularization framework which can learn task relations among multiple tasks, we propose a SParse covAriance based mulTi-taSk (SPATS) model to learn a sparse covariance by using the ℓ l regularization. The resulting objective function of the SPATS method is convex, which allows us to devise an alternating method to solve it. Moreover, some theoretical properties of the proposed model are studied. Experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed method.

Contextual bandits with linear payoffs, which are also known as linear bandits, provide a powerful alternative for solving practical problems of sequential decisions, e.g., online advertisements. In the era of big data, contextual data usually tend to be high-dimensional, which leads to new challenges for traditional linear bandits mostly designed for the setting of low-dimensional contextual data. Due to the curse of dimensionality, there are two challenges in most of the current bandit algorithms: the first is high time-complexity; and the second is extreme large upper regret bounds with high-dimensional data. In this paper, in order to attack the above two challenges effectively, we develop an algorithm of Contextual Bandits via RAndom Projection (CBRAP) in the setting of linear payoffs, which works especially for high-dimensional contextual data. The proposed CBRAP algorithm is time-efficient and flexible, because it enables players to choose an arm in a low-dimensional space, and relaxes the sparsity assumption of constant number of non-zero components in previous work. Besides, we prove an upper regret bound for the proposed algorithm, which is associated with reduced dimensions. By comparing with three benchmark algorithms, we demonstrate improved performance on cumulative payoffs of CBRAP during its sequential decisions on both synthetic and real-world datasets, as well as its superior time-efficiency.

Multi-label classification is a practical yet challenging task in machine learning related fields, since it requires the prediction of more than one label category for each input instance. We propose a novel deep neural networks (DNN) based model, Canonical Correlated AutoEncoder (C2AE), for solving this task. Aiming at better relating feature and label domain data for improved classification, we uniquely perform joint feature and label embedding by deriving a deep latent space, followed by the introduction of label-correlation sensitive loss function for recovering the predicted label outputs. Our C2AE is achieved by integrating the DNN architectures of canonical correlation analysis and autoencoder, which allows end-to-end learning and prediction with the ability to exploit label dependency. Moreover, our C2AE can be easily extended to address the learning problem with missing labels. Our experiments on multiple datasets with different scales confirm the effectiveness and robustness of our proposed method, which is shown to perform favorably against state-of-the-art methods for multi-label classification.

Model reuse attempts to construct a model by utilizing existing available models, mostly trained for other tasks, rather than building a model from scratch. It is helpful to reduce the time cost, data amount, and expertise required. Deep learning has achieved great success in various tasks involving images, voices and videos. There are several studies have the sense of model reuse, by trying to reuse pre-trained deep networks architectures or deep model features to train a new deep model. They, however, neglect the fact that there are many other fixed models or features available. In this paper, we propose a more thorough model reuse scheme, FMR (Fixed Model Reuse). FMR utilizes the learning power of deep models to implicitly grab the useful discriminative information from fixed model/features that have been widely used in general tasks. We firstly arrange the convolution layers of a deep network and the provided fixed model/features in parallel, fully connecting to the output layer nodes. Then, the dependencies between the output layer nodes and the fixed model/features are knockdown such that only the raw feature inputs are needed when the model is being used for testing, though the helpful information in the fixed model/features have already been incorporated into the model. On one hand, by the FMR scheme, the required amount of training data can be significantly reduced because of the reuse of fixed model/features. On the other hand, the fixed model/features are not explicitly used in testing, and thus, the scheme can be quite useful in applications where the fixed model/features are protected by patents or commercial secrets. Experiments on five real-world datasets validate the effectiveness of FMR compared with state-of-the-art deep methods.

With the better availability of healthcare data, such as Electronic Health Records (EHR), more and more data analytics methodologies are developed aiming at digging insights from them to improve the quality of care delivery. There are many challenges on analyzing EHR, such as high dimensionality and event sparsity. Moreover, different from other application domains, the EHR analysis algorithms need to be highly interpretable to make them clinically useful. This makes representation learning from EHRs of key importance. In this paper, we propose an algorithm called Predictive Task Guided Tensor Decomposition (TaGiTeD), to analyze EHRs. Specifically, TaGiTeD learns event interaction patterns that are highly predictive for certain tasks from EHRs with supervised tensor decomposition. Compared with unsupervised methods, TaGiTeD can learn effective EHR representations in a more focused way. This is crucial because most of the medical problems have very limited patient samples, which are not enough for unsupervised algorithms to learn meaningful representations form. We apply TaGiTeD on real world EHR data warehouse and demonstrate that TaGiTeD can learn representations that are both interpretable and predictive.

In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling high-dimensionality challenge in machine learning. Recently, various non-oblivious randomized reduction methods have been developed and deployed for solving many numerical problems such as matrix product approximation, low-rank matrix approximation, etc. However, they are less explored for the machine learning tasks, e.g., classification. More seriously, the theoretical analysis of excess risk bounds for risk minimization, an important measure of generalization performance, has not been established for non-oblivious randomized reduction methods. It therefore remains an open problem what is the benefit of using them over previous oblivious random projection based approaches. To tackle these challenges, we propose an algorithmic framework for employing non-oblivious randomized reduction method for general empirical risk minimizing in machine learning tasks, where the original high-dimensional features are projected onto a random subspace that is derived from the data with a small matrix approximation error. We then derive the first excess risk bound for the proposed non-oblivious randomized reduction approach without requiring strong assumptions on the training data. The established excess risk bound exhibits that the proposed approach provides much better generalization performance and it also sheds more insights about different randomized reduction approaches. Finally, we conduct extensive experiments on both synthetic and real-world benchmark datasets, whose dimension scales to O(10^7), to demonstrate the efficacy of our proposed approach.

The explosion of streaming data poses challenges to feature learning methods including linear discriminant analysis (LDA). Many existing LDA algorithms are not efficient enough to incrementally update with samples that sequentially arrive in various manners. First, we propose a new fast batch LDA (FLDA/QR) learning algorithm that uses the cluster centers to solve a lower triangular system that is optimized by the Cholesky-factorization. To take advantage of the intrinsically incremental mechanism of the matrix, we further develop an exact incremental algorithm (IFLDA/QR). The Gram-Schmidt process with reorthogonalization in IFLDA/QR significantly saves the space and time expenses compared with the rank-one QR-updating of most existing methods. IFLDA/QR is able to handle streaming data containing 1) new labeled samples in the existing classes, 2) samples of an entirely new (novel) class, and more significantly, 3) a chunk of examples mixed with those in 1) and 2). Both theoretical analysis and numerical experiments have demonstrated much lower space and time costs (2~10 times faster) than the state of the art, with comparable classification accuracy.

Direct contextual policy search methods learn to improve policy parameters and simultaneously generalize these parameters to different context or task variables. However, learning from high-dimensional context variables, such as camera images, is still a prominent problem in many real-world tasks. A naive application of unsupervised dimensionality reduction methods to the context variables, such as principal component analysis, is insufficient as task-relevant input may be ignored. In this paper, we propose a contextual policy search method in the model-based relative entropy stochastic search framework with integrated dimensionality reduction. We learn a model of the reward that is locally quadratic in both the policy parameters and the context variables. Furthermore, we perform supervised linear dimensionality reduction on the context variables by nuclear norm regularization. The experimental results show that the proposed method outperforms naive dimensionality reduction via principal component analysis and a state-of-the-art contextual policy search method.