We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean spaces, RSVGD has the advantage over SVGD of utilizing information geometry, and (ii) for inference tasks on Riemann manifolds, RSVGD brings the unique advantages of SVGD to the Riemannian world. To appropriately transfer to Riemann manifolds, we conceive novel and non-trivial techniques for RSVGD, which are required by the intrinsically different characteristics of general Riemann manifolds from Euclidean spaces. We also discover Riemannian Stein's Identity and Riemannian Kernelized Stein Discrepancy. Experimental results show the advantages over SVGD of exploring distribution geometry and the advantages of particle-efficiency, iteration-effectiveness and approximation flexibility over other inference methods on Riemann manifolds.

Traditional recommendation systems (RecSys) suffer from two problems: the exploitation-exploration dilemma and the cold-start problem. One solution to solving the exploitation-exploration dilemma is the contextual bandit policy, which adaptively exploits and explores user interests. As a result, the contextual bandit policy achieves increased rewards in the long run. The contextual bandit policy, however, may cause the system to explore more than needed in the cold-start situations, which can lead to worse short-term rewards. Cross-domain RecSys methods adopt transfer learning to leverage prior knowledge in a source RecSys domain to jump start the cold-start target RecSys. To solve the two problems together, in this paper, we propose the first applicable transferable contextual bandit (TCB) policy for the cross-domain recommendation. TCB not only benefits the exploitation but also accelerates the exploration in the target RecSys. TCB's exploration, in turn, helps to learn how to transfer between different domains. TCB is a general algorithm for both homogeneous and heterogeneous domains. We perform both theoretical regret analysis and empirical experiments. The empirical results show that TCB outperforms the state-of-the-art algorithms over time.

Most existing robust principal component analysis (PCA) involve mean estimation for extracting low-dimensional representation. However, they do not get the optimal mean for real data, which include outliers, under the different robust distances metric learning, such as L 1 -norm and L 2,1 -norm. This affects the robustness of algorithms. Motivated by the fact that the variance of data can be characterized by the variation between each pair of data, we propose a novel robust formulation for PCA. It avoids computing the mean of data in the criterion function. Our method employs L 2 ,p-norm as the distance metric to measure the variation in the criterion function and aims to seek the projection matrix that maximizes the sum of variation between each pair of the projected data. Both theoretical analysis and experimental results demonstrate that our methods are efficient and superior to most existing robust methods for data reconstruction.

For many real-world tagging problems, training labels are usually obtained through social tagging and are notoriously incomplete. Consequently, handling data with incomplete labels has become a difficult challenge, which usually leads to a degenerated performance on label prediction. To improve the generalization performance, in this paper, we first propose the Improved Cross-View learning (referred as ICVL) model, which considers both global and local patterns of label relationship to enrich the original label set. Further, by extending the ICVL model with an outlier detection mechanism, we introduce the Improved Cross-View learning with Outlier Detection (referred as ICVL-OD) model to remove the abnormal tags resulting from label enrichment. Extensive evaluations on three benchmark datasets demonstrate that ICVL and ICVL-OD outstand with superior performances in comparison with the competing methods.

We consider a new setting of online clustering of contextual cascading bandits, an online learning problem where the underlying cluster structure over users is unknown and needs to be learned from a random prefix feedback. More precisely, a learning agent recommends an ordered list of items to a user, who checks the list and stops at the first satisfactory item, if any. We propose an algorithm of CLUB-cascade for this setting and prove an n-step regret bound of order O(√n). Previous work corresponds to the degenerate case of only one cluster, and our general regret bound in this special case also significantly improves theirs. We conduct experiments on both synthetic and real data, and demonstrate the effectiveness of our algorithm and the advantage of incorporating online clustering method.

Some recent works in classification show that the data obtained from various views with different sensors for an object contributes to achieving a remarkable performance. Actually, in many real-world applications, each view often contains multiple features, which means that this type of data has a hierarchical structure, while most of existing works do not take these features with multi-layer structure into consideration simultaneously. In this paper, a probabilistic hierarchical model is proposed to address this issue and applied for classification. In our model, a latent variable is first learned to fuse the multiple features obtained from a same view, sensor or modality. Particularly, mapping matrices corresponding to a certain view are estimated to project the latent variable from a shared space to the multiple observations. Since this method is designed for the supervised purpose, we assume that the latent variables associated with different views are influenced by their ground-truth label. In order to effectively solve the proposed method, the Expectation-Maximization (EM) algorithm is applied to estimate the parameters and latent variables. Experimental results on the extensive synthetic and two real-world datasets substantiate the effectiveness and superiority of our approach as compared with state-of-the-art.

Variations of human body skeletons may be considered as dynamic graphs, which are generic data representation for numerous real-world applications. In this paper, we propose a spatio-temporal graph convolution (STGC) approach for assembling the successes of local convolutional filtering and sequence learning ability of autoregressive moving average. To encode dynamic graphs, the constructed multi-scale local graph convolution filters, consisting of matrices of local receptive fields and signal mappings, are recursively performed on structured graph data of temporal and spatial domain. The proposed model is generic and principled as it can be generalized into other dynamic models. We theoretically prove the stability of STGC and provide an upper-bound of the signal transformation to be learnt. Further, the proposed recursive model can be stacked into a multi-layer architecture. To evaluate our model, we conduct extensive experiments on four benchmark skeleton-based action datasets, including the large-scale challenging NTU RGB+D. The experimental results demonstrate the effectiveness of our proposed model and the improvement over the state-of-the-art.

The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many applications. To avoid overfitting to noisy data, the polynomials are often designed to approximately rather than exactly equal zero on the designated data. Although such approximations empirically demonstrate high performance, the sound algebraic structure of the vanishing ideal is lost. The present paper proposes a vanishing ideal that is tolerant to noisy data and also pursued to have a better algebraic structure. As a new problem, we simultaneously find a set of polynomials and data points for which the polynomials approximately vanish on the input data points, and almost exactly vanish on the discovered data points. In experimental classification tests, our method discovered much fewer and lower-degree polynomials than an existing state-of-the-art method. Consequently, our method accelerated the runtime of the classification tasks without degrading the classification accuracy.

Hashing has been widely used for large-scale approximate nearest neighbor search because of its storage and search efficiency. Recent work has found that deep supervised hashing can significantly outperform non-deep supervised hashing in many applications. However, most existing deep supervised hashing methods adopt a symmetric strategy to learn one deep hash function for both query points and database (retrieval) points. The training of these symmetric deep supervised hashing methods is typically time-consuming, which makes them hard to effectively utilize the supervised information for cases with large-scale database. In this paper, we propose a novel deep supervised hashing method, called asymmetric deep supervised hashing (ADSH), for large-scale nearest neighbor search. ADSH treats the query points and database points in an asymmetric way. More specifically, ADSH learns a deep hash function only for query points, while the hash codes for database points are directly learned. The training of ADSH is much more efficient than that of traditional symmetric deep supervised hashing methods. Experiments show that ADSH can achieve state-of-the-art performance in real applications.

In this paper, we propose two novel multi-dimensional tensor sparse coding (MDTSC) schemes using the t-linear combination. Based on the t-linear combination, the shifted versions of the bases are used for the data approximation, but without need to store them. Therefore, the dictionaries of the proposed schemes are more concise and the coefficients have richer physical explanations. Moreover, we propose an efficient alternating minimization algorithm, including the tensor coefficient learning and the tensor dictionary learning, to solve the proposed problems. For the tensor coefficient learning, we design a tensor-based fast iterative shrinkage algorithm. For the tensor dictionary learning, we first divide the problem into several nearly-independent subproblems in the frequency domain, and then utilize the Lagrange dual to further reduce the number of optimization variables. Experimental results on multi-dimensional signals denoising and reconstruction (3DTSC, 4DTSC, 5DTSC) show that the proposed algorithms are more efficient and outperform the state-of-the-art tensor-based sparse coding models.