Confidence-weighted (CW) learning is a successful online learning paradigm which maintains a Gaussian distribution over classifier weights and adopts a covariancematrix to represent the uncertainties of the weight vectors. However, there are two deficiencies in existing full CW learning paradigms, these being the sensitivity to irrelevant features, and the poor scalability to high dimensional data due to the maintenance of the covariance structure. In this paper, we begin by presenting an online-batch CW learning scheme, and then present a novel paradigm to learn sparse CW classifiers. The proposed paradigm essentially identifies feature groups and naturally builds a block diagonal covariance structure, making it very suitable for CW learning over very high-dimensional data.Extensive experimental results demonstrate the superior performance of the proposed methods over state-of-the-art counterparts on classification and feature selection tasks.

Unlike human learning, machine learning often fails to handle changes between training (source) and test (target) input distributions. Such domain shifts, common in practical scenarios, severely damage the performance of conventional machine learning methods. Supervised domain adaptation methods have been proposed for the case when the target data have labels, including some that perform very well despite being ``frustratingly easy'' to implement. However, in practice, the target domain is often unlabeled, requiring unsupervised adaptation. We propose a simple, effective, and efficient method for unsupervised domain adaptation called CORrelation ALignment (CORAL). CORAL minimizes domain shift by aligning the second-order statistics of source and target distributions, without requiring any target labels. Even though it is extraordinarily simple--it can be implemented in four lines of Matlab code--CORAL performs remarkably well in extensive evaluations on standard benchmark datasets.

Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization formulation. We fill this gap by presenting a novel Bayesian matrix completion method based on spectral regularization. In order to circumvent the difficulties of dealing with the orthonormality constraints of singular vectors, we derive a new equivalent form with relaxed constraints, which then leads us to design an adaptive version of spectral regularization feasible for Bayesian inference. Our Bayesian method requires no parameter tuning and can infer the number of latent factors automatically. Experiments on synthetic and real datasets demonstrate encouraging results on rank recovery and collaborative filtering, with notably good results for very sparse matrices.

The Schatten- p quasi-norm (0< p <1) is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schatten- p quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we first define two tractable Schatten quasi-norms, i.e., Frobenius/nuclear hybrid and bi-nuclear quasi-norms, and then prove that they are in essence the Schatten-2/3 and 1/2 quasi-norms, respectively, which lead to the design of very efficient algorithms that only need to update two much smaller factor matrices. We also design two efficient proximal alternating linearzied minimization algorithms for solving representative matrix completion problems. Finally, we provide the global convergence and performance guarantees for our algorithms, which have better convergence properties than existing algorithms. Experimental results on synthetic and real-world data show that our algorithms are more accurate than the state-of-the-art methods, and are orders of magnitude faster.

In recent data mining research, the graph clustering methods, such as normalized cut and ratio cut, have been well studied and applied to solve many unsupervised learning applications. The original graph clustering methods are NP-hard problems. Traditional approaches used spectral relaxation to solve the graph clustering problems. The main disadvantage of these approaches is that the obtained spectral solutions could severely deviate from the true solution. To solve this problem, in this paper, we propose a new relaxation mechanism for graph clustering methods. Instead of minimizing the squared distances of clustering results, we use the l1-norm distance. More important, considering the normalized consistency, we also use the l1-norm for the normalized terms in the new graph clustering relaxations. Due to the sparse result from the l1-norm minimization, the solutions of our new relaxed graph clustering methods get discrete values with many zeros, which are close to the ideal solutions. Our new objectives are difficult to be optimized, because the minimization problem involves the ratio of nonsmooth terms. The existing sparse learning optimization algorithms cannot be applied to solve this problem. In this paper, we propose a new optimization algorithm to solve this difficult non-smooth ratio minimization problem. The extensive experiments have been performed on three two-way clustering and eight multi-way clustering benchmark data sets. All empirical results show that our new relaxation methods consistently enhance the normalized cut and ratio cut clustering results.

Learning embeddings of entities and relations is an efficient and versatile method to perform machine learning on relational data such as knowledge graphs. In this work, we propose holographic embeddings (HolE) to learn compositional vector space representations of entire knowledge graphs. The proposed method is related to holographic models of associative memory in that it employs circular correlation to create compositional representations. By using correlation as the compositional operator, HolE can capture rich interactions but simultaneously remains efficient to compute, easy to train, and scalable to very large datasets. Experimentally, we show that holographic embeddings are able to outperform state-of-the-art methods for link prediction on knowledge graphs and relational learning benchmark datasets.

Conventional multi-label classification algorithms treat the target labels of the classification task as mere symbols that are void of an inherent semantics. However, in many cases textual descriptions of these labels are available or can be easily constructed from public document sources such as Wikipedia. In this paper, we investigate an approach for embedding documents and labels into a joint space while sharing word representations between documents and labels. For finding such embeddings, we rely on the text of documents as well as descriptions for the labels. The use of such label descriptions not only lets us expect an increased performance on conventional multi-label text classification tasks, but can also be used to make predictions for labels that have not been seen during the training phase. The potential of our method is demonstrated on the multi-label classification task of assigning keywords from the Medical Subject Headings (MeSH) to publications in biomedical research, both in a conventional and in a zero-shot learning setting.

In this study, we investigate expected CP decomposition — a special case of CP decomposition in which a tensor to be decomposed is given as the sum or average of tensor samples X ( t ) for t = 1,..., T . To determine this decomposition, we develope stochastic-gradient-descent-type algorithms with four appealing features: efficient memory use, ability to work in an online setting, robustness of parameter tuning, and simplicity. Our theoretical analysis show that the solutions do not diverge to infinity for any initial value or step size. Experimental results confirm that our algorithms significantly outperform all existing methods in terms of accuracy. We also show that they can successfully decompose a large tensor, containing billion-scale nonzero elements.

Multiple kernel k-means (MKKM) clustering aims to optimally combine a group of pre-specified kernels to improve clustering performance. However, we observe that existing MKKM algorithms do not sufficiently consider the correlation among these kernels. This could result in selecting mutually redundant kernels and affect the diversity of information sources utilized for clustering, which finally hurts the clustering performance. To address this issue, this paper proposes an MKKM clustering with a novel, effective matrix-induced regularization to reduce such redundancy and enhance the diversity of the selected kernels. We theoretically justify this matrix-induced regularization by revealing its connection with the commonly used kernel alignment criterion. Furthermore, this justification shows that maximizing the kernel alignment for clustering can be viewed as a special case of our approach and indicates the extendability of the proposed matrix-induced regularization for designing better clustering algorithms. As experimentally demonstrated on five challenging MKL benchmark data sets, our algorithm significantly improves existing MKKM and consistently outperforms the state-of-the-art ones in the literature, verifying the effectiveness and advantages of incorporating the proposed matrix-induced regularization.

Autoregressive integrated moving average (ARIMA) is one of the most popular linear models for time series forecasting due to its nice statistical properties and great flexibility. However, its parameters are estimated in a batch manner and its noise terms are often assumed to be strictly bounded, which restricts its applications and makes it inefficient for handling large-scale real data. In this paper, we propose online learning algorithms for estimating ARIMA models under relaxed assumptions on the noise terms, which is suitable to a wider range of applications and enjoys high computational efficiency. The idea of our ARIMA method is to reformulate the ARIMA model into a task of full information online optimization (without random noise terms). As a consequence, we can online estimation of the parameters in an efficient and scalable way. Furthermore, we analyze regret bounds of the proposed algorithms, which guarantee that our online ARIMA model is provably as good as the best ARIMA model in hindsight. Finally, our encouraging experimental results further validate the effectiveness and robustness of our method.