It is challenging to handle a large volume of labels in multi-label learning. However, existing approaches explicitly or implicitly assume that all the labels in the learning process are given, which could be easily violated in changing environments. In this paper, we define and study streaming label learning (SLL), i.e., labels are arrived on the fly, to model newly arrived labels with the help of the knowledge learned from past labels. The core of SLL is to explore and exploit the relationships between new labels and past labels and then inherit the relationship into hypotheses of labels to boost the performance of new classifiers. In specific, we use the label self-representation to model the label relationship, and SLL will be divided into two steps: a regression problem and a empirical risk minimization (ERM) problem. Both problems are simple and can be efficiently solved. We further show that SLL can generate a tighter generalization error bound for new labels than the general ERM framework with trace norm or Frobenius norm regularization. Finally, we implement extensive experiments on various benchmark datasets to validate the new setting. And results show that SLL can effectively handle the constantly emerging new labels and provides excellent classification performance.

When there are insufficient labeled samples for training a supervised model, we can adopt active learning to select the most informative samples for human labeling, or transfer learning to transfer knowledge from related labeled data source. Combining transfer learning with active learning has attracted much research interest in recent years. Most existing works follow the setting where the class labels in source domain are the same as the ones in target domain. In this paper, we focus on a more challenging cross-class setting where the class labels are totally different in two domains but related to each other in an intermediary attribute space, which is barely investigated before. We propose a novel and effective method that utilizes the attribute representation as the seed parameters to generate the classification models for classes. And we propose a joint learning framework that takes into account the knowledge from the related classes in source domain, and the information in the target domain. Besides, it is simple to perform uncertainty sampling, a fundamental technique for active learning, based on the framework. We conduct experiments on three benchmark datasets and the results demonstrate the efficacy of the proposed method.

Predictive state representations (PSRs) model dynamical systems using appropriately chosen predictions about future observations as a representation of the current state. In contrast to the hidden states posited by HMMs or RNNs, PSR states are directly observable in the training data; this gives rise to a moment-matching spectral algorithm for learning PSRs that is computationally efficient and statistically consistent when the model complexity matches that of the true system generating the data. In practice, however, model mismatch is inevitable and while spectral learning remains appealingly fast and simple it may fail to find optimal models. To address this problem, we investigate the use of gradient methods for improving spectrally-learned PSRs. We show that only a small amount of additional gradient optimization can lead to significant performance gains, and moreover that initializing gradient methods with the spectral learning solution yields better models in significantly less time than starting from scratch.

Matrix concentration inequalities have attracted much attention in diverse applications such as linear algebra, statistical estimation, combinatorial optimization, etc. In this paper, we present new Bernstein concentration inequalities depending only on the first moments of random matrices, whereas previous Bernstein inequalities are heavily relevant to the first and second moments. Based on those results, we analyze the empirical risk minimization in the presence of label noise. We find that many popular losses used in risk minimization can be decomposed into two parts, where the first part won't be affected and only the second part will be affected by noisy labels. We show that the influence of noisy labels on the second part can be reduced by our proposed LICS (Labeled Instance Centroid Smoothing) approach. The effectiveness of the LICS algorithm is justified both theoretically and empirically.

In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by certain Indepenent Component Analysis techniques, are simple, easy to implement and efficient. Geometrically, the proposed algorithms can be interpreted as hidden basis recovery by means of function optimization. We give a complete characterization of the contrast functions admissible for provable basis recovery. We show how these conditions can be interpreted as a "hidden convexity" of our optimization problem on the sphere; interestingly, we use efficient convex maximization rather than the more common convex minimization. We also show encouraging experimental results on real and simulated data.

We propose a probabilistic model for non-exhaustive and overlapping (NEO) bi-clustering. Our goal is to extract a few sub-matrices from the given data matrix, where entries of a sub-matrix are characterized by a specific distribution or parameters. Existing NEO biclustering methods typically require the number of sub-matrices to be extracted, which is essentially difficult to fix a priori. In this paper, we extend the plaid model, known as one of the best NEO bi-clustering algorithms, to allow infinite bi-clustering; NEO bi-clustering without specifying the number of sub-matrices. Our model can represent infinite sub-matrices formally. We develop a MCMC inference without the finite truncation, which potentially addresses all possible numbers of sub-matrices. Experiments quantitatively and qualitatively verify the usefulness of the proposed model. The results reveal that our model can offer more precise and in-depth analysis of sub-matrices.

Tensor decomposition methods are effective tools for modelling multidimensional array data (i.e., tensors). Among them, nonparametric Bayesian models, such as Infinite Tucker Decomposition (InfTucker), are more powerful than multilinear factorization approaches, including Tucker and PARAFAC, and usually achieve better predictive performance. However, they are difficult to handle massive data due to a prohibitively high training cost. To address this limitation, we propose Distributed infinite Tucker (DinTucker), a new hierarchical Bayesian model that enables local learning of InfTucker on subarrays and global information integration from local results. We further develop a distributed stochastic gradient descent algorithm, coupled with variational inference for model estimation. In addition, the connection between DinTucker and InfTucker is revealed in terms of model evidence. Experiments demonstrate that DinTucker maintains the predictive accuracy of InfTucker and is scalable on massive data: On multidimensional arrays with billions of elements from two real-world applications, DinTucker achieves significantly higher prediction accuracy with less training time, compared with the state-of-the-art large-scale tensor decomposition method, GigaTensor.

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient. Accordingly, there has been a lot of work on "superposition-structured" models where multiple structural constraints are imposed. To efficiently solve these "superposition-structured" statistical models, we develop a framework based on a proximal Newton-type method. Employing the smoothed conic dual approach with the LBFGS updating formula, we propose a scalable and extensible proximal quasi-Newton (SEP-QN) framework. Empirical analysis on various datasets shows that our framework is potentially powerful, and achieves super-linear convergence rate for optimizing some popular "superposition-structured" statistical models such as the fused sparse group lasso.

With the recent proliferation of large-scale learning problems, there have been a lot of interest on distributed machine learning algorithms, particularly those that are based on stochastic gradient descent (SGD) and its variants. However, existing algorithms either suffer from slow convergence due to the inherent variance of stochastic gradients, or have a fast linear convergence rate but at the expense of poorer solution quality. In this paper, we combine their merits by proposing a fast distributed asynchronous SGD-based algorithm with variance reduction. A constant learning rate can be used, and it is also guaranteed to converge linearly to the optimal solution. Experiments on the Google Cloud Computing Platform demonstrate that the proposed algorithm outperforms state-of-the-art distributed asynchronous algorithms in terms of both wall clock time and solution quality.

Stochastic gradient descent (SGD) and its variants have become more and more popular in machine learning due to their efficiency and effectiveness. To handle large-scale problems, researchers have recently proposed several parallel SGD methods for multicore systems. However, existing parallel SGD methods cannot achieve satisfactory performance in real applications. In this paper, we propose a fast asynchronous parallel SGD method, called AsySVRG, by designing an asynchronous strategy to parallelize the recently proposed SGD variant called stochastic variance reduced gradient (SVRG). AsySVRG adopts a lock-free strategy which is more efficient than other strategies with locks. Furthermore, we theoretically prove that AsySVRG is convergent with a linear convergence rate. Both theoretical and empirical results show that AsySVRG can outperform existing state-of-the-art parallel SGD methods like Hogwild! in terms of convergence rate and computation cost.