Unlike traditional LASSO enforcing sparsity on the variables, Generalized LASSO (GL) enforces sparsity on a linear transformation of the variables, gaining flexibility and success in many applications. However, many existing GL algorithms do not scale up to high-dimensional problems, and/or only work well for a specific choice of the transformation. We propose an efficient Matching Pursuit Generalized LASSO (MPGL) method, which overcomes these issues, and is guaranteed to converge to a global optimum. We formulate the GL problem as a convex quadratic constrained linear programming (QCLP) problem and tailor-make a cutting plane method. More specifically, our MPGL iteratively activates a subset of nonzero elements of the transformed variables, and solves a subproblem involving only the activated elements thus gaining significant speed-up. Moreover, MPGL is less sensitive to the choice of the trade-off hyper-parameter between data fitting and regularization, and mitigates the long-standing hyper-parameter tuning issue in many existing methods. Experiments demonstrate the superior efficiency and accuracy of the proposed method over the state-of-the-arts in both classification and image processing tasks.

Curriculum Learning (CL) mimics the cognitive process ofhumans and favors a learning algorithm to follow the logical learning sequence from simple examples to more difficult ones. Recent studies show that selecting the simplest curriculum examples from different modalities for graph-based label propagation can yield better performance than simply leveraging single modality. However, they forcibly requirethe curriculums generated by all modalities to be identical to a common curriculum, which discard the individuality ofevery modality and produce the inaccurate curriculum for the subsequent learning. Therefore, this paper proposes a novel multi-modal CL algorithm by comprehensively investigating both the individuality and commonality of different modalities. By considering the curriculums of multiple modalities altogether, their common preference on selecting the simplestexamples can be explored by a row-sparse matrix, and their distinct opinions are captured by a sparse noise matrix. As a consequence, a "soft" fusion of multiple curriculums from different modalities is achieved and the propagation quality can thus be improved. Comprehensive empirical studies reveal that our method can generate higher accuracy than the state-of-the-art multi-modal CL approach and label propagation algorithms on various image classification tasks.

Non-negative Matrix Factorization (NMF) has attracted much attention and been widely used in real-world applications. As a clustering method, it fails to handle the case where data points lie in a complicated geometry structure. Existing methods adopt single global centroid for each cluster, failing to capture the manifold structure. In this paper, we propose a novel local centroids structured NMF to address this drawback. Instead of using single centroid for each cluster, we introduce multiple local centroids for individual cluster such that the manifold structure can be captured by the local centroids. Such a novel NMF method can improve the clustering performance effectively. Furthermore, a novel bipartite graph is incorporated to obtain the clustering indicator directly without any post process. Experiments on both toy datasets and real-world datasets have verified the effectiveness of the proposed method.

We introduce an approach to learning from imbalanced class distributions that does not change the underlying data distribution. The ICC algorithm decomposes majority classes into smaller sub-classes that create a more balanced class distribution. In this paper, we explain how ICC can not only addressthe class imbalance problem but may also increase the expressive power of the hypothesis space. We validate ICC and analyze alternative decomposition methods on well-known machine learning datasets as well as new problems in pervasive computing. Our results indicate that ICC performs as well or better than existing approaches to handling class imbalance.

Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by the minimizer function. Existing methods usually pursue this by artificially designing the explicit form of SPL regularizer. In this paper, we study a group of new regularizer (named self-paced implicit regularizer) that is deduced from robust loss function. Based on the convex conjugacy theory, the minimizer function for self-paced implicit regularizer can be directly learned from the latent loss function, while the analytic form of the regularizer can be even unknown. A general framework (named SPL-IR) for SPL is developed accordingly. We demonstrate that the learning procedure of SPL-IR is associated with latent robust loss functions, thus can provide some theoretical insights for its working mechanism. We further analyze the relation between SPL-IR and half-quadratic optimization and provide a group of self-paced implicit regularizer. Finally, we implement SPL-IR to both supervised and unsupervised tasks, and experimental results corroborate our ideas and demonstrate the correctness and effectiveness of implicit regularizers.

Feature selection is an important technique in machine learning research. An effective and robust feature selection method is desired to simultaneously identify the informative features and eliminate the noisy ones of data. In this paper, we consider the unsupervised feature selection problem which is particularly difficult as there is not any class labels that would guide the search for relevant features. To solve this, we propose a novel algorithmic framework which performs unsupervised feature selection. Firstly, the proposed framework implements structure learning, where the data structures (including intrinsic distribution structure and the data segment) are found via a combination of the alternative optimization and clustering. Then, both the intrinsic data structure and data segmentation are formulated as regularization terms for discriminant feature selection. The results of the feature selection also affect the structure learning step in the following iterations. By leveraging the interactions between structure learning and feature selection, we are able to capture more accurate structure of data and select more informative features. Clustering and classification experiments on real world image data sets demonstrate the effectiveness of our method.

Online joint parameter and state estimation is a core problem for temporal models.Most existing methods are either restricted to a particular class of models (e.g., the Storvik filter) or computationally expensive (e.g., particle MCMC). We propose a novel nearly-black-box algorithm, the Assumed Parameter Filter (APF), a hybrid of particle filtering for state variables and assumed density filtering for parameter variables.It has the following advantages:(a) it is online and computationally efficient;(b) it is applicable to both discrete and continuous parameter spaces with arbitrary transition dynamics.On a variety of toy and real models, APF generates more accurate results within a fixed computation budget compared to several standard algorithms from the literature.

Training machine leaning algorithms on augmented data fromdifferent related sources is a challenging task. This problemarises in several applications, such as the Internet of Things(IoT), where data may be collected from devices with differentsettings. The learned model on such datasets can generalizepoorly due to distribution bias. In this paper we considerthe problem of classifying unseen datasets, given several labeledtraining samples drawn from similar distributions. Weexploit the intrinsic structure of samples in a latent subspaceand identify landmarks, a subset of training instances fromdifferent sources that should be similar. Incorporating subspacelearning and landmark selection enhances generalizationby alleviating the impact of noise and outliers, as well asimproving efficiency by reducing the size of the data. However,since addressing the two issues simultaneously resultsin an intractable problem, we relax the objective functionby leveraging the theory of nonlinear projection and solve atractable convex optimisation. Through comprehensive analysis,we show that our proposed approach outperforms stateof-the-art results on several benchmark datasets, while keepingthe computational complexity low.

The multi-label classification problem involves finding a model that maps a set of input features to more than one output label. Class imbalance is a serious issue in multi-label classification. We introduce an extension of structured forests, a type of random forest used for structured prediction, called Sparse Oblique Structured Hellinger Forests (SOSHF). We explore using structured forests in the general multi-label setting and propose a new imbalance-aware formulation by altering how the splitting functions are learned in two ways. First, we account for cost-sensitivity when converting the multi-label problem to a single-label problem at each node in the tree. Second, we introduce a new objective function for determining oblique splits based on the Hellinger distance, a splitting criterion that has been shown to be robust to class imbalance. We empirically validate our method on a number of benchmarks against standard and state-of-the-art multi-label classification algorithms with improved results.

In this paper, we consider the problem of actively learning a linear classifier through query synthesis where the learner can construct artificial queries in order to estimate the true decision boundaries. This problem has recently gained a lot of interest in automated science and adversarial reverse engineering for which only heuristic algorithms are known. In such applications, queries can be constructed de novo to elicit information (e.g., automated science) or to evade detection with minimal cost (e.g., adversarial reverse engineering). We develop a general framework, called dimension coupling (DC), that 1) reduces a d-dimensional learning problem to d-1 low dimensional sub-problems, 2) solves each sub-problem efficiently, 3) appropriately aggregates the results and outputs a linear classifier, and 4) provides a theoretical guarantee for all possible schemes of aggregation. The proposed method is proved resilient to noise. We show that the DC framework avoids the curse of dimensionality: its computational complexity scales linearly with the dimension. Moreover, we show that the query complexity of DC is near optimal (within a constant factor of the optimum algorithm). To further support our theoretical analysis, we compare the performance of DC with the existing work. We observe that DC consistently outperforms the prior arts in terms of query complexity while often running orders of magnitude faster.