Thompson sampling is one of the earliest randomized algorithms for multi-armed bandits (MAB). In this paper, we extend the Thompson sampling to Budgeted MAB, where there is random cost for pulling an arm and the total cost is constrained by a budget. We start with the case of Bernoulli bandits, in which the random rewards (costs) of an arm are independently sampled from a Bernoulli distribution. To implement the Thompson sampling algorithm in this case, at each round, we sample two numbers from the posterior distributions of the reward and cost for each arm, obtain their ratio, select the arm with the maximum ratio, and then update the posterior distributions. We prove that the distribution-dependent regret bound of this algorithm is O (ln B), where B denotes the budget. By introducing a Bernoulli trial, we further extend this algorithm to the setting that the rewards (costs) are drawn from general distributions, and prove that its regret bound remains almost the same. Our simulation results demonstrate the effectiveness of the proposed algorithm.

In this paper, we propose to represent and classify complicated objects. In order to represent the objects, we propose a multi-graph-view model which uses graphs constructed from multiple graph-views to represent an object. In addition, a bag based multi-graph model is further used to relax labeling by only requiring one label for a bag of graphs, which represent one object. In order to learn classification models, we propose a multi-graph-view bag learning algorithm (MGVBL), which aims to explore subgraph features from multiple graph-views for learning. By enabling a joint regularization across multiple graph-views, and enforcing labeling constraints at the bag and graph levels, MGVBL is able to discover most effective subgraph features across all graph-views for learning. Experiments on real-world learning tasks demonstrate the performance of MGVBL for complicated object classification.

Cross-modal hashing is designed to facilitate fast search across domains. In this work, we present a cross-modal hashing approach, called quantized correlation hashing (QCH), which takes into consideration the quantization loss over domains and the relation between domains. Unlike previous approaches that separate the optimization of the quantizer independent of maximization of domain correlation, our approach simultaneously optimizes both processes. The underlying relation between the domains that describes the same objects is established via maximizing the correlation between the hash codes across the domains. The resulting multi-modal objective function is transformed to a unimodal formalization, which is optimized through an alternative procedure. Experimental results on three real world datasets demonstrate that our approach outperforms the state-of-the-art multi-modal hashing methods.

Inspired by recent successes of deep learning in computer vision, we propose a novel framework for encoding time series as different types of images, namely, Gramian Angular Summation/Difference Fields (GASF/GADF) and Markov Transition Fields (MTF). This enables the use of techniques from computer vision for time series classification and imputation. We used Tiled Convolutional Neural Networks (tiled CNNs) on 20 standard datasets to learn high-level features from the individual and compound GASF-GADF-MTF images. Our approaches achieve highly competitive results when compared to nine of the current best time series classification approaches. Inspired by the bijection property of GASF on 0/1 rescaled data, we train Denoised Auto-encoders (DA) on the GASF images of four standard and one synthesized compound dataset. The imputation MSE on test data is reduced by 12.18% – 48.02% when compared to using the raw data. An analysis of the features and weights learned via tiled CNNs and DAs explains why the approaches work.

Many clustering methods highly depend on extracted features. In this paper, we propose a joint optimization framework in terms of both feature extraction and discriminative clustering. We utilize graph regularized sparse codes as the features, and formulate sparse coding as the constraint for clustering. Two cost functions are developed based on entropy-minimization and maximum-margin clustering principles, respectively, as the objectives to be minimized. Solving such a bi-level optimization mutually reinforces both sparse coding and clustering steps.  Experiments on several benchmark datasets verify remarkable performance improvements led by the proposed joint optimization.

As an important machine learning topic, dimensionality reduction has been widely studied and utilized in various kinds of areas. A multitude of dimensionality reduction methods have been developed, among which unsupervised dimensionality reduction is more desirable when obtaining label information requires onerous work. However, most previous unsupervised dimensionality reduction methods call for an affinity graph constructed beforehand, with which the following dimensionality reduction steps can be then performed. Separation of graph construction and dimensionality reduction leads the dimensionality reduction process highly dependent on quality of the input graph. In this paper, we propose a novel graph embedding method for unsupervised dimensionality reduction. We simultaneously conduct dimensionality reduction along with graph construction by assigning adaptive and optimal neighbors according to the projected local distances. Our method doesn’t need an affinity graph constructed in advance, but instead learns the graph concurrently with dimensionality reduction. Thus, the learned graph is optimal for dimensionality reduction. Meanwhile, our learned graph has an explicit block diagonal structure, from which the clustering results could be directly revealed without any postprocessing steps. Extensive empirical results on dimensionality reduction as well as clustering are presented to corroborate the performance of our method.

In predicate invention (PI), new predicates are introduced into a logical theory, usually by rewriting a group of closely-related rules to use a common invented predicate as a "subroutine". PI is difficult, since a poorly-chosen invented predicate may lead to error cascades. Here we suggest a "soft" version of predicate invention: instead of explicitly creating new predicates, we implicitly group closely-related rules by using structured sparsity to regularize their parameters together. We show that soft PI, unlike hard PI, consistently improves over previous strong baselines for structure-learning on two large-scale tasks.

Hashing method becomes popular for large scale similarity search due to its storage and computational efficiency. Many machine learning techniques, ranging from unsupervised to supervised, have been proposed to design compact hashing codes. Most of the existing hashing methods generate binary codes to efficiently find similar data examples to a query. However, the ranking accuracy among the retrieved data examples is not modeled. But in many real world applications, ranking measure is important for evaluating the quality of hashing codes.In this paper, we propose a novel Ranking Preserving Hashing (RPH) approach that directly optimizes a popular ranking measure, Normalized Discounted Cumulative Gain (NDCG), to obtain effective hashing codes with high ranking accuracy. The main difficulty in the direct optimization of NDCG measure is that it depends on the ranking order of data examples, which forms a non-convex non-smooth optimization problem. We address this challenge by optimizing the expectation of NDCG measure calculated based on a linear hashing function. A gradient descent method is designed to achieve the goal. An extensive set of experiments on two large scale datasets demonstrate the superior ranking performance of the proposed approach over several state-of-the-art hashing methods.

Hashing approach becomes popular for fast similarity search in many large scale applications.Real world data are usually with multiple modalities or having different representations from multiple sources. Various hashing methods have been proposed to generate compact binary codes from multi-modal data.However, most existing multi-modal hashing techniques assume that each data example appears in all modalities, or at least there is one modality containing all data examples. But in real applications, it is often the case that every modality suffers from the missing of some data and therefore results in many partial examples,i.e., examples with some modalities missing.In this paper, we present a novel hashing approach to deal with Partial Multi-Modal data. In particular, the hashing codes are learned by simultaneously ensuring the data consistency among different modalities via latent subspace learning, and preserving data similarity within the same modality through graph Laplacian. We then further improve the codes via orthogonal rotation based on the orthogonal invariant property of our formulation.Experiments on two multi-modal datasets demonstrate the superior performance of the proposed approach over several state-of-the-art multi-modal hashing methods

SVM in advance, and this limits their applications to largescale problems. To address this issue, several methods for Support vector machines (SVMs) play a very dominant selecting a set of basis vectors are proposed. They include role in data classification due to their good sampling from the training set in the Nystrom method generalization performance. However, they suffer [Williams and Seeger, 2001] and variants of the Incomplete from the high computational complexity in the Cholesky factorization [Bach and Jordan, 2005], core vector classification phase when there are a considerable machine (CVM) [Tsang et al., 2005], relevance vector machine number of support vectors (SVs). Then it is desirable (RVM)[Tipping, 2001], and relevance units machine to design efficient algorithms in the classification (RUM)[Gao and Zhang, 2009]. Wu et al. [Wu et al., 2006] phase to deal with the datasets of realtime add one constraint on the number of basis vectors to the standard pattern recognition systems. To this end, we SVM optimization problem, and then solve this modified propose a novel classifier called HMLSVMs (Hierarchical nonconvex problem to build sparse kernel learning algorithms Mixing Linear Support Vector Machines) (SKLA). Joachims and Yu [Joachims and Yu, 2009] in this paper, which has a hierarchical structure explore a new sparse kernel SVMs via cutting plane training, with a mixing linear SVMs classifier at each node called cutting-plane subspace pursuit (CPSP).Although and predicts the label of a sample using only a the above methods prunes the SVs and reduces computational few hyperplanes. We also give a generalization complexity in classification phase, when a new test sample is error bound for the class of locally linear SVMs introduced, they still need to compare it with these pruned (LLSVMs) based on the Rademacher theory, which SVs via kernel calculations to predict the label of the test ensures that overfitting can be effectively avoided.