Supervised dimensionality reduction has shown great advantages in finding predictive subspaces. Previous methods rarely consider the popular maximum margin principle and are prone to overfitting to usually small training data, especially for those under the maximum likelihood framework. In this paper, we present a posterior-regularized Bayesian approach to combine Principal Component Analysis (PCA) with the max-margin learning. Based on the data augmentation idea for max-margin learning and the probabilistic interpretation of PCA, our method can automatically infer the weight and penalty parameter of max-margin learning machine, while finding the most appropriate PCA subspace simultaneously under the Bayesian framework. We develop a fast mean-field variational inference algorithm to approximate the posterior. Experimental results on various classification tasks show that our method outperforms a number of competitors.

Support Vector Machine (SVM) is a fundamental technique in machine learning. A long time challenge facing SVM is how to deal with outliers (caused by mislabeling), as they could make the classes in SVM nonseparable. Existing techniques, such as soft margin SVM, ν-SVM, and Core-SVM, can alleviate the problem to certain extent, but cannot completely resolve the issue. Recently, there are also techniques available for explicit outlier removal. But they suffer from high time complexity and cannot guarantee quality of solution. In this paper, we present a new combinatorial approach, called Random Gradient Descent Tree (or RGD-tree), to explicitly deal with outliers; this results in a new algorithm called RGD-SVM. Our technique yields provably good solution and can be efficiently implemented for practical purpose. The time and space complexities of our approach only linearly depend on the input size and the dimensionality of the space, which are significantly better than existing ones. Experiments on benchmark datasets suggest that our technique considerably outperforms several popular techniques in most of the cases.

In recommendation systems, one is interested in the ranking of the predicted items as opposed to other losses such as the mean squared error. Although a variety of ways to evaluate rankings exist in the literature, here we focus on the Area Under the ROC Curve (AUC) as it widely used and has a strong theoretical underpinning. In practical recommendation, only items at the top of the ranked list are presented to the users. With this in mind we propose a class of objective functions which primarily represent a smooth surrogate for the real AUC, and in a special case we show how to prioritise the top of the list. This loss is differentiable and is optimised through a carefully designed stochastic gradient-descent-based algorithm which scales linearly with the size of the data. We mitigate sample bias present in the data by sampling observations according to a certain power-law based distribution. In addition, we provide computation results as to the efficacy of the proposed method using synthetic and real data.

Much of the focus on finding good representations in reinforcement learning has been on learning complex non-linear predictors of value. Policy gradient algorithms, which directly represent the policy, often need fewer parameters to learn good policies. However, they typically employ a fixed parametric representation that may not be sufficient for complex domains. This paper introduces the Policy Tree algorithm, which can learn an adaptive representation of policy in the form of a decision tree over different instantiations of a base policy. Policy gradient is used both to optimize the parameters and to grow the tree by choosing splits that enable the maximum local increase in the expected return of the policy. Experiments show that this algorithm can choose genuinely helpful splits and significantly improve upon the commonly used linear Gibbs softmax policy, which we choose as our base policy.

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning in the original space. However, the manifold in reduced-dimensional subspace is likely to exhibit altered properties in contrast with the original space. Thus, applying manifold information obtained from the original space to the clustering process in a low-dimensional subspace is prone to inferior performance. Aiming to address this issue, we propose a novel convex algorithm that mines the manifold structure in the low-dimensional subspace. In addition, our unified learning process makes the manifold learning particularly tailored for the clustering. Compared with other related methods, the proposed algorithm results in more structured clustering result. To validate the efficacy of the proposed algorithm, we perform extensive experiments on several benchmark datasets in comparison with some state-of-the-art clustering approaches. The experimental results demonstrate that the proposed algorithm has quite promising clustering performance.

Training a structured prediction model involves performing several loss-augmented inference steps. Over the lifetime of the training, many of these inference problems, although different, share the same solution. We propose AI-DCD, an Amortized Inference framework for Dual Coordinate Descent method, an approximate learning algorithm, that accelerates the training process by exploiting this redundancy of solutions, without compromising the performance of the model. We show the efficacy of our method by training a structured SVM using dual coordinate descent for an entityrelation extraction task. Our method learns the same model as an exact training algorithm would, but call the inference engine only in 10% – 24% of the inference problems encountered during training. We observe similar gains on a multi-label classification task and with a Structured Perceptron model for the entity-relation task.

The global financial crisis occurred in 2008 and its contagion to other regions, as well as the long-lasting impact on different markets, show that it is increasingly important to understand the complicated coupling relationships across financial markets. This is indeed very difficult as complex hidden coupling relationships exist between different financial markets in various countries, which are very hard to model. The couplings involve interactions between homogeneous markets from various countries (we call intra-market coupling), interactions between heterogeneous markets (inter-market coupling) and interactions between current and past market behaviors (temporal coupling). Very limited work has been done towards modeling such complex couplings, whereas some existing methods predict market movement by simply aggregating indicators from various markets but ignoring the inbuilt couplings. As a result, these methods are highly sensitive to observations, and may often fail when financial indicators change slightly. In this paper, a coupled deep belief network is designed to accommodate the above three types of couplings across financial markets. With a deep-architecture model to capture the high-level coupled features, the proposed approach can infer market trends. Experimental results on data of stock and currency markets from three countries show that our approach outperforms other baselines, from both technical and business perspectives.

Current manifold alignment methods can effectively align data sets that are drawn from a non-intersecting set of manifolds. However, as data sets become increasingly high-dimensional and complex, this assumption may not hold. This paper proposes a novel manifold alignment algorithm, low rank alignment (LRA), that uses a low rank representation (instead of a nearest neighbor graph construction) to embed and align data sets drawn from mixtures of manifolds. LRA does not require the tuning of a sensitive nearest neighbor hyperparameter or prior knowledge of the number of manifolds, both of which are common drawbacks with existing techniques. We demonstrate the effectiveness of our algorithm in two real-world applications: a transfer learning task in spectroscopy and a canonical information retrieval task.

We consider a budgeted variant of the problem of learning from expert advice with N experts. Each queried expert incurs a cost and there is a given budget B on the total cost of experts that can be queried in any prediction round. We provide an online learning algorithm for this setting with regret after T prediction rounds bounded by O(sqrt(C log(N)T/B)), where C is the total cost of all experts. We complement this upper bound with a nearly matching lower bound Omega(sqrt(CT/B)) on the regret of any algorithm for this problem. We also provide experimental validation of our algorithm.

Active learning is a subfield of machine learning that has been successfully used in many applications including text classification and bioinformatics. One of the fundamental branches of active learning is query synthesis, where the learning agent constructs artificial queries from scratch in order to reveal sensitive information about the true decision boundary. Nevertheless, the existing literature on membership query synthesis has focused on finite concept classes with a limited extension to real-world applications. In this paper, we present an efficient spectral algorithm for membership query synthesis for halfspaces, whose sample complexity is experimentally shown to be near-optimal. At each iteration, the algorithm consists of two steps. First, a convex optimization problem is solved that provides an approximate characterization of the version space. Second, a principal component is extracted, which yields a synthetic query that shrinks the version space exponentially fast. Unlike traditional methods in active learning, the proposed method can be readily extended into the batch setting by solving for the top k eigenvectors in the second step. Experimentally, it exhibits a significant improvement over traditional approaches such as uncertainty sampling and representative sampling. For example, to learn a halfspace in the Euclidean plane with 25 dimensions and an estimation error of 1E-4, the proposed algorithm uses less than 3% of the number of queries required by uncertainty sampling.