Restricted Boltzmann Machines (RBMs) are an important class of latent variable models for representing vector data. An under-explored area is multimode data, where each data point is a matrix or a tensor. Standard RBMs applying to such data would require vectorizing matrices and tensors, thus resulting in unnecessarily high dimensionality and at the same time, destroying the inherent higher-order interaction structures. This paper introduces Tensor-variate Restricted Boltzmann Machines (TvRBMs) which generalize RBMs to capture the multiplicative interaction between data modes and the latent variables. TvRBMs are highly compact in that the number of free parameters grows only linear with the number of modes. We demonstrate the capacity of TvRBMs on three real-world applications: handwritten digit classification, face recognition and EEG-based alcoholic diagnosis. The learnt features of the model are more discriminative than the rivals, resulting in better classification performance.

We investigate a problem at the intersection of machine learning and security: training-set attacks on machine learners. In such attacks an attacker contaminates the training data so that a specific learning algorithm would produce a model profitable to the attacker. Understanding training-set attacks is important as more intelligent agents (e.g. spam filters and robots) are equipped with learning capability and can potentially be hacked via data they receive from the environment. This paper identifies the optimal training-set attack on a broad family of machine learners. First we show that optimal training-set attack can be formulated as a bilevel optimization problem. Then we show that for machine learners with certain Karush-Kuhn-Tucker conditions we can solve the bilevel problem efficiently using gradient methods on an implicit function. As examples, we demonstrate optimal training-set attacks on Support VectorMachines, logistic regression, and linear regression with extensive experiments. Finally, we discuss potential defenses against such attacks.

This paper is concerned with model-based clustering of discrete data. Latent class models (LCMs) are usually used for the task. An LCM consists of a latent variable and a number of attributes. It makes the overly restrictive assumption that the attributes are mutually independent given the latent variable. We propose a novel method to relax the assumption. The key idea is to partition the attributes into groups such that correlations among the attributes in each group can be properly modeled by using one single latent variable. The latent variables for the attribute groups are then used to build a number of models and one of them is chosen to produce the clustering results. Extensive empirical studies have been conducted to compare the new method with LCM and several other methods (K-means, kernel K-means and spectral clustering) that are not model-based. The new method outperforms the alternative methods in most cases and the differences are often large.

In this paper, we address the problem of large-scale multi-view spectral clustering. In many real-world applications, data can be represented in various heterogeneous features or views. Different views often provide different aspects of information that are complementary to each other. Several previous methods of clustering have demonstrated that better accuracy can be achieved using integrated information of all the views than just using each view individually. One important class of such methods is multi-view spectral clustering, which is based on graph Laplacian. However, existing methods are not applicable to large-scale problem for their high computational complexity. To this end, we propose a novel large-scale multi-view spectral clustering approach based on the bipartite graph. Our method uses local manifold fusion to integrate heterogeneous features. To improve efficiency, we approximate the similarity graphs using bipartite graphs. Furthermore, we show that our method can be easily extended to handle the out-of-sample problem. Extensive experimental results on five benchmark datasets demonstrate the effectiveness and efficiency of the proposed method, where our method runs up to nearly 3000 times faster than the state-of-the-art methods.

Lasso is a popular method for high-dimensional variable selection, but it hinges on a tuning parameter that is difficult to calibrate in practice. In this study, we introduce TREX, an alternative to Lasso with an inherent calibration to all aspects of the model. This adaptation to the entire model renders TREX an estimator that does not require any calibration of tuning parameters. We show that TREX can outperform cross-validated Lasso in terms of variable selection and computational efficiency. We also introduce a bootstrapped version of TREX that can further improve variable selection. We illustrate the promising performance of TREX both on synthetic data and on two biological data sets from the fields of genomics and proteomics.

Curriculum learning (CL) or self-paced learning (SPL) represents a recently proposed learning regime inspired by the learning process of humans and animals that gradually proceeds from easy to more complex samples in training. The two methods share a similar conceptual learning paradigm, but differ in specific learning schemes. In CL, the curriculum is predetermined by prior knowledge, and remain fixed thereafter. Therefore, this type of method heavily relies on the quality of prior knowledge while ignoring feedback about the learner. In SPL, the curriculum is dynamically determined to adjust to the learning pace of the leaner. However, SPL is unable to deal with prior knowledge, rendering it prone to overfitting. In this paper, we discover the missing link between CL and SPL, and propose a unified framework named self-paced curriculum leaning (SPCL). SPCL is formulated as a concise optimization problem that takes into account both prior knowledge known before training and the learning progress during training. In comparison to human education, SPCL is analogous to "instructor-student-collaborative" learning mode, as opposed to "instructor-driven" in CL or "student-driven" in SPL. Empirically, we show that the advantage of SPCL on two tasks.

Pool-based active learning is an important technique that helps reduce labeling efforts within a pool of unlabeled instances. Currently, most pool-based active learning strategies are constructed based on some human-designed philosophy; that is, they reflect what human beings assume to be “good labeling questions.” However, while such human-designed philosophies can be useful on specific data sets, it is often difficult to establish the theoretical connection of those philosophies to the true learning performance of interest. In addition, given that a single human-designed philosophy is unlikely to work on all scenarios, choosing and blending those strategies under different scenarios is an important but challenging practical task. This paper tackles this task by letting the machines adaptively “learn” from the performance of a set of given strategies on a particular data set. More specifically, we design a learning algorithm that connects active learning with the well-known multi-armed bandit problem. Further, we postulate that, given an appropriate choice for the multi-armed bandit learner, it is possible to estimate the performance of different strategies on the fly. Extensive empirical studies of the resulting ALBL algorithm confirm that it performs better than state-of-the-art strategies and a leading blending algorithm for active learning, all of which are based on human-designed philosophy.

Topic modeling is a powerful tool for uncovering latent structure in many domains, including medicine, finance, and vision. The goals for the model vary depending on the application: sometimes the discovered topics are used for prediction or another downstream task. In other cases, the content of the topic may be of intrinsic scientific interest. Unfortunately, even when one uses modern sparse techniques, discovered topics are often difficult to interpret due to the high dimensionality of the underlying space. To improve topic interpretability, we introduce Graph-Sparse LDA, a hierarchical topic model that uses knowledge of relationships between words (e.g., as encoded by an ontology). In our model, topics are summarized by a few latent concept-words from the underlying graph that explain the observed words. Graph-Sparse LDA recovers sparse, interpretable summaries on two real-world biomedical datasets while matching state-of-the-art prediction performance.

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.