Multi-output inference tasks, such as multi-label classification, have become increasingly important in recent years. A popular method for multi-label classification is classifier chains, in which the predictions of individual classifiers are cascaded along a chain, thus taking into account inter-label dependencies and improving the overall performance. Several varieties of classifier chain methods have been introduced, and many of them perform very competitively across a wide range of benchmark datasets. However, scalability limitations become apparent on larger datasets when modeling a fully-cascaded chain. In particular, the methods' strategies for discovering and modeling a good chain structure constitutes a mayor computational bottleneck. In this paper, we present the classifier trellis (CT) method for scalable multi-label classification. We compare CT with several recently proposed classifier chain methods to show that it occupies an important niche: it is highly competitive on standard multi-label problems, yet it can also scale up to thousands or even tens of thousands of labels.

While computer and communication technologies have provided effective means to scale up many aspects of education, the submission and grading of assessments such as homework assignments and tests remains a weak link. In this paper, we study the problem of automatically grading the kinds of open response mathematical questions that figure prominently in STEM (science, technology, engineering, and mathematics) courses. Our data-driven framework for mathematical language processing (MLP) leverages solution data from a large number of learners to evaluate the correctness of their solutions, assign partial-credit scores, and provide feedback to each learner on the likely locations of any errors. MLP takes inspiration from the success of natural language processing for text data and comprises three main steps. First, we convert each solution to an open response mathematical question into a series of numerical features. Second, we cluster the features from several solutions to uncover the structures of correct, partially correct, and incorrect solutions. We develop two different clustering approaches, one that leverages generic clustering algorithms and one based on Bayesian nonparametrics. Third, we automatically grade the remaining (potentially large number of) solutions based on their assigned cluster and one instructor-provided grade per cluster. As a bonus, we can track the cluster assignment of each step of a multistep solution and determine when it departs from a cluster of correct solutions, which enables us to indicate the likely locations of errors to learners. We test and validate MLP on real-world MOOC data to demonstrate how it can substantially reduce the human effort required in large-scale educational platforms.

Applying traditional collaborative filtering to digital publishing is challenging because user data is very sparse due to the high volume of documents relative to the number of users. Content based approaches, on the other hand, is attractive because textual content is often very informative. In this paper we describe large-scale content based collaborative filtering for digital publishing. To solve the digital publishing recommender problem we compare two approaches: latent Dirichlet allocation (LDA) and deep belief nets (DBN) that both find low-dimensional latent representations for documents. Efficient retrieval can be carried out in the latent representation. We work both on public benchmarks and digital media content provided by Issuu, an online publishing platform. This article also comes with a newly developed deep belief nets toolbox for topic modeling tailored towards performance evaluation of the DBN model and comparisons to the LDA model.

Given a data sample with its feature vector, SC tries to learn a codebook with some codeworks, and approximate the data sample as the linear combination of the codewords. SC assume that only a few codewords in the codebook are enough to represent the data sample, thus the combination coefficients should be sparse, i.e. most of the coefficients are zeros, leaving only a few of them non-zeros. The linear combination coefficients of the data sample could be its new representation. Because they are sparse, the coefficient vector is often referred to as the sparse code. To solve the sparse code, one usually minimizes the approximation error with regard to the codebook and the sparse code, and at the same time seeks the sparsity of the sparse code. Although SC has been used in many pattern recognition applications, such as palmprint recognition [24], dynamic texture recognition [25], human action recognition [26], [27], [28], speech recognition [29], digit recognition [30], image annotation [31], [32], [33], and face recognition [34], in most cases, SC is used as an unsupervised learning method. When SC is performed to the training data set, it is assumed that the class labels of the training samples are unavailable. Then after the sparse codes are learned, they will be used to learn a classifier. Thus the class labels are ignored during the sparse coding procedure.

Identifying and understanding modular organizations is centrally important in the study of complex systems. Several approaches to this problem have been advanced, many framed in information-theoretic terms. Our treatment starts from the complementary point of view of statistical modeling and prediction of dynamical systems. It is known that for finite amounts of training data, simpler models can have greater predictive power than more complex ones. We use the trade-off between model simplicity and predictive accuracy to generate optimal multiscale decompositions of dynamical networks into weakly-coupled, simple modules. State-dependent and causal versions of our method are also proposed.

The problem of inference in a Markov random field (MRF) arises in many applied domains, e.g. in machine learning, computer vision, natural language processing, etc. In this paper we focus on one important type of inference: maximum a posteriori (MAP) inference, often referred to as MRF energy minimization. Inference of this type is a combinatorial optimization problem, i.e. an optimization problem with the finite domain. The most studied case of MRF energy minimization is the situation when the energy can be represented as a sum of terms (potentials) that depend on only one or two variables each (unary and pairwise potentials). In this setting the energy is said to be defined by a graph where the nodes correspond to the variables and the edges to the pairwise potentials. Minimization of energies defined on graphs in known to be NPhard in general [8] but can be done exactly in polynomial time in a number of special cases, e.g. if the graph defining the energy is acyclic [36] or if the energy is submodular in standard [28] or multi-label sense [10]. One way to go beyond pairwise potentials is to add higher-order summands to the energy. For example, Kohli et al. [23] and Ladický et al. [32] use high-order potentials based on superpixels (image regions) for semantic image segmentation; Delong et al. [11] use label cost potentials for geometric model fitting tasks. To be tractable, high-order potentials need to have a compact representation.

In many problems arising in the natural sciences, technology, business and politics, it is crucial to understand the specific connections among the objects under study: for example, the interactions between members of a political party; the firing of synapses in a neuronal network; or citation patterns in reference literature. Mathematically, these objects and their connections are modeled as graphs, and a common goal is to find clusters of similar vertices within a graph. Both model-based and heuristic-based techniques have been proposed for clustering the vertices in a graphs [14, 2, 5, 19]. In this paper we focus on probabilistic performance guarantees for spectral-based techniques which 1 have elements of both model-and heuristic-based methods [18, 20]. We study the consistency of mean squared error clustering via the adjacency spectral embedding for three nested classes of models, each an examples of latent position models [7]: - the stochastic blockmodel where vertices in the same cluster are stochastically equivalent [8], - the degree-corrected stochastic blockmodel where stochastic equivalence holds up to a scaling factor [9], - and the random dot product graph where a natural vertex clustering may not exist [27].

The computation of the global minimum energy conformation (GMEC) is an important and challenging topic in structure-based computational protein design. In this paper, we propose a new protein design algorithm based on the AND/OR branch-and-bound (AOBB) search, which is a variant of the traditional branch-and-bound search algorithm, to solve this combinatorial optimization problem. By integrating with a powerful heuristic function, AOBB is able to fully exploit the graph structure of the underlying residue interaction network of a backbone template to significantly accelerate the design process. Tests on real protein data show that our new protein design algorithm is able to solve many prob- lems that were previously unsolvable by the traditional exact search algorithms, and for the problems that can be solved with traditional provable algorithms, our new method can provide a large speedup by several orders of magnitude while still guaranteeing to find the global minimum energy conformation (GMEC) solution.

N RECENT years, wind has made an increasing contribution to the world's energy supply mix. However, there is still much to be done in all areas of the technology for it to reach its full potential. Currently, horizontal-axis wind turbines (HAWTs) are the most commonly used form. However, "modern wind farms comprised of HAWTs require significant land resources to separate each wind turbine from the adjacent turbine wakes. This aerodynamic constraint limits the amount of power that can be extracted from a given wind farm footprint. The resulting inefficiency of HAWT farms is currently compensated by using taller wind turbines to access greater wind resources at high altitudes, but this solution comes at the expense of higher engineering costs and greater visual, acoustic, radar and environmental impact" [1]. This has forced wind energy systems away from high energy demand population centres and towards remote locations with higher distribution costs. In contrast, vertical-axis wind turbines (VAWTs) do not need to be oriented to wind direction and can be positioned closely together, potentially resulting in much higher efficiency. VAWT can also be easier to manufacture, may scale more easily, are typically inherently lightweight with little or no noise pollution, and are more able to tolerate extreme weather conditions [2].

We are interested in a general data - based prediction task: g iven a train ing data matrix ( TrX), a training outcome vector ( TrY) and a test data matrix ( TeX), predict test outcome vector (). In the era of big data, two practically conflicting challenges are eminent: (1) the prior knowledge on the subject (a lso known as domain specific knowledge) is largely insufficient; (2) computation and storage cost of big data is unaffordable. To meet these aforementioned challenge s, this paper is devoted to modeling large number of observations without domain specific k nowledge, using regression and classification. The methods widely used for regression and classification can be classified as: linear regression, k nearest neighbor (KNN) [1], support vector machine (SVM) [2], neural network (NN) [3, 4], extreme learning machine (ELM) [5], deep learning (DL) [6], random forest (RF) [7] and boosting (GBM) [8] among others . Each method performs well on some types of datasets but has its own limitations on others [9 - 12] . A method with reasonable performance on boarder, if not universe, datasets is highly desired .