Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well as the need for {\em real-time} processing of streaming data pose major challenges to this end. In this context, the present paper permeates benefits from rank minimization to scalable imputation of missing data, via tracking low-dimensional subspaces and unraveling latent (possibly multi-way) structure from \emph{incomplete streaming} data. For low-rank matrix data, a subspace estimator is proposed based on an exponentially-weighted least-squares criterion regularized with the nuclear norm. After recasting the non-separable nuclear norm into a form amenable to online optimization, real-time algorithms with complementary strengths are developed and their convergence is established under simplifying technical assumptions. In a stationary setting, the asymptotic estimates obtained offer the well-documented performance guarantees of the {\em batch} nuclear-norm regularized estimator. Under the same unifying framework, a novel online (adaptive) algorithm is developed to obtain multi-way decompositions of \emph{low-rank tensors} with missing entries, and perform imputation as a byproduct. Simulated tests with both synthetic as well as real Internet and cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithms, and their superior performance relative to state-of-the-art alternatives.

Social network has gained remarkable attention in the last decade. Accessing social network sites such as Twitter, Facebook LinkedIn and Google+ through the internet and the web 2.0 technologies has become more affordable. People are becoming more interested in and relying on social network for information, news and opinion of other users on diverse subject matters. The heavy reliance on social network sites causes them to generate massive data characterised by three computational issues namely; size, noise and dynamism. These issues often make social network data very complex to analyse manually, resulting in the pertinent use of computational means of analysing them. Data mining provides a wide range of techniques for detecting useful knowledge from massive datasets like trends, patterns and rules [44]. Data mining techniques are used for information retrieval, statistical modelling and machine learning. These techniques employ data pre-processing, data analysis, and data interpretation processes in the course of data analysis. This survey discusses different data mining techniques used in mining diverse aspects of the social network over decades going from the historical techniques to the up-to-date models, including our novel technique named TRCM. All the techniques covered in this survey are listed in the Table.1 including the tools employed as well as names of their authors.

Massive Open Online Courses (MOOCs) bring together thousands of people from different geographies and demographic backgrounds -- but to date, little is known about how they learn or communicate. We introduce a new content-analysed MOOC dataset and use Bayesian Non-negative Matrix Factorization (BNMF) to extract communities of learners based on the nature of their online forum posts. We see that BNMF yields a superior probabilistic generative model for online discussions when compared to other models, and that the communities it learns are differentiated by their composite students' demographic and course performance indicators. These findings suggest that computationally efficient probabilistic generative modelling of MOOCs can reveal important insights for educational researchers and practitioners and help to develop more intelligent and responsive online learning environments.

Brain decoding is a data analysis paradigm for neuroimaging experiments that is based on predicting the stimulus presented to the subject from the concurrent brain activity. In order to make inference at the group level, a straightforward but sometimes unsuccessful approach is to train a classifier on the trials of a group of subjects and then to test it on unseen trials from new subjects. The extreme difficulty is related to the structural and functional variability across the subjects. We call this approach "decoding across subjects". In this work, we address the problem of decoding across subjects for magnetoencephalographic (MEG) experiments and we provide the following contributions: first, we formally describe the problem and show that it belongs to a machine learning sub-field called transductive transfer learning (TTL). Second, we propose to use a simple TTL technique that accounts for the differences between train data and test data. Third, we propose the use of ensemble learning, and specifically of stacked generalization, to address the variability across subjects within train data, with the aim of producing more stable classifiers. On a face vs. scramble task MEG dataset of 16 subjects, we compare the standard approach of not modelling the differences across subjects, to the proposed one of combining TTL and ensemble learning. We show that the proposed approach is consistently more accurate than the standard one.

The intent of this research is to generate a set of non-dominated policies from which one of two agents (the leader) can select a most preferred policy to control a dynamic system that is also affected by the control decisions of the other agent (the follower). The problem is described by an infinite horizon, partially observed Markov game (POMG). At each decision epoch, each agent knows: its past and present states, its past actions, and noise corrupted observations of the other agent's past and present states. The actions of each agent are determined at each decision epoch based on these data. The leader considers multiple objectives in selecting its policy. The follower considers a single objective in selecting its policy with complete knowledge of and in response to the policy selected by the leader. This leader-follower assumption allows the POMG to be transformed into a specially structured, partially observed Markov decision process (POMDP). This POMDP is used to determine the follower's best response policy. A multi-objective genetic algorithm (MOGA) is used to create the next generation of leader policies based on the fitness measures of each leader policy in the current generation. Computing a fitness measure for a leader policy requires a value determination calculation, given the leader policy and the follower's best response policy. The policies from which the leader can select a most preferred policy are the non-dominated policies of the final generation of leader policies created by the MOGA. An example is presented that illustrates how these results can be used to support a manager of a liquid egg production process (the leader) in selecting a sequence of actions to best control this process over time, given that there is an attacker (the follower) who seeks to contaminate the liquid egg production process with a chemical or biological toxin.

Making sense of the physical world has always been at the core of mapping. Up until recently, this has always dependent on using the human eye. Using airborne lasers, it has become possible to quickly "see" more of the world in many more dimensions. The resulting enormous point clouds serve as data sources for applications far beyond the original mapping purposes ranging from flooding protection and forestry to threat mitigation. In order to process these large quantities of data, novel methods are required. In this contribution, we develop models to automatically classify ground cover and soil types. Using the logic of machine learning, we critically review the advantages of supervised and unsupervised methods. Focusing on decision trees, we improve accuracy by including beam vector components and using a genetic algorithm. We find that our approach delivers consistently high quality classifications, surpassing classical methods.

We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as penalties and a norm constraint. HCGS extends conditional gradient methods to cases with multiple nonsmooth terms, in which standard conditional gradient methods may be difficult to apply. The HCGS algorithm borrows techniques from smoothing proximal methods and requires first-order computations (subgradients and proximity operations). Unlike proximal methods, HCGS benefits from the advantages of conditional gradient methods, which render it more efficient on certain large scale optimization problems. We demonstrate these advantages with simulations on two matrix optimization problems: regularization of matrices with combined $\ell_1$ and trace norm penalties; and a convex relaxation of sparse PCA.

We consider the problem of bottom-up compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boolean operators (usually called an Apply function). While such a polytime Apply function is known to exist for certain languages (e.g., OBDDs) and not exist for others (e.g., DNNF), its existence for certain languages remains unknown. Among the latter is the recently introduced language of Sentential Decision Diagrams (SDDs), for which a polytime Apply function exists for unreduced SDDs, but remains unknown for reduced ones (i.e. canonical SDDs). We resolve this open question in this paper and consider some of its theoretical and practical implications. Some of the findings we report question the common wisdom on the relationship between bottom-up compilation, language canonicity and the complexity of the Apply function.

In a sequential auction with multiple bidding agents, it is highly challenging to determine the ordering of the items to sell in order to maximize the revenue due to the fact that the autonomy and private information of the agents heavily influence the outcome of the auction. The main contribution of this paper is two-fold. First, we demonstrate how to apply machine learning techniques to solve the optimal ordering problem in sequential auctions. We learn regression models from historical auctions, which are subsequently used to predict the expected value of orderings for new auctions. Given the learned models, we propose two types of optimization methods: a black-box best-first search approach, and a novel white-box approach that maps learned models to integer linear programs (ILP) which can then be solved by any ILP-solver. Although the studied auction design problem is hard, our proposed optimization methods obtain good orderings with high revenues. Our second main contribution is the insight that the internal structure of regression models can be efficiently evaluated inside an ILP solver for optimization purposes. To this end, we provide efficient encodings of regression trees and linear regression models as ILP constraints. This new way of using learned models for optimization is promising. As the experimental results show, it significantly outperforms the black-box best-first search in nearly all settings.

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function, endowed with an easily computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new set of analytic step-size selection and correction procedures based on the structure of the problem. We describe concrete algorithmic instances of our framework for several interesting applications and demonstrate them numerically on both synthetic and real data.