If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods with rich theory but poor computational complexity and by the relative ease of mapping matrices onto distributed architectures, we introduce a scalable divide-and-conquer framework for noisy matrix factorization. We present a thorough theoretical analysis of this framework in which we characterize the statistical errors introduced by the "divide" step and control their magnitude in the "conquer" step, so that the overall algorithm enjoys high-probability estimation guarantees comparable to those of its base algorithm. We also present experiments in collaborative filtering and video background modeling that demonstrate the near-linear to superlinear speed-ups attainable with this approach.

Perhaps surprisingly, it is possible to predict how long an algorithm will take to run on a previously unseen input, using machine learning techniques to build a model of the algorithm's runtime as a function of problem-specific instance features. Such models have important applications to algorithm analysis, portfolio-based algorithm selection, and the automatic configuration of parameterized algorithms. Over the past decade, a wide variety of techniques have been studied for building such models. Here, we describe extensions and improvements of existing models, new families of models, and -- perhaps most importantly -- a much more thorough treatment of algorithm parameters as model inputs. We also comprehensively describe new and existing features for predicting algorithm runtime for propositional satisfiability (SAT), travelling salesperson (TSP) and mixed integer programming (MIP) problems. We evaluate these innovations through the largest empirical analysis of its kind, comparing to a wide range of runtime modelling techniques from the literature. Our experiments consider 11 algorithms and 35 instance distributions; they also span a very wide range of SAT, MIP, and TSP instances, with the least structured having been generated uniformly at random and the most structured having emerged from real industrial applications. Overall, we demonstrate that our new models yield substantially better runtime predictions than previous approaches in terms of their generalization to new problem instances, to new algorithms from a parameterized space, and to both simultaneously.

The support vector machine (SVM) is a widely used method for classification. Although many efforts have been devoted to develop efficient solvers, it remains challenging to apply SVM to large-scale problems. A nice property of SVM is that the non-support vectors have no effect on the resulting classifier. Motivated by this observation, we present fast and efficient screening rules to discard non-support vectors by analyzing the dual problem of SVM via variational inequalities (DVI). As a result, the number of data instances to be entered into the optimization can be substantially reduced. Some appealing features of our screening method are: (1) DVI is safe in the sense that the vectors discarded by DVI are guaranteed to be non-support vectors; (2) the data set needs to be scanned only once to run the screening, whose computational cost is negligible compared to that of solving the SVM problem; (3) DVI is independent of the solvers and can be integrated with any existing efficient solvers. We also show that the DVI technique can be extended to detect non-support vectors in the least absolute deviations regression (LAD). To the best of our knowledge, there are currently no screening methods for LAD. We have evaluated DVI on both synthetic and real data sets. Experiments indicate that DVI significantly outperforms the existing state-of-the-art screening rules for SVM, and is very effective in discarding non-support vectors for LAD. The speedup gained by DVI rules can be up to two orders of magnitude.

We study the relationship between social media output and National Football League (NFL) games, using a dataset containing messages from Twitter and NFL game statistics. Specifically, we consider tweets pertaining to specific teams and games in the NFL season and use them alongside statistical game data to build predictive models for future game outcomes (which team will win?) and sports betting outcomes (whichteamwill winwiththepointspread?will thetotalpointsbe over/under the line?). We experiment with several feature sets and find that simple features using large volumes of tweets can match or exceed the performance of more traditional features that use game statistics.

The recent success stories of machine learning (ML) driven applications have created an increasing demand for scalable ML solutions. Nonetheless, ML researchers often prefer to code their solutions in statistical computing languages such as MATLAB or R, as these languages allow them to code in fewer lines using syntax that resembles high-level pseudocode. MATLAB and R allow researchers to avoid low-level implementation details, leading to quickly developed prototypes that are often sufficient for small scale exploration. However, these prototypes are typically ad-hoc, non-robust, and non-scalable implementations. In contrast, industrial implementations of these solutions often require a relatively heavy amount of development effort and are difficult to change once implemented.

Despite its size and complexity, the human cortex exhibits striking anatomical regularities, suggesting there may simple meta-algorithms underlying cortical learning and computation. We expect such meta-algorithms to be of interest since they need to operate quickly, scalably and effectively with little-to-no specialized assumptions. This note focuses on a specific question: How can neurons use vast quantities of unlabeled data to speed up learning from the comparatively rare labels provided by reward systems? As a partial answer, we propose randomized co-training as a biologically plausible meta-algorithm satisfying the above requirements. As evidence, we describe a biologically-inspired algorithm, Correlated Nystrom Views (XNV) that achieves state-of-the-art performance in semi-supervised learning, and sketch work in progress on a neuronal implementation.

We propose an active learning method for discovering low-dimensional structure in high-dimensional Gaussian process (GP) tasks. Such problems are increasingly frequent and important, but have hitherto presented severe practical difficulties. We further introduce a novel technique for approximately marginalizing GP hyperparameters, yielding marginal predictions robust to hyperparameter mis-specification. Our method offers an efficient means of performing GP regression, quadrature, or Bayesian optimization in high-dimensional spaces.

The functional and structural representation of the brain as a complex network is marked by the fact that the comparison of noisy and intrinsically correlated high-dimensional structures between experimental conditions or groups shuns typical mass univariate methods. Furthermore most network estimation methods cannot distinguish between real and spurious correlation arising from the convolution due to nodes' interaction, which thus introduces additional noise in the data. We propose a machine learning pipeline aimed at identifying multivariate differences between brain networks associated to different experimental conditions. The pipeline (1) leverages the deconvolved individual contribution of each edge and (2) maps the task into a sparse classification problem in order to construct the associated "sparse deconvolved predictive network", i.e., a graph with the same nodes of those compared but whose edge weights are defined by their relevance for out of sample predictions in classification. We present an application of the proposed method by decoding the covert attention direction (left or right) based on the single-trial functional connectivity matrix extracted from high-frequency magnetoencephalography (MEG) data. Our results demonstrate how network deconvolution matched with sparse classification methods outperforms typical approaches for MEG decoding.

Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we remove this restriction, and provide guaranteed community detection for a family of probabilistic network models with overlapping communities, termed as the mixed membership Dirichlet model, first introduced by Airoldi et al. This model allows for nodes to have fractional memberships in multiple communities and assumes that the community memberships are drawn from a Dirichlet distribution. Moreover, it contains the stochastic block model as a special case. We propose a unified approach to learning these models via a tensor spectral decomposition method. Our estimator is based on low-order moment tensor of the observed network, consisting of 3-star counts. Our learning method is fast and is based on simple linear algebraic operations, e.g. singular value decomposition and tensor power iterations. We provide guaranteed recovery of community memberships and model parameters and present a careful finite sample analysis of our learning method. As an important special case, our results match the best known scaling requirements for the (homogeneous) stochastic block model.

Current studies about motor imagery based rehabilitation training systems for stroke subjects lack an appropriate analytic method, which can achieve a considerable classification accuracy, at the same time detects gradual changes of imagery patterns during rehabilitation process and disinters potential mechanisms about motor function recovery. In this study, we propose an adaptive boosting algorithm based on the cortex plasticity and spectral band shifts. This approach models the usually predetermined spatial-spectral configurations in EEG study into variable preconditions, and introduces a new heuristic of stochastic gradient boost for training base learners under these preconditions. We compare our proposed algorithm with commonly used methods on datasets collected from 2 months' clinical experiments. The simulation results demonstrate the effectiveness of the method in detecting the variations of stroke patients' EEG patterns. By chronologically reorganizing the weight parameters of the learned additive model, we verify the spatial compensatory mechanism on impaired cortex and detect the changes of accentuation bands in spectral domain, which may contribute important prior knowledge for rehabilitation practice.