We propose a new framework for single-channel source separation that lies between the fully supervised and unsupervised setting. Instead of supervision, we provide input features for each source signal and use convex methods to estimate the correlations between these features and the unobserved signal decomposition. We analyze the case of $\ell_2$ loss theoretically and show that recovery of the signal components depends only on cross-correlation between features for different signals, not on correlations between features for the same signal. Contextually supervised source separation is a natural fit for domains with large amounts of data but no explicit supervision; our motivating application is energy disaggregation of hourly smart meter data (the separation of whole-home power signals into different energy uses). Here we apply contextual supervision to disaggregate the energy usage of thousands homes over four years, a significantly larger scale than previously published efforts, and demonstrate on synthetic data that our method outperforms the unsupervised approach.

Real world systems typically feature a variety of different dependency types and topologies that complicate model selection for probabilistic graphical models. We introduce the ensemble-of-forests model, a generalization of the ensemble-of-trees model. Our model enables structure learning of Markov random fields (MRF) with multiple connected components and arbitrary potentials. We present two approximate inference techniques for this model and demonstrate their performance on synthetic data. Our results suggest that the ensemble-of-forests approach can accurately recover sparse, possibly disconnected MRF topologies, even in presence of non-Gaussian dependencies and/or low sample size. We applied the ensemble-of-forests model to learn the structure of perturbed signaling networks of immune cells and found that these frequently exhibit non-Gaussian dependencies with disconnected MRF topologies. In summary, we expect that the ensemble-of-forests model will enable MRF structure learning in other high dimensional real world settings that are governed by non-trivial dependencies.

Neurons in cortical circuits exhibit coordinated spiking activity, and can produce correlated synchronous spikes during behavior and cognition. We recently developed a method for estimating the dynamics of correlated ensemble activity by combining a model of simultaneous neuronal interactions (e.g., a spin-glass model) with a state-space method (Shimazaki et al. 2012 PLoS Comput Biol 8 e1002385). This method allows us to estimate stimulus-evoked dynamics of neuronal interactions which is reproducible in repeated trials under identical experimental conditions. However, the method may not be suitable for detecting stimulus responses if the neuronal dynamics exhibits significant variability across trials. In addition, the previous model does not include effects of past spiking activity of the neurons on the current state of ensemble activity. In this study, we develop a parametric method for simultaneously estimating the stimulus and spike-history effects on the ensemble activity from single-trial data even if the neurons exhibit dynamics that is largely unrelated to these effects. For this goal, we model ensemble neuronal activity as a latent process and include the stimulus and spike-history effects as exogenous inputs to the latent process. We develop an expectation-maximization algorithm that simultaneously achieves estimation of the latent process, stimulus responses, and spike-history effects. The proposed method is useful to analyze an interaction of internal cortical states and sensory evoked activity.

The modelling, analysis, and visualisation of dynamic geospatial phenomena has been identified as a key developmental challenge for next-generation Geographic Information Systems (GIS). In this context, the envisaged paradigmatic extensions to contemporary foundational GIS technology raises fundamental questions concerning the ontological, formal representational, and (analytical) computational methods that would underlie their spatial information theoretic underpinnings. We present the conceptual overview and architecture for the development of high-level semantic and qualitative analytical capabilities for dynamic geospatial domains. Building on formal methods in the areas of commonsense reasoning, qualitative reasoning, spatial and temporal representation and reasoning, reasoning about actions and change, and computational models of narrative, we identify concrete theoretical and practical challenges that accrue in the context of formal reasoning about `space, events, actions, and change'. With this as a basis, and within the backdrop of an illustrated scenario involving the spatio-temporal dynamics of urban narratives, we address specific problems and solutions techniques chiefly involving `qualitative abstraction', `data integration and spatial consistency', and `practical geospatial abduction'. From a broad topical viewpoint, we propose that next-generation dynamic GIS technology demands a transdisciplinary scientific perspective that brings together Geography, Artificial Intelligence, and Cognitive Science. Keywords: artificial intelligence; cognitive systems; human-computer interaction; geographic information systems; spatio-temporal dynamics; computational models of narrative; geospatial analysis; geospatial modelling; ontology; qualitative spatial modelling and reasoning; spatial assistance systems

Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the observed data. In this paper, we present a novel framework incorporating sparsity in different domains.We decompose the observed covariance matrix into a sparse Gaussian Markov model (with a sparse precision matrix) and a sparse independence model (with a sparse covariance matrix). Our framework incorporates sparse covariance and sparse precision estimation as special cases and thus introduces a richer class of high-dimensional models. We characterize sufficient conditions for identifiability of the two models, \viz Markov and independence models. We propose an efficient decomposition method based on a modification of the popular $\ell_1$-penalized maximum-likelihood estimator ($\ell_1$-MLE). We establish that our estimator is consistent in both the domains, i.e., it successfully recovers the supports of both Markov and independence models, when the number of samples $n$ scales as $n = \Omega(d^2 \log p)$, where $p$ is the number of variables and $d$ is the maximum node degree in the Markov model. Our experiments validate these results and also demonstrate that our models have better inference accuracy under simple algorithms such as loopy belief propagation.

Removing or filtering outliers and mislabeled instances prior to training a learning algorithm has been shown to increase classification accuracy. A popular approach for handling outliers and mislabeled instances is to remove any instance that is misclassified by a learning algorithm. However, an examination of which learning algorithms to use for filtering as well as their effects on multiple learning algorithms over a large set of data sets has not been done. Previous work has generally been limited due to the large computational requirements to run such an experiment, and, thus, the examination has generally been limited to learning algorithms that are computationally inexpensive and using a small number of data sets. In this paper, we examine 9 learning algorithms as filtering algorithms as well as examining the effects of filtering in the 9 chosen learning algorithms on a set of 54 data sets. In addition to using each learning algorithm individually as a filter, we also use the set of learning algorithms as an ensemble filter and use an adaptive algorithm that selects a subset of the learning algorithms for filtering for a specific task and learning algorithm. We find that for most cases, using an ensemble of learning algorithms for filtering produces the greatest increase in classification accuracy. We also compare filtering with a majority voting ensemble. The voting ensemble significantly outperforms filtering unless there are high amounts of noise present in the data set. Additionally, we find that a majority voting ensemble is robust to noise as filtering with a voting ensemble does not increase the classification accuracy of the voting ensemble.

Optimizing over the set of orthogonal matrices is a central component in problems like sparse-PCA or tensor decomposition. Unfortunately, such optimization is hard since simple operations on orthogonal matrices easily break orthogonality, and correcting orthogonality usually costs a large amount of computation. Here we propose a framework for optimizing orthogonal matrices, that is the parallel of coordinate-descent in Euclidean spaces. It is based on {\em Givens-rotations}, a fast-to-compute operation that affects a small number of entries in the learned matrix, and preserves orthogonality. We show two applications of this approach: an algorithm for tensor decomposition that is used in learning mixture models, and an algorithm for sparse-PCA. We study the parameter regime where a Givens rotation approach converges faster and achieves a superior model on a genome-wide brain-wide mRNA expression dataset.

Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on the tuning parameters that balance the trade-off between model fitting and model sparsity. Existing tuning criteria mainly follow the route of minimizing the estimated prediction error or maximizing the posterior model probability, such as cross-validation, AIC and BIC. This article introduces a general tuning parameter selection criterion based on a novel concept of variable selection stability. The key idea is to select the tuning parameters so that the resultant penalized regression model is stable in variable selection. The asymptotic selection consistency is established for both fixed and diverging dimensions. The effectiveness of the proposed criterion is also demonstrated in a variety of simulated examples as well as an application to the prostate cancer data.

For classifying time series, a nearest-neighbor approach is widely used in practice with performance often competitive with or better than more elaborate methods such as neural networks, decision trees, and support vector machines. We develop theoretical justification for the effectiveness of nearest-neighbor-like classification of time series. Our guiding hypothesis is that in many applications, such as forecasting which topics will become trends on Twitter, there aren't actually that many prototypical time series to begin with, relative to the number of time series we have access to, e.g., topics become trends on Twitter only in a few distinct manners whereas we can collect massive amounts of Twitter data. To operationalize this hypothesis, we propose a latent source model for time series, which naturally leads to a "weighted majority voting" classification rule that can be approximated by a nearest-neighbor classifier. We establish nonasymptotic performance guarantees of both weighted majority voting and nearest-neighbor classification under our model accounting for how much of the time series we observe and the model complexity. Experimental results on synthetic data show weighted majority voting achieving the same misclassification rate as nearest-neighbor classification while observing less of the time series. We then use weighted majority to forecast which news topics on Twitter become trends, where we are able to detect such "trending topics" in advance of Twitter 79% of the time, with a mean early advantage of 1 hour and 26 minutes, a true positive rate of 95%, and a false positive rate of 4%.

The detection of anomalous activity in graphs is a statistical problem that arises in many applications, such as network surveillance, disease outbreak detection, and activity monitoring in social networks. Beyond its wide applicability, graph structured anomaly detection serves as a case study in the difficulty of balancing computational complexity with statistical power. In this work, we develop from first principles the generalized likelihood ratio test for determining if there is a well connected region of activation over the vertices in the graph in Gaussian noise. Because this test is computationally infeasible, we provide a relaxation, called the Lovasz extended scan statistic (LESS) that uses submodularity to approximate the intractable generalized likelihood ratio. We demonstrate a connection between LESS and maximum a-posteriori inference in Markov random fields, which provides us with a poly-time algorithm for LESS. Using electrical network theory, we are able to control type 1 error for LESS and prove conditions under which LESS is risk consistent. Finally, we consider specific graph models, the torus, k-nearest neighbor graphs, and epsilon-random graphs. We show that on these graphs our results provide near-optimal performance by matching our results to known lower bounds.