Dynamic functional connectivity (FC) has in recent years become a topic of interest in the neuroimaging community. Several models and methods exist for both functional magnetic resonance imaging (fMRI) and electroencephalography (EEG), and the results point towards the conclusion that FC exhibits dynamic changes. The existing approaches modeling dynamic connectivity have primarily been based on time-windowing the data and k-means clustering. We propose a non-parametric generative model for dynamic FC in fMRI that does not rely on specifying window lengths and number of dynamic states. Rooted in Bayesian statistical modeling we use the predictive likelihood to investigate if the model can discriminate between a motor task and rest both within and across subjects. We further investigate what drives dynamic states using the model on the entire data collated across subjects and task/rest. We find that the number of states extracted are driven by subject variability and preprocessing differences while the individual states are almost purely defined by either task or rest. This questions how we in general interpret dynamic FC and points to the need for more research on what drives dynamic FC.

The counting grid is a grid of microtopics, sparse word/feature distributions. The generative model associated with the grid does not use these microtopics individually, but in predefined groups which can only be (ad)mixed as such. Each allowed group corresponds to one of all possible overlapping rectangular windows into the grid. The capacity of the model is controlled by the ratio of the grid size and the window size. This paper builds upon the basic counting grid model and it shows that hierarchical reasoning helps avoid bad local minima, produces better classification accuracy and, most interestingly, allows for extraction of large numbers of coherent microtopics even from small datasets. We evaluate this in terms of consistency, diversity and clarity of the indexed content, as well as in a user study on word intrusion tasks. We demonstrate that these models work well as a technique for embedding raw images and discuss interesting parallels between hierarchical CG models and other deep architectures.

We consider online optimization in the 1-lookahead setting, where the objective does not decompose additively over the rounds of the online game. The resulting formulation enables us to deal with non-stationary and/or long-term constraints , which arise, for example, in online display advertising problems. We propose an on-line primal-dual algorithm for which we obtain dynamic cumulative regret guarantees. They depend on the convexity and the smoothness of the non-additive penalty, as well as terms capturing the smoothness with which the residuals of the non-stationary and long-term constraints vary over the rounds. We conduct experiments on synthetic data to illustrate the benefits of the non-additive penalty and show vanishing regret convergence on live traffic data collected by a display advertising platform in production.

A good clustering can help a data analyst to explore and understand a data set, but what constitutes a good clustering may depend on domain-specific and application-specific criteria. These criteria can be difficult to formalize, even when it is easy for an analyst to know a good clustering when she sees one. We present a new approach to interactive clustering for data exploration, called \ciif, based on a particularly simple feedback mechanism, in which an analyst can choose to reject individual clusters and request new ones. The new clusters should be different from previously rejected clusters while still fitting the data well. We formalize this interaction in a novel Bayesian prior elicitation framework. In each iteration, the prior is adapted to account for all the previous feedback, and a new clustering is then produced from the posterior distribution. To achieve the computational efficiency necessary for an interactive setting, we propose an incremental optimization method over data minibatches using Lagrangian relaxation. Experiments demonstrate that \ciif can produce accurate and diverse clusterings.

Robots are becoming more commonplace in human environments, such as schools, homes, hospitals, and work settings, and are expected to accomplish a wide variety of tasks. Given the near infinite number of tasks robots might be expected to perform in these varied settings, it is not feasible for robot designers to completely pre-program machines before they are deployed. Many researchers have suggested this problem can be addressed via end-user robot programming, where users can modify and create new behaviors for their robot to best suit their needs and preferences [2], [1]. Learning from demonstration (LfD) is one such method that enables people to readily develop custom robot behavior [2]. In LfD, a learner automatically creates a mapping between states and actions by watching a teacher perform the task; the learner can then replicate the teacher's actions. The main benefit of LfD is that it is an intuitive way for people to teach robots and does not require the teacher to have highly specialized knowledge, such as the ability to directly program the robot [3]. There has been significant research in how to design and implement LfD systems, including how people want to teach robots. Work by Thomaz et al. [23] showed that LfD systems could be improved for both the teacher and learner if greater communicative channels could be employed during the learning process. We build upon this work, and specifically are interested in ways to enable human teachers to have more efficient and naturalistic interactions, by way of a common human-human interaction (HHI) phenomena: grounding sequences.

In decentralized networks (of sensors, connected objects, etc.), there is an important need for efficient algorithms to optimize a global cost function, for instance to learn a global model from the local data collected by each computing unit. In this paper, we address the problem of decentralized minimization of pairwise functions of the data points, where these points are distributed over the nodes of a graph defining the communication topology of the network. This general problem finds applications in ranking, distance metric learning and graph inference, among others. We propose new gossip algorithms based on dual averaging which aims at solving such problems both in synchronous and asynchronous settings. The proposed framework is flexible enough to deal with constrained and regularized variants of the optimization problem. Our theoretical analysis reveals that the proposed algorithms preserve the convergence rate of centralized dual averaging up to an additive bias term. We present numerical simulations on Area Under the ROC Curve (AUC) maximization and metric learning problems which illustrate the practical interest of our approach.

Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient.

Bayesian inference has great promise for the privacy-preserving analysis of sensitive data, as posterior sampling automatically preserves differential privacy, an algorithmic notion of data privacy, under certain conditions (Dimitrakakis et al., 2014; Wang et al., 2015b). While this one posterior sample (OPS) approach elegantly provides privacy "for free," it is data inefficient in the sense of asymptotic relative efficiency (ARE). We show that a simple alternative based on the Laplace mechanism, the workhorse of differential privacy, is as asymptotically efficient as non-private posterior inference, under general assumptions. This technique also has practical advantages including efficient use of the privacy budget for MCMC. We demonstrate the practicality of our approach on a time-series analysis of sensitive military records from the Afghanistan and Iraq wars disclosed by the Wikileaks organization.

We introduce a new framework for unsupervised learning of representations based on a novel hierarchical decomposition of information. Intuitively, data is passed through a series of progressively fine-grained sieves. Each layer of the sieve recovers a single latent factor that is maximally informative about multivariate dependence in the data. The data is transformed after each pass so that the remaining unexplained information trickles down to the next layer. Ultimately, we are left with a set of latent factors explaining all the dependence in the original data and remainder information consisting of independent noise. We present a practical implementation of this framework for discrete variables and apply it to a variety of fundamental tasks in unsupervised learning including independent component analysis, lossy and lossless compression, and predicting missing values in data. The hope of finding a succinct principle that elucidates the brain's information processing abilities has often kindled interest in information-theoretic ideas (Barlow, 1989; Simoncelli & Olshausen, 2001). In machine learning, on the other hand, the past decade has witnessed a shift in focus toward expressive, hierarchical models, with successes driven by increasingly effective ways to leverage labeled data to learn rich models (Schmidhuber, 2015; Bengio et al., 2013). Information-theoretic ideas like the venerable InfoMax principle (Linsker, 1988; Bell & Sejnowski, 1995) can be and are applied in both contexts with empirical success but they do not allow us to quantify the information value of adding depth to our representations.

Consider a two-class clustering problem where we observe $X_i = \ell_i \mu + Z_i$, $Z_i \stackrel{iid}{\sim} N(0, I_p)$, $1 \leq i \leq n$. The feature vector $\mu\in R^p$ is unknown but is presumably sparse. The class labels $\ell_i\in\{-1, 1\}$ are also unknown and the main interest is to estimate them. We are interested in the statistical limits. In the two-dimensional phase space calibrating the rarity and strengths of useful features, we find the precise demarcation for the Region of Impossibility and Region of Possibility. In the former, useful features are too rare/weak for successful clustering. In the latter, useful features are strong enough to allow successful clustering. The results are extended to the case of colored noise using Le Cam's idea on comparison of experiments. We also extend the study on statistical limits for clustering to that for signal recovery and that for hypothesis testing. We compare the statistical limits for three problems and expose some interesting insight. We propose classical PCA and Important Features PCA (IF-PCA) for clustering. For a threshold $t > 0$, IF-PCA clusters by applying classical PCA to all columns of $X$ with an $L^2$-norm larger than $t$. We also propose two aggregation methods. For any parameter in the Region of Possibility, some of these methods yield successful clustering. We find an interesting phase transition for IF-PCA. Our results require delicate analysis, especially on post-selection Random Matrix Theory and on lower bound arguments.