We introduce a new Bayesian admixture model intended for exploratory analysis ofcommunication networks--specifically, the discovery and visualization of topic-specific subnetworks in email data sets. Our model produces principled visualizations ofemail networks, i.e., visualizations that have precise mathematical interpretations in terms of our model and its relationship to the observed data. We validate our modeling assumptions by demonstrating that our model achieves better link prediction performance than three state-of-the-art network models and exhibits topic coherence comparable to that of latent Dirichlet allocation. We showcase our model's ability to discover and visualize topic-specific communication patternsusing a new email data set: the New Hanover County email network. We provide an extensive analysis of these communication patterns, leading us to recommend our model for any exploratory analysis of email networks or other similarly-structured communication data. Finally, we advocate for principled visualization asa primary objective in the development of new network models.

Clustering is a key component in data analysis toolbox. Despite its importance, scalable algorithms often eschew rich statistical models in favor of simpler descriptions such as $k$-means clustering. In this paper we present a sampler, capable of estimating mixtures of exponential families. At its heart lies a novel proposal distribution using random projections to achieve high throughput in generating proposals, which is crucial for clustering models with large numbers of clusters.

We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers' positions on specific political issues. Our model can be used to explore how a lawmaker's voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model's utility in interpreting an inherently multi-dimensional space.

In this paper, we consider the problem of clustering data points into lowdimensional subspacesin the presence of outliers. We pose the problem using a density estimation formulation with an associated generative model. Based on this probability model, we first develop an iterative expectation-maximization (EM) algorithm andthen derive its global solution. In addition, we develop two Bayesian methods based on variational Bayesian (VB) approximation, which are capable of automatic dimensionality selection. While the first method is based on an alternating optimizationscheme for all unknowns, the second method makes use of recent results in VB matrix factorization leading to fast and effective estimation. Both methods are extended to handle sparse outliers for robustness and can handle missingvalues. Experimental results suggest that proposed methods are very effective in subspace clustering and identifying outliers.

We propose a novel method for scalable parallelization of SMC algorithms, Entangled Monte Carlo simulation (EMC). EMC avoids the transmission of particles between nodes, and instead reconstructs them from the particle genealogy. In particular, we show that we can reduce the communication to the particle weights for each machine while efficiently maintaining implicit global coherence of the parallel simulation. We explain methods to efficiently maintain a genealogy of particles from which any particle can be reconstructed. We demonstrate using examples from Bayesian phylogenetic that the computational gain from parallelization using EMC significantly outweighs the cost of particle reconstruction. The timing experiments show that reconstruction of particles is indeed much more efficient as compared to transmission of particles.

Parametric policy search algorithms are one of the methods of choice for the optimisation of Markov Decision Processes, with Expectation Maximisation and natural gradient ascent being considered the current state of the art in the field. In this article we provide a unifying perspective of these two algorithms by showing that their step-directions in the parameter space are closely related to the search direction of an approximate Newton method. This analysis leads naturally to the consideration of this approximate Newton method as an alternative gradient-based method for Markov Decision Processes. We are able show that the algorithm has numerous desirable properties, absent in the naive application of Newton's method, that make it a viable alternative to either Expectation Maximisation or natural gradient ascent. Empirical results suggest that the algorithm has excellent convergence and robustness properties, performing strongly in comparison to both Expectation Maximisation and natural gradient ascent.

Bayesian inference provides a unifying framework for addressing problems in machine learning, artificial intelligence, and robotics, as well as the problems facing the human mind. Unfortunately, exact Bayesian inference is intractable in all but the simplest models. Therefore minds and machines have to approximate Bayesian inference. Approximate inference algorithms can achieve a wide range of time-accuracy tradeoffs, but what is the optimal tradeoff? We investigate time-accuracy tradeoffs using the Metropolis-Hastings algorithm as a metaphor for the mind's inference algorithm(s). We find that reasonably accurate decisions are possible long before the Markov chain has converged to the posterior distribution, i.e. during the period known as burn-in. Therefore the strategy that is optimal subject to the mind's bounded processing speed and opportunity costs may perform so few iterations that the resulting samples are biased towards the initial value. The resulting cognitive process model provides a rational basis for the anchoring-and-adjustment heuristic. The model's quantitative predictions are tested against published data on anchoring in numerical estimation tasks. Our theoretical and empirical results suggest that the anchoring bias is consistent with approximate Bayesian inference.

Derivative Free Optimization (DFO) is attractive when the objective function's derivatives are not available and evaluations are costly. Moreover, if the function evaluations are noisy, then approximating gradients by finite differences is difficult. This paper gives quantitative lower bounds on the performance of DFO with noisy function evaluations, exposing a fundamental and unavoidable gap between optimization performance based on noisy evaluations versus noisy gradients. This challenges the conventional wisdom that the method of finite differences is comparable to a stochastic gradient. However, there are situations in which DFO is unavoidable, and for such situations we propose a new DFO algorithm that is proved to be near optimal for the class of strongly convex objective functions. A distinctive feature of the algorithm is that it only uses Boolean-valued function comparisons, rather than evaluations. This makes the algorithm useful in an even wider range of applications, including optimization based on paired comparisons from human subjects, for example. Remarkably, we show that regardless of whether DFO is based on noisy function evaluations or Boolean-valued function comparisons, the convergence rate is the same.

We propose a new stochastic gradient method for optimizing the sum of
 a finite set of smooth functions, where the sum is strongly convex.
 While standard stochastic gradient methods
 converge at sublinear rates for this problem, the proposed method incorporates a memory of previous gradient values in order to achieve a linear convergence 
rate. In a machine learning context, numerical experiments indicate that the new algorithm can dramatically outperform standard
 algorithms, both in terms of optimizing the training error and reducing the test error quickly.

We study the problem of adaptive control of a high dimensional linear quadratic (LQ) system. Previous work established the asymptotic convergence to an optimal controller for various adaptive control schemes. More recently, an asymptotic regret bound of $\tilde{O}(\sqrt{T})$ was shown for $T \gg p$ where $p$ is the dimension of the state space. In this work we consider the case where the matrices describing the dynamic of the LQ system are sparse and their dimensions are large. We present an adaptive control scheme that for $p \gg 1$ and $T \gg \polylog(p)$ achieves a regret bound of $\tilde{O}(p \sqrt{T})$. In particular, our algorithm has an average cost of $(1+\eps)$ times the optimum cost after $T = \polylog(p) O(1/\eps^2)$. This is in comparison to previous work on the dense dynamics where the algorithm needs $\Omega(p)$ samples before it can estimate the unknown dynamic with any significant accuracy. We believe our result has prominent applications in the emerging area of computational advertising, in particular targeted online advertising and advertising in social networks.