Identification and comparison of nonlinear dynamical systems using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our method involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible without solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and delay differential equations, and provide a comprehensive comparison with current state of the art methods.

There has been a clear distinction between induction or training time and diagnosis time active information acquisition. While active learning during induction focuses on acquiring data that promises to provide the best classification model, the goal at diagnosis time focuses completely on next features to observe about the test case at hand in order to make better predictions about the case. We introduce a model and inferential methods that breaks this distinction. The methods can be used to extend case libraries under a budget but, more fundamentally, provide a framework for guiding agents to collect data under scarce resources, focused by diagnostic challenges. This extension to active learning leads to a new class of policies for real-time diagnosis, where recommended information-gathering sequences include actions that simultaneously seek new data for the case at hand and for cases in the training set.

Research in animal learning and behavioral neuroscience has distinguished between two forms of action control: a habit-based form, which relies on stored action values, and a goal-directed form, which forecasts and compares action outcomes based on a model of the environment. While habit-based control has been the subject of extensive computational research, the computational principles underlying goal-directed control in animals have so far received less attention. In the present paper, we advance a computational framework for goal-directed control in animals and humans. We take three empirically motivated points as founding premises: (1) Neurons in dorsolateral prefrontal cortex represent action policies, (2) Neurons in orbitofrontal cortex represent rewards, and (3) Neural computation, across domains, can be appropriately understood as performing structured probabilistic inference. On a purely computational level, the resulting account relates closely to previous work using Bayesian inference to solve Markov decision problems, but extends this work by introducing a new algorithm, which provably converges on optimal plans. On a cognitive and neuroscientific level, the theory provides a unifying framework for several different forms of goal-directed action selection, placing emphasis on a novel form, within which orbitofrontal reward representations directly drive policy selection.

We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network.

We describe a novel class of distributions, called Mondrian processes, which can be interpreted as probability distributions over kd-tree data structures. Mondrian processesare multidimensional generalizations of Poisson processes and this connection allows us to construct multidimensional generalizations of the stickbreaking processdescribed by Sethuraman (1994), recovering the Dirichlet process in one dimension. After introducing the Aldous-Hoover representation for jointly and separately exchangeable arrays, we show how the process can be used as a nonparametric prior distribution in Bayesian models of relational data.

We introduce the first temporal-difference learning algorithm that is stable with linear function approximation and off-policy training, for any finite Markov decision process, target policy, and exciting behavior policy, and whose complexity scales linearly in the number of parameters. We consider an i.i.d.\ policy-evaluation setting in which the data need not come from on-policy experience. The gradient temporal-difference (GTD) algorithm estimates the expected update vector of the TD(0) algorithm and performs stochastic gradient descent on its L_2 norm. Our analysis proves that its expected update is in the direction of the gradient, assuring convergence under the usual stochastic approximation conditions to the same least-squares solution as found by the LSTD, but without its quadratic computational complexity. GTD is online and incremental, and does not involve multiplying by products of likelihood ratios as in importance-sampling methods.

Extensive labeled data for image annotation systems, which learn to assign class labels to image regions, is difficult to obtain. We explore a hybrid model framework for utilizing partially labeled data that integrates a generative topic model for image appearance with discriminative label prediction. We propose three alternative formulations for imposing a spatial smoothness prior on the image labels. Tests of the new models and some baseline approaches on two real image datasets demonstrate the effectiveness of incorporating the latent structure.

Selective attention is a most intensively studied psychological phenomenon, rife with theoretical suggestions and schisms. A critical idea is that of limited capacity, the allocation of which has produced half a century's worth of conflict about such phenomena as early and late selection. An influential resolution of this debate is based on the notion of perceptual load (Lavie, 2005, TICS, 9: 75), which suggests that low-load, easy tasks, because they underuse the total capacity of attention, mandatorily lead to the processing of stimuli that are irrelevant to the current attentional set; whereas high-load, difficult tasks grab all resources for themselves, leaving distractors high and dry. We argue that this theory presents a challenge to Bayesian theories of attention, and suggest an alternative, statistical, account of key supporting data.

Hierarchical probabilistic modeling of discrete data has emerged as a powerful tool for text analysis. Posterior inference in such models is intractable, and practitioners rely on approximate posterior inference methods such as variational inference or Gibbs sampling. There has been much research in designing better approximations, but there is yet little theoretical understanding of which of the available techniques are appropriate, and in which data analysis settings. In this paper we provide the beginnings of such understanding. We analyze the improvement that the recently proposed collapsed variational inference (CVB) provides over mean field variational inference (VB) in latent Dirichlet allocation. We prove that the difference in the tightness of the bound on the likelihood of a document decreases as $O(k-1) + \log m /m$, where $k$ is the number of topics in the model and $m$ is the number of words in a document. As a consequence, the advantage of CVB over VB is lost for long documents but increases with the number of topics. We demonstrate empirically that the theory holds, using simulated text data and two text corpora. We provide practical guidelines for choosing an approximation.

Supervised topic models utilize document's side information for discovering predictive low dimensional representations of documents. Existing models apply the likelihood-based estimation. In this paper, we present a general framework of max-margin supervised topic models for both continuous and categorical response variables. Our approach, the maximum entropy discrimination latent Dirichlet allocation (MedLDA), utilizes the max-margin principle to train supervised topic models and estimate predictive topic representations that are arguably more suitable for prediction tasks. The general principle of MedLDA can be applied to perform joint max-margin learning and maximum likelihood estimation for arbitrary topic models, directed or undirected, and supervised or unsupervised, when the supervised side information is available. We develop efficient variational methods for posterior inference and parameter estimation, and demonstrate qualitatively and quantitatively the advantages of MedLDA over likelihood-based topic models on movie review and 20 Newsgroups data sets.