We investigate a topic at the interface of machine learning and cognitive science. Human active learning, where learners can actively query the world for information, is contrasted with passive learning from random examples. Furthermore, we compare human active learning performance with predictions from statistical learning theory. We conduct a series of human category learning experiments inspired by a machine learning task for which active and passive learning error bounds are well understood, and dramatically distinct. Our results indicate that humans are capable of actively selecting informative queries, and in doing so learn better and faster than if they are given random training data, as predicted by learning theory. However, the improvement over passive learning is not as dramatic as that achieved by machine active learning algorithms. To the best of our knowledge, this is the first quantitative study comparing human category learning in active versus passive settings.

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.

We develop the syntactic topic model (STM), a nonparametric Bayesian model of parsed documents. The STM generates words that are both thematically and syntactically constrained, which combines the semantic insights of topic models with the syntactic information available from parse trees. Each word of a sentence is generated by a distribution that combines document-specific topic weights and parse-tree-specific syntactic transitions. Words are assumed to be generated in an order that respects the parse tree. We derive an approximate posterior inference method based on variational methods for hierarchical Dirichlet processes, and we report qualitative and quantitative results on both synthetic data and hand-parsed documents.

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 novel method for inducing synchronous context free grammars (SCFGs) from a corpus of parallel string pairs. SCFGs can model equivalence between strings in terms of substitutions, insertions and deletions, and the reordering of sub-strings. We develop a non-parametric Bayesian model and apply it to a machine translation task, using priors to replace the various heuristics commonly used in this field. Using a variational Bayes training procedure, we learn the latent structure of translation equivalence through the induction of synchronous grammar categories for phrasal translations, showing improvements in translation performance over previously proposed maximum likelihood models.

We address the problem of learning classifiers for several related tasks that may differ in their joint distribution of input and output variables. For each task, small - possibly even empty - labeled samples and large unlabeled samples are available. While the unlabeled samples reflect the target distribution, the labeled samples may be biased. We derive a solution that produces resampling weights which match the pool of all examples to the target distribution of any given task. Our work is motivated by the problem of predicting sociodemographic features for users of web portals, based on the content which they have accessed. Here, questionnaires offered to a small portion of each portal's users produce biased samples. Transfer learning enables us to make predictions even for new portals with few or no training data and improves the overall prediction accuracy.

We show how smoother priors can preserve the benefits of these sparse priors while adding stability to the Maximum A-Posteriori (MAP) estimate that makes it more useful for prediction problems. Additionally, we show how to calculate the derivative of the MAP estimate efficiently withimplicit differentiation. One prior that can be differentiated this way is KL-regularization. We demonstrate its effectiveness on a wide variety of applications, andfind that online optimization of the parameters of the KL-regularized model can significantly improve prediction performance.

Almost all successful machine learning algorithms and cognitive models require powerful representations capturing the features that are relevant to a particular problem. We draw on recent work in nonparametric Bayesian statistics to define a rational model of human feature learning that forms a featural representation from raw sensory data without pre-specifying the number of features. By comparing how the human perceptual system and our rational model use distributional and category information to infer feature representations, we seek to identify some of the forces that govern the process by which people separate and combine sensory primitives to form features.

We present a generative model for performing sparse probabilistic projections, which includes sparse principal component analysis and sparse canonical correlation analysis as special cases. Sparsity is enforced by means of automatic relevance determination or by imposing appropriate prior distributions, such as generalised hyperbolic distributions. We derive a variational Expectation-Maximisation algorithm for the estimation of the hyperparameters and show that our novel probabilistic approach compares favourably to existing techniques. We illustrate how the proposed method can be applied in the context of cryptoanalysis as a pre-processing tool for the construction of template attacks.

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.