Representing examples in a way that is compatible with the underlying classifier can greatly enhance the performance of a learning system. In this paper we investigate scalable techniques for inducing discriminative features by taking advantage of simple second order structure in the data. We focus on multiclass classification and show that features extracted from the generalized eigenvectors of the class conditional second moments lead to classifiers with excellent empirical performance. Moreover, these features have attractive theoretical properties, such as inducing representations that are invariant to linear transformations of the input. We evaluate classifiers built from these features on three different tasks, obtaining state of the art results.

Logistic Gaussian process (LGP) priors provide a flexible alternative for modelling unknown densities. The smoothness properties of the density estimates can be controlled through the prior covariance structure of the LGP, but the challenge is the analytically intractable inference. In this paper, we present approximate Bayesian inference for LGP density estimation in a grid using Laplace's method to integrate over the non-Gaussian posterior distribution of latent function values and to determine the covariance function parameters with type-II maximum a posteriori (MAP) estimation. We demonstrate that Laplace's method with MAP is sufficiently fast for practical interactive visualisation of 1D and 2D densities. Our experiments with simulated and real 1D data sets show that the estimation accuracy is close to a Markov chain Monte Carlo approximation and state-of-the-art hierarchical infinite Gaussian mixture models. We also construct a reduced-rank approximation to speed up the computations for dense 2D grids, and demonstrate density regression with the proposed Laplace approach.

Bayesian optimization (BO) aims to minimize a given blackbox function using a model that is updated whenever new evidence about the function becomes available. Here, we address the problem of BO under partially right-censored response data, where in some evaluations we only obtain a lower bound on the function value. The ability to handle such response data allows us to adaptively censor costly function evaluations in minimization problems where the cost of a function evaluation corresponds to the function value. One important application giving rise to such censored data is the runtime-minimizing variant of the algorithm configuration problem: finding settings of a given parametric algorithm that minimize the runtime required for solving problem instances from a given distribution. We demonstrate that terminating slow algorithm runs prematurely and handling the resulting right-censored observations can substantially improve the state of the art in model-based algorithm configuration.

The \emph{Mixed-Membership Stochastic Blockmodel (MMSB)} is a popular framework for modeling social network relationships. It can fully exploit each individual node's participation (or membership) in a social structure. Despite its powerful representations, this model makes an assumption that the distributions of relational membership indicators between two nodes are independent. Under many social network settings, however, it is possible that certain known subgroups of people may have high or low correlations in terms of their membership categories towards each other, and such prior information should be incorporated into the model. To this end, we introduce a \emph{Copula Mixed-Membership Stochastic Blockmodel (cMMSB)} where an individual Copula function is employed to jointly model the membership pairs of those nodes within the subgroup of interest. The model enables the use of various Copula functions to suit the scenario, while maintaining the membership's marginal distribution, as needed, for modeling membership indicators with other nodes outside of the subgroup of interest. We describe the proposed model and its inference algorithm in detail for both the finite and infinite cases. In the experiment section, we compare our algorithms with other popular models in terms of link prediction, using both synthetic and real world data.

Effectively modelling hidden structures in a network is very practical but theoretically challenging. Existing relational models only involve very limited information, namely the binary directional link data, embedded in a network to learn hidden networking structures. There is other rich and meaningful information (e.g., various attributes of entities and more granular information than binary elements such as "like" or "dislike") missed, which play a critical role in forming and understanding relations in a network. In this work, we propose an informative relational model (InfRM) framework to adequately involve rich information and its granularity in a network, including metadata information about each entity and various forms of link data. Firstly, an effective metadata information incorporation method is employed on the prior information from relational models MMSB and LFRM. This is to encourage the entities with similar metadata information to have similar hidden structures. Secondly, we propose various solutions to cater for alternative forms of link data. Substantial efforts have been made towards modelling appropriateness and efficiency, for example, using conjugate priors. We evaluate our framework and its inference algorithms in different datasets, which shows the generality and effectiveness of our models in capturing implicit structures in networks.

We consider a multilingual weakly supervised learning scenario where knowledge from annotated corpora in a resource-rich language is transferred via bitext to guide the learning in other languages. Past approaches project labels across bitext and use them as features or gold labels for training. We propose a new method that projects model expectations rather than labels, which facilities transfer of model uncertainty across language boundaries. We encode expectations as constraints and train a discriminative CRF model using Generalized Expectation Criteria (Mann and McCallum, 2010). Evaluated on standard Chinese-English and German-English NER datasets, our method demonstrates F1 scores of 64% and 60% when no labeled data is used. Attaining the same accuracy with supervised CRFs requires 12k and 1.5k labeled sentences. Furthermore, when combined with labeled examples, our method yields significant improvements over state-of-the-art supervised methods, achieving best reported numbers to date on Chinese OntoNotes and German CoNLL-03 datasets.

This paper considers the problem of networks reconstruction from heterogeneous data using a Gaussian Graphical Mixture Model (GGMM). It is well known that parameter estimation in this context is challenging due to large numbers of variables coupled with the degeneracy of the likelihood. We propose as a solution a penalized maximum likelihood technique by imposing an $l_{1}$ penalty on the precision matrix. Our approach shrinks the parameters thereby resulting in better identifiability and variable selection. We use the Expectation Maximization (EM) algorithm which involves the graphical LASSO to estimate the mixing coefficients and the precision matrices. We show that under certain regularity conditions the Penalized Maximum Likelihood (PML) estimates are consistent. We demonstrate the performance of the PML estimator through simulations and we show the utility of our method for high dimensional data analysis in a genomic application.

Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of random regression forests and prove that our algorithm is consistent. We also provide an empirical evaluation, comparing our algorithm and other theoretically tractable random forest models to the random forest algorithm used in practice. Our experiments provide insight into the relative importance of different simplifications that theoreticians have made to obtain tractable models for analysis.

In this paper we propose a flexible and efficient framework for handling multi-armed bandits, combining sequential Monte Carlo algorithms with hierarchical Bayesian modeling techniques. The framework naturally encompasses restless bandits, contextual bandits, and other bandit variants under a single inferential model. Despite the model's generality, we propose efficient Monte Carlo algorithms to make inference scalable, based on recent developments in sequential Monte Carlo methods. Through two simulation studies, the framework is shown to outperform other empirical methods, while also naturally scaling to more complex problems for which existing approaches can not cope. Additionally, we successfully apply our framework to online video-based advertising recommendation, and show its increased efficacy as compared to current state of the art bandit algorithms.

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.