Gaussian processes:iterative sparse approximations

In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.

Chromatic dispersion compensation using full-field maximum-likelihood sequence estimation

We investigate full-field detection-based maximum-likelihood sequence estimation (MLSE) for chromatic dispersion compensation in 10 Gbit/s OOK optical communication systems. Important design criteria are identified to optimize the system performance. It is confirmed that approximately 50% improvement in transmission reach can be achieved compared to conventional direct-detection MLSE at both 4 and 16 states. It is also shown that full-field MLSE is more robust to the noise and the associated noise amplifications in full-field reconstruction, and consequently exhibits better tolerance to nonoptimized system parameters than full-field feedforward equalizer. Experiments over 124 km spans of field-installed single-mode fiber without optical dispersion compensation using full-field MLSE verify the theoretically predicted performance benefits.

Perceptions of a changing world induce hope and promote peace in intractable conflicts

The importance of hope in promoting conciliatory attitudes has been asserted in the field of conflict resolution. However, little is known about conditions inducing hope, especially in intractable conflicts, where reference to the outgroup may backfire. In the current research, five studies yielded convergent support for the hypothesis that hope for peace stems from a general perception of the world as changing. In Study 1, coders observed associations between belief in a changing world, hope regarding peace, and support for concessions. Study 2 revealed the hypothesized relations using self-reported measures. Studies 3 and 4 established causality by instilling a perception of the world as changing (vs. unchanging) using narrative and drawing manipulations. Study 5 compared the changing world message with a control condition during conflict escalation. Across studies, although the specific context was not referred to, the belief in a changing world increased support for concessions through hope for peace.

Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.