Function Embeddings for Multi-modal Bayesian Inference

Tractable Bayesian inference is a fundamental challenge in robotics and machine learning. Standard approaches such as Gaussian process regression and Kalman filtering make strong Gaussianity assumptions about the underlying distributions. Such assumptions, however, can quickly break down when dealing with complex systems such as the dynamics of a robot or multi-variate spatial models. In this thesis we aim to solve Bayesian regression and filtering problems without making assumptions about the underlying distributions. We develop techniques to produce rich posterior representations for complex, multi-modal phenomena. Our work extends kernel Bayes' rule (KBR), which uses empirical estimates of distributions derived from a set of training samples and embeds them into a high-dimensional reproducing kernel Hilbert space (RKHS). Bayes' rule itself occurs on elements of this space. Our first contribution is the development of an efficient method for estimating posterior density functions from kernel Bayes' rule, applied to both filtering and regression. By embedding fixed-mean mixtures of component distributions, we can efficiently find an approximate pre-image by optimising the mixture weights using a convex quadratic program. The result is a complex, multi-modal posterior representation. Our next contributions are methods for estimating cumulative distributions and quantile estimates from the posterior embedding of kernel Bayes' rule. We examine a number of novel methods, including those based on our density estimation techniques, as well as directly estimating the cumulative through use of the reproducing property of RKHSs. Finally, we develop a novel method for scaling kernel Bayes' rule inference to large datasets, using a reduced-set construction optimised using the posterior likelihood. This method retains the ability to perform multi-output inference, as well as our earlier contributions to represent explicitly non-Gaussian posteriors and quantile estimates

Analysis of movement variability in cycling : An exploratory study

The purpose of this study was to determine the test-retest repeatability of Blue Trident inertial measurement units (IMUs) and VICON Nexus kinematic modelling in analysing the Lyapunov Exponent (LyE) during a maximal effort 4000 m cycling bout in different body segments/joints. An additional aim was to determine if changes in the LyE existed across a trial. Twelve novice cyclists completed four sessions of cycling; one was a familiarisation session to determine a bike fit and become better accustomed to the time trial position and pacing of a 4000 m effort. IMUs were attached to the head, thorax, pelvis and left and right shanks to analyse segment accelerations, respectively, and reflective markers were attached to the participant to analyse neck, thorax, pelvis, hip, knee and ankle segment/joint angular kinematics, respectively. Both the IMU and VICON Nexus test-retest repeatability ranged from poor to excellent at the different sites. In each session, the head and thorax IMU acceleration LyE increased across the bout, whilst pelvic and shank acceleration remained consistent. Differences across sessions were evident in VICON Nexus segment/joint angular kinematics, but no consistent trend existed. The improved reliability and the ability to identify a consistent trend in performance, combined with their improved portability and reduced cost, advocate for the use of IMUs in analysing movement variability in cycling. However, additional research is required to determine the applicability of analysing movement variability during cycling

Global cultural evolutionary model of humpback whale song

Funding: ECG is funded by a Royal Society University Research Fellowship (UF160081). RFL and LZ are funded by the BBSRC (BB/R008736/2). LL was supported by a Leverhulme Trust Grant to Luke Rendell (among other recipients; grant reference RPG-2013-367)Humpback whale song is an extraordinary example of vocal cultural behaviour. In northern popula-tions, the complex songs show long-lasting traditions that slowly evolve, while in the South Pacific, pe-riodic revolutions occur when songs are adopted from neighbouring populations and rapidly spread. In this species, vocal learning cannot be studied in the laboratory, learning is instead inferred from the songs’ complexity and patterns of transmission. Here, we used individual-based cultural evolutionary simulations of the entire Southern and Northern Hemisphere humpback whale populations to formalise this process of inference. We modelled processes of song mutation and patterns of contact among popu-lations and compared our model with patterns of song theme sharing measured in South Pacific popula-tions. Low levels of mutation in combination with rare population interactions were sufficient to closely fit the pattern of diversity in the South Pacific, including the distinctive pattern of West-to-East revolu-tions. Interestingly, the same learning parameters that gave rise to revolutions in the Southern Hemi-sphere simulations gave rise to evolutionary patterns of cultural evolution in the Northern Hemisphere populations. Our study demonstrates how cultural evolutionary approaches can be used to make infer-ences about the learning processes underlying cultural transmission and how they might generate emergent population-level processes.Publisher PDFPeer reviewe

Experimental Evaluation of delay/loss-based TCP congestion control algorithms.

We present initial experimental results for TCP Illinois and Compound TCP. These tests are for relatively simple scenarios yet they are sufficient to highlight several interesting issues. We observe that both TCP Illinois and Compound TCP can exhibit poor scaling behaviour as path BDP increases. As a result, link utilisation can be low and network responsiveness can become sluggish as BDP increases. We also document a number of important implementation issues observed during our tests

Helping decisions and kin recognition in long-tailed tits: is call similarity used to direct help towards kin?

Most cooperative breeders live in discrete family groups, but in a minority, breeding populations comprise extended social networks of conspecifics that vary in relatedness. Selection for effective kin recognition may be expected for more related individuals in such kin neighbourhoods to maximize indirect fitness. Using a long-term social pedigree, molecular genetics, field observations and acoustic analyses, we examine how vocal similarity affects helping decisions in the long-tailed tit Aegithalos caudatus. Long-tailed tits are cooperative breeders in which help is typically redirected by males that have failed in their own breeding attempts towards the offspring of male relatives living within kin neighbourhoods. We identify a positive correlation between call similarity and kinship, suggesting that vocal cues offer a plausible mechanism for kin discrimination. Furthermore, we show that failed breeders choose to help males with calls more similar to their own. However, although helpers fine-tune their provisioning rates according to how closely related they are to recipients, their effort was not correlated with their vocal similarity to helped breeders. We conclude that although vocalizations are an important part of the recognition system of long-tailed tits, discrimination is likely to be based on prior association and may involve a combination of vocal and non-vocal cues. This article is part of the theme issue 'Signal detection theory in recognition systems: from evolving models to experimental tests'