This dissertation aims mainly at obtaining robust variants of Gaussian processes (GPs) that do not require using non-Gaussian likelihoods to compensate for outliers in the training data. Bayesian kernel methods, and in particular GPs, have been used to solve a variety of machine learning problems, equating or exceeding the performance of other successful techniques. That is the case of a recently proposed approach to GP-based novelty detection that uses standard GPs (i.e. GPs employing Gaussian likelihoods). However, standard GPs are sensitive to outliers in training data, and this limitation carries over to GP-based novelty detection. This limitation has been typically addressed by using robust non-Gaussian likelihoods. However, non-Gaussian likelihoods lead to analytically intractable inferences, which require using approximation techniques that are typically complex and computationally expensive. Inspired by the use of weights in quasi-robust statistics, this work introduces a particular type of weight functions, called here data weighers, in order to obtain robust GPs that do not require approximation techniques and retain the simplicity of standard GPs. This work proposes implicit weighted variants of batch GP, online GP, and sparse online GP (SOGP) that employ weighted Gaussian likelihoods. Mathematical expressions for calculating the posterior implicit weighted GPs are derived in this work. In our experiments, novelty detection based on our weighted batch GPs consistently and significantly outperformed standard batch GP-based novelty detection whenever data was contaminated with outliers. Additionally, our experiments show that novelty detection based on online GPs can perform similarly to batch GP-based novelty detection. Membership scores previously introduced by other authors are also compared in our experiments.

This thesis considers the problem of performing inference on undirected graphical models with continuous state spaces. These models represent conditional independence structures that can appear in the context of Bayesian Machine Learning. In the thesis, we focus on computational methods and applications. The aim of the thesis is to demonstrate that the factorisation structure corresponding to the conditional independence structure present in high-dimensional models can be exploited to decrease the computational complexity of inference algorithms. First, we consider the smoothing problem on Hidden Markov Models (HMMs) and discuss novel algorithms that have sub-quadratic computational complexity in the number of particles used. We show they perform on par with existing state-of-the-art algorithms with a quadratic complexity. Further, a novel class of rejection free samplers for graphical models known as the Local Bouncy Particle Sampler (LBPS) is explored and applied on a very large instance of the Probabilistic Matrix Factorisation (PMF) problem. We show the method performs slightly better than Hamiltonian Monte Carlo methods (HMC). It is also the first such practical application of the method to a statistical model with hundreds of thousands of dimensions. In a second part of the thesis, we consider approximate Bayesian inference methods and in particular the Expectation Propagation (EP) algorithm. We show it can be applied as the backbone of a novel distributed Bayesian inference mechanism. Further, we discuss novel variants of the EP algorithms and show that a specific type of update mechanism, analogous to the mirror descent algorithm outperforms all existing variants and is robust to Monte Carlo noise. Lastly, we show that EP can be used to help the Particle Belief Propagation (PBP) algorithm in order to form cheap and adaptive proposals and significantly outperform classical PBP.

<p dir="ltr">Personalized thermal controls are beneficial for occupant comfort and productivity in office buildings. Recent research efforts on learning personal thermal comfort support the integration of personalized preferences in optimal building control and further implementation in real buildings. This Thesis presents the development and field implementation of personal preference-based thermal control in real offices, emphasizing the role of model predictive control (MPC) and low-cost local sensing. Probabilistic thermal preference profiles, a low-cost thermal sensing network and a MPC framework were integrated into a centralized building management and control system. The customized, preference-based HVAC control implemented in the offices indicated the comfort benefits of monitoring local thermal conditions (vs wall thermostats) for different preference profiles and showed 28-35% energy savings with personalized MPC (vs personalized static setpoint control).</p><p dir="ltr">Regarding the practical limitations in collecting sufficient data from occupants to train their thermal comfort model, we present a Bayesian meta-learning approach for developing reliable, data-driven personalized thermal comfort models using limited data from individuals. A high-dimensional neural network was developed, considering general thermal comfort impact factors (environmental variables, clothing level and metabolic rate) as well as personal thermal characteristics (expressed as a vector of continuous latent variables) as model inputs. The model parameters in the neural network were trained with subsets of ASHRAE RP-884 database. The trained neural network is transferrable, so that the thermal preferences of new individuals can be predicted by inferring their personal thermal characteristics using limited data. The results show that the developed Bayesian meta-learning approach to infer personal thermal comfort performs better than existing methods, especially when using limited data.</p><p dir="ltr">Moreover, this Thesis also discusses the potential of balancing thermal comfort and energy cost by setting dynamic temperature constraints in personalized MPC. A co-simulation framework of EnergyPlus and MPC is constructed using EnergyPlus Python API. Dynamic temperature constraints are selected based on personal thermal profile, weather conditions and utility rate variations. The performance of the personalized MPC with dynamic constraints demonstrates a balance between thermal comfort and energy cost in cooling season.</p>