Learning Inconsistent Preferences with Kernel Methods

We propose a probabilistic kernel approach for preferential learning from pairwise duelling data using Gaussian Processes. Different from previous methods, we do not impose a total order on the item space, hence can capture more expressive latent preferential structures such as inconsistent preferences and clusters of comparable items. Furthermore, we prove the universality of the proposed kernels, i.e. that the corresponding reproducing kernel Hilbert Space (RKHS) is dense in the space of skew-symmetric preference functions. To conclude the paper, we provide an extensive set of numerical experiments on simulated and real-world datasets showcasing the competitiveness of our proposed method with state-of-the-art

Towards trustworthy machine learning with kernels

Machine Learning has become an indispensable aspect of various safety-critical industries like healthcare, law, and automotive. Hence, it is crucial to ensure that our machine learning models function appropriately and instil trust among their users. This thesis focuses on improving the safety and transparency of Machine Learning by advocating for more principled uncertainty quantification and more effective explainability tools. Specifically, the use of Kernel Mean Embeddings (KME) and Gaussian Processes (GP) is prevalent in this work since they can represent probability distribution with minimal distributional assumptions and capture uncertainty well, respectively. I dedicate Chapter 2 to introduce these two methodologies. Chapter 3 demonstrates an effective use of these methods in conjunction with each other to tackle a statistical downscaling problem, in which a Deconditional Gaussian process is proposed. Chapter 4 considers a causal data fusion problem, where multiple causal graphs are combined for inference. I introduce BayesIMP, an algorithm built using KME and GPs, to draw causal conclusion while accounting for the uncertainty in the data and model. In Chapter 5, I present RKHS-SHAP to model explainability for kernel methods that utilizes Shapley values. Specifically, I propose to estimate the value function in the cooperative game using KMEs, circumventing the need for any parametric density estimations. A Shapley regulariser is also proposed to regulate the amount of contributions certain features can have to the model. Chapter 6 presents a generalised preferential Gaussian processes for modelling preference with non-rankable structure, which sets the scene for Chapter 7, where I built upon my research and propose Pref-SHAP to explain preference models

Scalable Bayesian Preference Learning for Crowds

We propose a scalable Bayesian preference learning method for jointly predicting the preferences of individuals as well as the consensus of a crowd from pairwise labels. Peoples' opinions often differ greatly, making it difficult to predict their preferences from small amounts of personal data. Individual biases also make it harder to infer the consensus of a crowd when there are few labels per item. We address these challenges by combining matrix factorisation with Gaussian processes, using a Bayesian approach to account for uncertainty arising from noisy and sparse data. Our method exploits input features, such as text embeddings and user metadata, to predict preferences for new items and users that are not in the training set. As previous solutions based on Gaussian processes do not scale to large numbers of users, items or pairwise labels, we propose a stochastic variational inference approach that limits computational and memory costs. Our experiments on a recommendation task show that our method is competitive with previous approaches despite our scalable inference approximation. We demonstrate the method's scalability on a natural language processing task with thousands of users and items, and show improvements over the state of the art on this task. We make our software publicly available for future work