Graph neural networks (GNNs) have shown superiority in many prediction tasks over graphs due to their impressive capability of capturing nonlinear relations in graph-structured data. However, for node classification tasks, often, only marginal improvement of GNNs over their linear counterparts has been observed. Previous works provide very few understandings of this phenomenon. In this work, we resort to Bayesian learning to deeply investigate the functions of non-linearity in GNNs for node classification tasks. Given a graph generated from the statistical model CSBM, we observe that the max-a-posterior estimation of a node label given its own and neighbors' attributes consists of two types of non-linearity, a possibly non-linear transformation of node attributes and a ReLU-activated feature aggregation from neighbors. The latter surprisingly matches the type of non-linearity used in many GNN models. By further imposing Gaussian assumption on node attributes, we prove that the superiority of those ReLU activations is only significant when the node attributes are far more informative than the graph structure, which nicely matches many previous empirical observations. A similar argument can be achieved when there is a distribution shift of node attributes between the training and testing datasets. Finally, we verify our theory on both synthetic and real-world networks.

We propose a model-based lifelong reinforcement-learning approach that estimates a hierarchical Bayesian posterior distilling the common structure shared across different tasks. The learned posterior combined with a sample-based Bayesian exploration procedure increases the sample efficiency of learning across a family of related tasks. We first derive an analysis of the relationship between the sample complexity and the initialization quality of the posterior in the finite MDP setting. We next scale the approach to continuous-state domains by introducing a Variational Bayesian Lifelong Reinforcement Learning algorithm that can be combined with recent model-based deep RL methods, and that exhibits backward transfer. Experimental results on several challenging domains show that our algorithms achieve both better forward and backward transfer performance than state-of-the-art lifelong RL methods.

We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification tasks. Our central results leverage the Dirichlet posteriors studied recently by Zantedeschi et al. [2021] for training voting classifiers; in contrast to that work our bounds apply to non-randomised votes via the use of margins. Our contributions add perspective to the debate on the "margins theory" proposed by Schapire et al. [1998] for the generalisation of ensemble classifiers.

When robots enter everyday human environments, they need to understand their tasks and how they should perform those tasks. To encode these, reward functions, which specify the objective of a robot, are employed. However, designing reward functions can be extremely challenging for complex tasks and environments. A promising approach is to learn reward functions from humans. Recently, several robot learning works embrace this approach and leverage human demonstrations to learn the reward functions. Known as inverse reinforcement learning, this approach relies on a fundamental assumption: humans can provide near-optimal demonstrations to the robot. Unfortunately, this is rarely the case: human demonstrations to the robot are often suboptimal due to various reasons, e.g., difficulty of teleoperation, robot having high degrees of freedom, or humans' cognitive limitations. This thesis is an attempt towards learning reward functions from human users by using other, more reliable data modalities. Specifically, we study how reward functions can be learned using comparative feedback, in which the human user compares multiple robot trajectories instead of (or in addition to) providing demonstrations. To this end, we first propose various forms of comparative feedback, e.g., pairwise comparisons, best-of-many choices, rankings, scaled comparisons; and describe how a robot can use these various forms of human feedback to infer a reward function, which may be parametric or non-parametric. Next, we propose active learning techniques to enable the robot to ask for comparison feedback that optimizes for the expected information that will be gained from that user feedback. Finally, we demonstrate the applicability of our methods in a wide variety of domains, ranging from autonomous driving simulations to home robotics, from standard reinforcement learning benchmarks to lower-body exoskeletons.

The problem of sequentially transferring from a source object track and a model to another Bayesian filter has become ubiquitous. Due to the lack of a structural model that can capture the dependence among different models, the transfer may not be fully specified. In this paper, we introduce a novel Bayesian model that accounts for the model-jump from which the object can choose a model and follow. We aim to track the trajectory of the object while sequentially transferring from the source object to the target object. The main idea is to impute the dynamical model while tracking the object and estimating the state parameters of the moving object according to discretized dynamic systems. We demonstrate this procedure can handle the model mismatch as it sequentially corrects the predictive model. Particularly, for a fixed number of motion models, the object can learn what motion to follow at each time step. We employ a prior model for each model and then adaptively correct for changing one model to another to robustly estimate object trajectory under various motions. More concretely, we propose a robust Bayesian recipe to handle the model-jump and then integrate it with a Markov chain Monte Carlo (MCMC) approach to sample from the posterior distribution. We demonstrate through experiments the advantage of accounting for model-jump in our proposed method for knowledge transfer between learning tasks in Bayesian transfer learning.

We focus on using the predictive uncertainty signal calculated by Bayesian neural networks to guide learning in the self-same task the model is being trained on. Not opting for costly Monte Carlo sampling of weights, we propagate the approximate hidden variance in an end-to-end manner, throughout a variational Bayesian adaptation of a ResNet with attention and squeeze-and-excitation blocks, in order to identify data samples that should contribute less into the loss value calculation. We, thus, propose uncertainty-aware, data-specific label smoothing, where the smoothing probability is dependent on this epistemic uncertainty. We show that, through the explicit usage of the epistemic uncertainty in the loss calculation, the variational model is led to improved predictive and calibration performance. This core machine learning methodology is exemplified at wildlife call detection, from audio recordings made via passive acoustic monitoring equipment in the animals' natural habitats, with the future goal of automating large scale annotation in a trustworthy manner.

Sharpness-aware minimization (SAM) aims to improve the generalisation of gradient-based learning by seeking out flat minima. In this work, we establish connections between SAM and Mean-Field Variational Inference (MFVI) of neural network parameters. We show that both these methods have interpretations as optimizing notions of flatness, and when using the reparametrisation trick, they both boil down to calculating the gradient at a perturbed version of the current mean parameter. This thinking motivates our study of algorithms that combine or interpolate between SAM and MFVI. We evaluate the proposed variational algorithms on several benchmark datasets, and compare their performance to variants of SAM. Taking a broader perspective, our work suggests that SAM-like updates can be used as a drop-in replacement for the reparametrisation trick.

Despite the impressive performance of Artificial Intelligence (AI) systems, their robustness remains elusive and constitutes a key issue that impedes large-scale adoption. Robustness has been studied in many domains of AI, yet with different interpretations across domains and contexts. In this work, we systematically survey the recent progress to provide a reconciled terminology of concepts around AI robustness. We introduce three taxonomies to organize and describe the literature both from a fundamental and applied point of view: 1) robustness by methods and approaches in different phases of the machine learning pipeline; 2) robustness for specific model architectures, tasks, and systems; and in addition, 3) robustness assessment methodologies and insights, particularly the trade-offs with other trustworthiness properties. Finally, we identify and discuss research gaps and opportunities and give an outlook on the field. We highlight the central role of humans in evaluating and enhancing AI robustness, considering the necessary knowledge humans can provide, and discuss the need for better understanding practices and developing supportive tools in the future.

We introduce a simple modification to the standard maximum likelihood estimation (MLE) framework. Rather than maximizing a single unconditional likelihood of the data under the model, we maximize a family of noise conditional likelihoods consisting of the data perturbed by a continuum of noise levels. We find that models trained this way are more robust to noise, obtain higher test likelihoods, and generate higher quality images. They can also be sampled from via a novel score-based sampling scheme which combats the classical covariate shift problem that occurs during sample generation in autoregressive models. Applying this augmentation to autoregressive image models, we obtain 3.32 bits per dimension on the ImageNet 64x64 dataset, and substantially improve the quality of generated samples in terms of the Frechet Inception distance (FID) -- from 37.50 to 12.09 on the CIFAR-10 dataset. Likelihood maximization models, i.e., models trained by maximizing log-likelihood, are a leading class of modern generative models. Of these, autoregressive models boast state-of-the-art performance in many domains, including images Child et al. (2019), text Vaswani et al. (2017), and audio Oord et al. (2016). However, while log-likelihood is broadly agreed upon as one of the most rigorous metrics for goodness-of-fit in statistical and generative modeling, models with high likelihoods do not necessarily produce samples of high visual quality.

Applications of Structural Health Monitoring (SHM) combined with Machine Learning (ML) techniques enhance real-time performance tracking and increase structural integrity awareness of civil, aerospace and automotive infrastructures. This SHM-ML synergy has gained popularity in the last years thanks to the anticipation of maintenance provided by arising ML algorithms and their ability of handling large quantities of data and considering their influence in the problem. In this paper we develop a novel ML nearest-neighbors-alike algorithm based on the principle of maximum entropy to predict fatigue damage (Palmgren-Miner index) in composite materials by processing the signals of Lamb Waves -- a non-destructive SHM technique -- with other meaningful features such as layup parameters and stiffness matrices calculated from the Classical Laminate Theory (CLT). The full data analysis cycle is applied to a dataset of delamination experiments in composites. The predictions achieve a good level of accuracy, similar to other ML algorithms, e.g. Neural Networks or Gradient-Boosted Trees, and computation times are of the same order of magnitude. The key advantages of our proposal are: (1) The automatic determination of all the parameters involved in the prediction, so no hyperparameters have to be set beforehand, which saves time devoted to hypertuning the model and also represents an advantage for autonomous, self-supervised SHM. (2) No training is required, which, in an \textit{online learning} context where streams of data are fed continuously to the model, avoids repeated training -- essential for reliable real-time, continuous monitoring.