Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often not smooth. Current state-of-the-art methods often address these difficulties by replacing the posterior density with a smooth approximation that is amenable to efficient exploration by using Langevin Markov chain Monte Carlo (MCMC) methods. An alternative approach is based on data augmentation and relaxation, where auxiliary variables are introduced in order to construct an approximate augmented posterior distribution that is amenable to efficient exploration by Gibbs sampling. This paper proposes a new accelerated proximal MCMC method called latent space SK-ROCK (ls SK-ROCK), which tightly combines the benefits of the two aforementioned strategies. Additionally, instead of viewing the augmented posterior distribution as an approximation of the original model, we propose to consider it as a generalisation of this model. Following on from this, we empirically show that there is a range of values for the relaxation parameter for which the accuracy of the model improves, and propose a stochastic optimisation algorithm to automatically identify the optimal amount of relaxation for a given problem. In this regime, ls SK-ROCK converges faster than competing approaches from the state of the art, and also achieves better accuracy since the underlying augmented Bayesian model has a higher Bayesian evidence. The proposed methodology is demonstrated with a range of numerical experiments related to image deblurring and inpainting, as well as with comparisons with alternative approaches from the state of the art. An open-source implementation of the proposed MCMC methods is available from https://github.com/luisvargasmieles/ls-MCMC.

Constructing decision trees online is a classical machine learning problem. Existing works often assume that features are readily available for each incoming data point. However, in many real world applications, both feature values and the labels are unknown a priori and can only be obtained at a cost. For example, in medical diagnosis, doctors have to choose which tests to perform (i.e., making costly feature queries) on a patient in order to make a diagnosis decision (i.e., predicting labels). We provide a fresh perspective to tackle this practical challenge. Our framework consists of an active planning oracle embedded in an online learning scheme for which we investigate several information acquisition functions. Specifically, we employ a surrogate information acquisition function based on adaptive submodularity to actively query feature values with a minimal cost, while using a posterior sampling scheme to maintain a low regret for online prediction. We demonstrate the efficiency and effectiveness of our framework via extensive experiments on various real-world datasets. Our framework also naturally adapts to the challenging setting of online learning with concept drift and is shown to be competitive with baseline models while being more flexible.

Implicit neural representations (INRs) have achieved impressive results for scene reconstruction and computer graphics, where their performance has primarily been assessed on reconstruction accuracy. As INRs make their way into other domains, where model predictions inform high-stakes decision-making, uncertainty quantification of INR inference is becoming critical. To that end, we study a Bayesian reformulation of INRs, UncertaINR, in the context of computed tomography, and evaluate several Bayesian deep learning implementations in terms of accuracy and calibration. We find that they achieve well-calibrated uncertainty, while retaining accuracy competitive with other classical, INR-based, and CNN-based reconstruction techniques. Contrary to common intuition in the Bayesian deep learning literature, we find that INRs obtain the best calibration with computationally efficient Monte Carlo dropout, outperforming Hamiltonian Monte Carlo and deep ensembles. Moreover, in contrast to the best-performing prior approaches, UncertaINR does not require a large training dataset, but only a handful of validation images.

We formulated the sense of the presence of a remote participant in hybrid communication using a Bayesian framework. We also applied the knowledge gained from the simulation with the Bayesian model to the avatar robot's intervention behavior and encouraged the local participants to speak by intervening in the remote participant's behavior using an avatar robot. We then modeled the influence of the avatar robot's behavior on the local participants' statements using an active inference framework that included the presence of a remote participant as a latent variable. Based on the simulation results, we designed the gaze behavior of an avatar robot. Finally, we examined the effectiveness of the designed gaze behavior of the avatar robot. The gaze behavior expressed more of the remote participant's attention and interest in local participants, but local participants expressed fewer opinions in the meeting tasks. The results suggest that gaze behavior increased the presence of the remote participant and discouraged the local participant from speaking in the context of the experimental task. We believe that presence has a sufficiently large influence on whether participants want to express an opinion. It is worth investigating the influence of presence and its control methods using Bayesian models.

Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems, modeling is much more challenging for stochastic systems in which one is interested in obtaining a predictive distribution over future trajectories. Existing methods are either computationally slow since they rely on Monte Carlo sampling or make simplifying assumptions such that the predictive distribution is unimodal. In this work, we present a deep state-space model which employs graph neural networks in order to model the underlying interacting dynamical system. The predictive distribution is multimodal and has the form of a Gaussian mixture model, where the moments of the Gaussian components can be computed via deterministic moment matching rules. Our moment matching scheme can be exploited for sample-free inference, leading to more efficient and stable training compared to Monte Carlo alternatives. Furthermore, we propose structured approximations to the covariance matrices of the Gaussian components in order to scale up to systems with many agents. We benchmark our novel framework on two challenging autonomous driving datasets. Both confirm the benefits of our method compared to state-of-the-art methods. We further demonstrate the usefulness of our individual contributions in a carefully designed ablation study and provide a detailed runtime analysis of our proposed covariance approximations. Finally, we empirically demonstrate the generalization ability of our method by evaluating its performance on unseen scenarios.

We study pseudo labelling and its generalisation for semi-supervised segmentation of medical images. Pseudo labelling has achieved great empirical successes in semi-supervised learning, by utilising raw inferences on unlabelled data as pseudo labels for self-training. In our paper, we build a connection between pseudo labelling and the Expectation Maximization algorithm which partially explains its empirical successes. We thereby realise that the original pseudo labelling is an empirical estimation of its underlying full formulation. Following this insight, we demonstrate the full generalisation of pseudo labels under Bayes' principle, called Bayesian Pseudo Labels. We then provide a variational approach to learn to approximate Bayesian Pseudo Labels, by learning a threshold to select good quality pseudo labels. In the rest of the paper, we demonstrate the applications of Pseudo Labelling and its generalisation Bayesian Psuedo Labelling in semi-supervised segmentation of medical images on: 1) 3D binary segmentation of lung vessels from CT volumes; 2) 2D multi class segmentation of brain tumours from MRI volumes; 3) 3D binary segmentation of brain tumours from MRI volumes. We also show that pseudo labels can enhance the robustness of the learnt representations.

Many works show that node-level predictions of Graph Neural Networks (GNNs) are unrobust to small, often termed adversarial, changes to the graph structure. However, because manual inspection of a graph is difficult, it is unclear if the studied perturbations always preserve a core assumption of adversarial examples: that of unchanged semantic content. To address this problem, we introduce a more principled notion of an adversarial graph, which is aware of semantic content change. Using Contextual Stochastic Block Models (CSBMs) and real-world graphs, our results uncover: $i)$ for a majority of nodes the prevalent perturbation models include a large fraction of perturbed graphs violating the unchanged semantics assumption; $ii)$ surprisingly, all assessed GNNs show over-robustness - that is robustness beyond the point of semantic change. We find this to be a complementary phenomenon to adversarial examples and show that including the label-structure of the training graph into the inference process of GNNs significantly reduces over-robustness, while having a positive effect on test accuracy and adversarial robustness. Theoretically, leveraging our new semantics-aware notion of robustness, we prove that there is no robustness-accuracy tradeoff for inductively classifying a newly added node.

Answering these questions will help guide decision-making on both the data and model selection when factoring fairness into account. With the proliferation of algorithmic decision-making, increased The contributions that this paper make are: (i) provide experimental scrutiny has been placed on these systems. This paper explores results over different metrics of fairness across different models the relationship between the quality of the training data and the and datasets; (ii) answer questions related to the impact of data overall fairness of the models trained with such data in the context quality on fairness (e.g., Does label accuracy increase fairness?); of supervised classification. We measure key fairness metrics across and (iii) provide a starting point and datasets for future research a range of algorithms over multiple image classification datasets into the impact of data quality on supervised classification fairness.

The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In parallel, large language models (LLMs) have been increasingly applied to semantic parsing applications, tasked with inferring logical representations from natural language. While existing LLM explorations have been largely restricted to literal language use, in this work, we evaluate the capacity of LLMs to infer the meanings of pragmatic utterances. Specifically, we explore the case of threshold estimation on the gradable adjective ``strong'', contextually conditioned on a strength prior, then extended to composition with qualification, negation, polarity inversion, and class comparison. We find that LLMs can derive context-grounded, human-like distributions over the interpretations of several complex pragmatic utterances, yet struggle composing with negation. These results inform the inferential capacity of statistical language models, and their use in pragmatic and semantic parsing applications. All corresponding code is made publicly available (https://github.com/benlipkin/probsem/tree/CogSci2023).

How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam's razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We also re-examine the connection between the marginal likelihood and PAC-Bayes bounds and use this connection to further elucidate the shortcomings of the marginal likelihood for model selection. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning.