Building machines capable of efficiently collaborating with humans has been a longstanding goal in artificial intelligence. Especially in the presence of uncertainties, optimal cooperation often requires that humans and artificial agents model each other's behavior and use these models to infer underlying goals, beliefs or intentions, potentially involving multiple levels of recursion. Empirical evidence for such higherorder Level 1 Level 2 Level 3 Level 2 cognition in human behavior is also provided by previous works in cognitive science, linguistics, and robotics. We advocate for a new paradigm for active learning for human feedback that utilises humans as active data sources while accounting for their higher levels of agency. In particular, we discuss how increasing level of agency results in qualitatively different forms of rational communication between an active learning system and a teacher. Additionally, we provide a practical example of active learning using a higher-order cognitive model. This is accompanied by a computational study Level 3 Level 4 Level 5 Level 4 that underscores the unique behaviors that this model produces.

This study introduces a novel methodology for modelling patient emotions from online patient experience narratives. We employed metadata network topic modelling to analyse patient-reported experiences from Care Opinion, revealing key emotional themes linked to patient-caregiver interactions and clinical outcomes. We develop a probabilistic, context-specific emotion recommender system capable of predicting both multilabel emotions and binary sentiments using a naive Bayes classifier using contextually meaningful topics as predictors. The superior performance of our predicted emotions under this model compared to baseline models was assessed using the information retrieval metrics nDCG and Q-measure, and our predicted sentiments achieved an F1 score of 0.921, significantly outperforming standard sentiment lexicons. This method offers a transparent, cost-effective way to understand patient feedback, enhancing traditional collection methods and informing individualised patient care. Our findings are accessible via an R package and interactive dashboard, providing valuable tools for healthcare researchers and practitioners.

In this work, we propose an original method for aggregating multiple clustering coming from different sources of information. Each partition is encoded by a co-membership matrix between observations. Our approach uses a mixture of multilayer Stochastic Block Models (SBM) to group co-membership matrices with similar information into components and to partition observations into different clusters, taking into account their specificities within the components. The identifiability of the model parameters is established and a variational Bayesian EM algorithm is proposed for the estimation of these parameters. The Bayesian framework allows for selecting an optimal number of clusters and components. The proposed approach is compared using synthetic data with consensus clustering and tensor-based algorithms for community detection in large-scale complex networks. Finally, the method is utilized to analyze global food trading networks, leading to structures of interest.

We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling. In this paper, we propose a generative model combining diffusion maps and Langevin dynamics. Diffusion maps are used to approximate the drift term from the available training samples, which is then implemented in a discrete-time Langevin sampler to generate new samples. By setting the kernel bandwidth to match the time step size used in the unadjusted Langevin algorithm, our method effectively circumvents any stability issues typically associated with time-stepping stiff stochastic differential equations. More precisely, we introduce a novel split-step scheme, ensuring that the generated samples remain within the convex hull of the training samples. Our framework can be naturally extended to generate conditional samples. We demonstrate the performance of our proposed scheme through experiments on synthetic datasets with increasing dimensions and on a stochastic subgrid-scale parametrization conditional sampling problem.

Federated Learning (FL) involves training a model over a dataset distributed among clients, with the constraint that each client's dataset is localized and possibly heterogeneous. In FL, small and noisy datasets are common, highlighting the need for well-calibrated models that represent the uncertainty of predictions. The closest FL techniques to achieving such goals are the Bayesian FL methods which collect parameter samples from local posteriors, and aggregate them to approximate the global posterior. To improve scalability for larger models, one common Bayesian approach is to approximate the global predictive posterior by multiplying local predictive posteriors. In this work, we demonstrate that this method gives systematically overconfident predictions, and we remedy this by proposing $\beta$-Predictive Bayes, a Bayesian FL algorithm that interpolates between a mixture and product of the predictive posteriors, using a tunable parameter $\beta$. This parameter is tuned to improve the global ensemble's calibration, before it is distilled to a single model. Our method is evaluated on a variety of regression and classification datasets to demonstrate its superiority in calibration to other baselines, even as data heterogeneity increases. Code available at https://github.com/hasanmohsin/betaPredBayesFL

The goal of Causal Discovery is to find automated search methods for learning causal structures from observational data. In some cases all variables of the interested causal mechanism are measured, and the task is to predict the effects one measured variable has on another. In contrast, sometimes the variables of primary interest are not directly observable but instead inferred from their manifestations in the data. These are referred to as latent variables. One commonly known example is the psychological construct of intelligence, which cannot directly measured so researchers try to assess through various indicators such as IQ tests. In this case, casual discovery algorithms can uncover underlying patterns and structures to reveal the causal connections between the latent variables and between the latent and observed variables. This thesis focuses on two questions in causal discovery: providing an alternative definition of k-Triangle Faithfulness that (i) is weaker than strong faithfulness when applied to the Gaussian family of distributions, (ii) can be applied to non-Gaussian families of distributions, and (iii) under the assumption that the modified version of Strong Faithfulness holds, can be used to show the uniform consistency of a modified causal discovery algorithm; relaxing the sufficiency assumption to learn causal structures with latent variables. Given the importance of inferring cause-and-effect relationships for understanding and forecasting complex systems, the work in this thesis of relaxing various simplification assumptions is expected to extend the causal discovery method to be applicable in a wider range with diversified causal mechanism and statistical phenomena.

The Laplace approximation provides a closed-form model selection objective for neural networks (NN). Online variants, which optimise NN parameters jointly with hyperparameters, like weight decay strength, have seen renewed interest in the Bayesian deep learning community. However, these methods violate Laplace's method's critical assumption that the approximation is performed around a mode of the loss, calling into question their soundness. This work re-derives online Laplace methods, showing them to target a variational bound on a mode-corrected variant of the Laplace evidence which does not make stationarity assumptions. Online Laplace and its mode-corrected counterpart share stationary points where 1. the NN parameters are a maximum a posteriori, satisfying the Laplace method's assumption, and 2. the hyperparameters maximise the Laplace evidence, motivating online methods. We demonstrate that these optima are roughly attained in practise by online algorithms using full-batch gradient descent on UCI regression datasets. The optimised hyperparameters prevent overfitting and outperform validation-based early stopping.

In this manuscript, we present various proposed methods estimate the prevalence of disease, a critical prerequisite for the adequate interpretation of screening tests. To address the limitations of these approaches, which revolve primarily around their a posteriori nature, we introduce a novel method to estimate the pretest probability of disease, a priori, utilizing the Logit function from the logistic regression model. This approach is a modification of McGee's heuristic, originally designed for estimating the posttest probability of disease. In a patient presenting with $n_\theta$ signs or symptoms, the minimal bound of the pretest probability, $\phi$, can be approximated by: $\phi \approx \frac{1}{5}{ln\left[\displaystyle\prod_{\theta=1}^{i}\kappa_\theta\right]}$ where $ln$ is the natural logarithm, and $\kappa_\theta$ is the likelihood ratio associated with the sign or symptom in question.

In practical compressed sensing (CS), the obtained measurements typically necessitate quantization to a limited number of bits prior to transmission or storage. This nonlinear quantization process poses significant recovery challenges, particularly with extreme coarse quantization such as 1-bit. Recently, an efficient algorithm called QCS-SGM was proposed for quantized CS (QCS) which utilizes score-based generative models (SGM) as an implicit prior. Due to the adeptness of SGM in capturing the intricate structures of natural signals, QCS-SGM substantially outperforms previous QCS methods. However, QCS-SGM is constrained to (approximately) row-orthogonal sensing matrices as the computation of the likelihood score becomes intractable otherwise. To address this limitation, we introduce an advanced variant of QCS-SGM, termed QCS-SGM+, capable of handling general matrices effectively. The key idea is a Bayesian inference perspective on the likelihood score computation, wherein expectation propagation is employed for its approximate computation. Extensive experiments are conducted, demonstrating the substantial superiority of QCS-SGM+ over QCS-SGM for general sensing matrices beyond mere row-orthogonality.

Language models are often trained on text alone, without additional grounding. There is debate as to how much of natural language semantics can be inferred from such a procedure. We prove that entailment judgments between sentences can be extracted from an ideal language model that has perfectly learned its target distribution, assuming the training sentences are generated by Gricean agents, i.e., agents who follow fundamental principles of communication from the linguistic theory of pragmatics. We also show entailment judgments can be decoded from the predictions of a language model trained on such Gricean data. Our results reveal a pathway for understanding the semantic information encoded in unlabeled linguistic data and a potential framework for extracting semantics from language models.