Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification. We propose predictive variational inference (PVI): a general inference framework that seeks and samples from an optimal posterior density such that the resulting posterior predictive distribution is as close to the true data generating process as possible, while this this closeness is measured by multiple scoring rules. By optimizing the objective, the predictive variational inference is generally not the same as, or even attempting to approximate, the Bayesian posterior, even asymptotically. Rather, we interpret it as implicit hierarchical expansion. Further, the learned posterior uncertainty detects heterogeneity of parameters among the population, enabling automatic model diagnosis. This framework applies to both likelihood-exact and likelihood-free models. We demonstrate its application in real data examples.

Accurate uncertainty quantification for causal effects is essential for robust decision making in complex systems, but remains challenging in non-parametric settings. One promising framework represents conditional distributions in a reproducing kernel Hilbert space and places Gaussian process priors on them to infer posteriors on causal effects, but requires restrictive nuclear dominant kernels and approximations that lead to unreliable uncertainty estimates. In this work, we introduce a method, IMPspec, that addresses these limitations via a spectral representation of the Hilbert space. We show that posteriors in this model can be obtained explicitly, by extending a result in Hilbert space regression theory. We also learn the spectral representation to optimise posterior calibration. Our method achieves state-of-the-art performance in uncertainty quantification and causal Bayesian optimisation across simulations and a healthcare application.

Ultrasound (US) has the unique potential to offer access to medical imaging to anyone, everywhere. Devices have become ultra-portable and cost-effective, akin to the stethoscope. Nevertheless US image quality and diagnostic efficacy are still highly operator- and patient-dependent. In difficult-to-image patients, image quality is often insufficient for reliable diagnosis. In this paper, we put forth that US imaging systems can be recast as information-seeking agents that engage in reciprocal interactions with their anatomical environment. Such agents autonomously adapt their transmit-receive sequences to fully personalize imaging and actively maximize information gain in-situ. To that end, we will show that the sequence of pulse-echo experiments that a US system performs can be interpreted as a perception-action loop: the action is the data acquisition, probing tissue with acoustic waves and recording reflections at the detection array, and perception is the inference of the anatomical and or functional state, potentially including associated diagnostic quantities. We then equip systems with a mechanism to actively reduce uncertainty and maximize diagnostic value across a sequence of experiments, treating action and perception jointly using Bayesian inference given generative models of the environment and action-conditional pulse-echo observations. Since the representation capacity of the generative models dictates both the quality of inferred anatomical states and the effectiveness of inferred sequences of future imaging actions, we will be greatly leveraging the enormous advances in deep generative modelling that are currently disrupting many fields and society at large. Finally, we show some examples of cognitive, closed-loop, US systems that perform active beamsteering and adaptive scanline selection, based on deep generative models that track anatomical belief states.

In recent years, Full-Waveform Inversion (FWI) has been extensively used to derive high-resolution subsurface velocity models from seismic data. However, due to the nonlinearity and ill-posed nature of the problem, FWI requires a good starting model to avoid producing non-physical solutions. Moreover, conventional optimization methods fail to quantify the uncertainty associated with the recovered solution, which is critical for decision-making processes. Bayesian inference offers an alternative approach as it directly or indirectly evaluates the posterior probability density function. For example, Markov Chain Monte Carlo (MCMC) methods generate multiple sample chains to characterize the solution's uncertainty. Despite their ability to theoretically handle any form of distribution, MCMC methods require many sampling steps; this limits their usage in high-dimensional problems with computationally intensive forward modeling, as is the FWI case. Variational Inference (VI), on the other hand, provides an approximate solution to the posterior distribution in the form of a parametric or non-parametric proposal distribution. Among the various algorithms used in VI, Stein Variational Gradient Descent (SVGD) is recognized for its ability to iteratively refine a set of samples to approximate the target distribution. However, mode and variance-collapse issues affect SVGD in high-dimensional inverse problems. This study aims to improve the performance of SVGD within the context of FWI by utilizing, for the first time, an annealed variant of SVGD and combining it with a multi-scale strategy. Additionally, we demonstrate that Principal Component Analysis (PCA) can be used to evaluate the performance of the optimization process. Clustering techniques are also employed to provide more rigorous and meaningful statistical analysis of the particles in the presence of multi-modal distributions.

Natural Language Processing (NLP) is a vital computational method for addressing language processing, analysis, and generation. NLP tasks form the core of many daily applications, from automatic text correction to speech recognition. While significant research has focused on NLP tasks for the English language, less attention has been given to Modern Standard Arabic and Dialectal Arabic. Globalization has also contributed to the rise of Code-Switching (CS), where speakers mix languages within conversations and even within individual words (intra-word CS). This is especially common in Arab countries, where people often switch between dialects or between dialects and a foreign language they master. CS between Arabic and English is frequent in Egypt, especially on social media. Consequently, a significant amount of code-switched content can be found online. Such code-switched data needs to be investigated and analyzed for several NLP tasks to tackle the challenges of this multilingual phenomenon and Arabic language challenges. No work has been done before for several integral NLP tasks on Arabic-English CS data. In this work, we focus on the Named Entity Recognition (NER) task and other tasks that help propose a solution for the NER task on CS data, e.g., Language Identification. This work addresses this gap by proposing and applying state-of-the-art techniques for Modern Standard Arabic and Arabic-English NER. We have created the first annotated CS Arabic-English corpus for the NER task. Also, we apply two enhancement techniques to improve the NER tagger on CS data using CS contextual embeddings and data augmentation techniques. All methods showed improvements in the performance of the NER taggers on CS data. Finally, we propose several intra-word language identification approaches to determine the language type of a mixed text and identify whether it is a named entity or not.

The transferable belief model, as a semantic interpretation of Dempster-Shafer theory, enables agents to perform reasoning and decision making in imprecise and incomplete environments. The model offers distinct semantics for handling unreliable testimonies, allowing for a more reasonable and general process of belief transfer compared to the Bayesian approach. However, because both the belief masses and the structure of focal sets must be considered when updating belief functions-leading to extra computational complexity during reasoning-the transferable belief model has gradually lost favor among researchers in recent developments. In this paper, we implement the transferable belief model on quantum circuits and demonstrate that belief functions offer a more concise and effective alternative to Bayesian approaches within the quantum computing framework. Furthermore, leveraging the unique characteristics of quantum computing, we propose several novel belief transfer approaches. More broadly, this paper introduces a new perspective on basic information representation for quantum AI models, suggesting that belief functions are more suitable than Bayesian approach for handling uncertainty on quantum circuits.

A critical bottleneck for scientific progress is the costly nature of computer simulations for complex systems. Surrogate models provide an appealing solution: such models are trained on simulator evaluations, then used to emulate and quantify uncertainty on the expensive simulator at unexplored inputs. In many applications, one often has available data on related systems. For example, in designing a new jet turbine, there may be existing studies on turbines with similar configurations. A key question is how information from such "source" systems can be transferred for effective surrogate training on the "target" system of interest. We thus propose a new LOcal transfer Learning Gaussian Process (LOL-GP) model, which leverages a carefully-designed Gaussian process to transfer such information for surrogate modeling. The key novelty of the LOL-GP is a latent regularization model, which identifies regions where transfer should be performed and regions where it should be avoided. This "local transfer" property is desirable in scientific systems: at certain parameters, such systems may behave similarly and thus transfer is beneficial; at other parameters, they may behave differently and thus transfer is detrimental. By accounting for local transfer, the LOL-GP can rectify a critical limitation of "negative transfer" in existing transfer learning models, where the transfer of information worsens predictive performance. We derive a Gibbs sampling algorithm for efficient posterior predictive sampling on the LOL-GP, for both the multi-source and multi-fidelity transfer settings. We then show, via a suite of numerical experiments and an application for jet turbine design, the improved surrogate performance of the LOL-GP over existing methods.

We present a novel Bayesian tomography approach for Coherence Imaging Spectroscopy (CIS) that simultaneously reconstructs ion temperature and velocity distributions in plasmas. Utilizing nonlinear Gaussian Process Tomography (GPT) with the Laplace approximation, we model prior distributions of log-emissivity, temperature, and velocity as Gaussian processes. This framework rigorously incorporates nonlinear effects and temperature dependencies often neglected in conventional CIS tomography, enabling robust reconstruction even in the region of high temperature and velocity. By applying a log-Gaussian process, we also address issues like velocity divergence in low-emissivity regions. Validated with phantom simulations and experimental data from the RT-1 device, our method reveals detailed spatial structures of ion temperature and toroidal ion flow characteristic of magnetospheric plasma. This work significantly broadens the scope of CIS tomography, offering a robust tool for plasma diagnostics and facilitating integration with complementary measurement techniques.

Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that decision-making is, therefore, a double-Bayesian process. The paper shows how this duality implies intrinsic uncertainty in decisions and how it incorporates explainability. The proposed approach understands that Bayesian learning is tantamount to finding a base for a logarithmic function measuring uncertainty, with solutions being fixed points. Furthermore, following this approach, the golden ratio describes possible solutions satisfying Bayes' theorem. The double-Bayesian framework suggests using a learning rate and momentum weight with values similar to those used in the literature to train neural networks with stochastic gradient descent.

This paper introduces the Bayesian Confidence Estimator (BACON) for deep neural networks. Current practice of interpreting Softmax values in the output layer as probabilities of outcomes is prone to extreme predictions of class probability. In this work we extend Waagen's method of representing the terminal layers with a geometric model, where the probability associated with an output vector is estimated with Bayes' Rule using validation data to provide likelihood and normalization values. This estimator provides superior ECE and ACE calibration error compared to Softmax for ResNet-18 at 85% network accuracy, and EfficientNet-B0 at 95% network accuracy, on the CIFAR-10 dataset with an imbalanced test set, except for very high accuracy edge cases. In addition, when using the ACE metric, BACON demonstrated improved calibration error when estimating probabilities for the imbalanced test set when using actual class distribution fractions.