Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete data, statistical dependencies between features must be estimated in a computationally tractable way, while also dealing with missing data. There is a need for a computationally tractable approach that considers the statistical dependencies between features and can handle missing values. We here develop a multivariate version of FLDA (MUDRA) to tackle this issue and describe an efficient expectation/conditional-maximization (ECM) algorithm to infer its parameters. We assess its predictive power on the "Articulary Word Recognition" data set and show its improvement over the state-of-the-art, especially in the case of missing data. MUDRA allows interpretable classification of data sets with large proportions of missing data, which will be particularly useful for medical or psychological data sets.

Trustworthy ML systems should not only return accurate predictions, but also a reliable representation of their uncertainty. Bayesian methods are commonly used to quantify both aleatoric and epistemic uncertainty, but alternative approaches, such as evidential deep learning methods, have become popular in recent years. The latter group of methods in essence extends empirical risk minimization (ERM) for predicting second-order probability distributions over outcomes, from which measures of epistemic (and aleatoric) uncertainty can be extracted. This paper presents novel theoretical insights of evidential deep learning, highlighting the difficulties in optimizing second-order loss functions and interpreting the resulting epistemic uncertainty measures. With a systematic setup that covers a wide range of approaches for classification, regression and counts, it provides novel insights into issues of identifiability and convergence in second-order loss minimization, and the relative (rather than absolute) nature of epistemic uncertainty measures.

Bayesian neural networks (BNNs) have recently gained popularity due to their ability to quantify model uncertainty. However, specifying a prior for BNNs that captures relevant domain knowledge is often extremely challenging. In this work, we propose a framework for integrating general forms of domain knowledge (i.e., any knowledge that can be represented by a loss function) into a BNN prior through variational inference, while enabling computationally efficient posterior inference and sampling. Specifically, our approach results in a prior over neural network weights that assigns high probability mass to models that better align with our domain knowledge, leading to posterior samples that also exhibit this behavior. We show that BNNs using our proposed domain knowledge priors outperform those with standard priors (e.g., isotropic Gaussian, Gaussian process), successfully incorporating diverse types of prior information such as fairness, physics rules, and healthcare knowledge and achieving better predictive performance. We also present techniques for transferring the learned priors across different model architectures, demonstrating their broad utility across various settings.

Covariate adjustment is a ubiquitous method used to estimate the average treatment effect (ATE) from observational data. Assuming a known graphical structure of the data generating model, recent results give graphical criteria for optimal adjustment, which enables efficient estimation of the ATE. However, graphical approaches are challenging for high-dimensional and complex data, and it is not straightforward to specify a meaningful graphical model of non-Euclidean data such as texts. We propose an general framework that accommodates adjustment for any subset of information expressed by the covariates. We generalize prior works and leverage these results to identify the optimal covariate information for efficient adjustment. This information is minimally sufficient for prediction of the outcome conditionally on treatment. Based on our theoretical results, we propose the Debiased Outcome-adapted Propensity Estimator (DOPE) for efficient estimation of the ATE, and we provide asymptotic results for the DOPE under general conditions. Compared to the augmented inverse propensity weighted (AIPW) estimator, the DOPE can retain its efficiency even when the covariates are highly predictive of treatment. We illustrate this with a single-index model, and with an implementation of the DOPE based on neural networks, we demonstrate its performance on simulated and real data. Our results show that the DOPE provides an efficient and robust methodology for ATE estimation in various observational settings.

We study automated security response for an IT infrastructure and formulate the interaction between an attacker and a defender as a partially observed, non-stationary game. We relax the standard assumption that the game model is correctly specified and consider that each player has a probabilistic conjecture about the model, which may be misspecified in the sense that the true model has probability 0. This formulation allows us to capture uncertainty about the infrastructure and the intents of the players. To learn effective game strategies online, we design a novel method where a player iteratively adapts its conjecture using Bayesian learning and updates its strategy through rollout. We prove that the conjectures converge to best fits, and we provide a bound on the performance improvement that rollout enables with a conjectured model. To characterize the steady state of the game, we propose a variant of the Berk-Nash equilibrium. We present our method through an advanced persistent threat use case. Simulation studies based on testbed measurements show that our method produces effective security strategies that adapt to a changing environment. We also find that our method enables faster convergence than current reinforcement learning techniques.

This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It additionally implements a Monte Carlo algorithm specifically tailored for sampling from the resulting posterior distribution, based on an asymptotically exact data augmentation (AXDA). The proposed algorithm is an approximate instance of split Gibbs sampling (SGS) which embeds one Langevin Monte Carlo step. The proposed method is applied to common imaging tasks such as deblurring, inpainting and super-resolution, demonstrating its efficacy through extensive numerical experiments. These contributions advance Bayesian inference in imaging by leveraging data-driven regularization strategies within a probabilistic framework.

Fine-tuning large language models can improve task specific performance, although a general understanding of what the fine-tuned model has learned, forgotten and how to trust its predictions is still missing. We derive principled uncertainty quantification for fine-tuned LLMs with posterior approximations using computationally efficient low-rank adaptation ensembles. We analyze three common multiple-choice datasets using low-rank adaptation ensembles based on Mistral-7b, and draw quantitative and qualitative conclusions on their perceived complexity and model efficacy on the different target domains during and after fine-tuning. In particular, backed by the numerical experiments, we hypothesise about signals from entropic uncertainty measures for data domains that are inherently difficult for a given architecture to learn.

Bayesian active learning is based on information theoretical approaches that focus on maximising the information that new observations provide to the model parameters. This is commonly done by maximising the Bayesian Active Learning by Disagreement (BALD) acquisitions function. However, we highlight that it is challenging to estimate BALD when the new data points are subject to censorship, where only clipped values of the targets are observed. To address this, we derive the entropy and the mutual information for censored distributions and derive the BALD objective for active learning in censored regression ($\mathcal{C}$-BALD). We propose a novel modelling approach to estimate the $\mathcal{C}$-BALD objective and use it for active learning in the censored setting. Across a wide range of datasets and models, we demonstrate that $\mathcal{C}$-BALD outperforms other Bayesian active learning methods in censored regression.

A persistent challenge in conditional image synthesis has been to generate diverse output images from the same input image despite only one output image being observed per input image. GAN-based methods are prone to mode collapse, which leads to low diversity. To get around this, we leverage Implicit Maximum Likelihood Estimation (IMLE) which can overcome mode collapse fundamentally. IMLE uses the same generator as GANs but trains it with a different, non-adversarial objective which ensures each observed image has a generated sample nearby. Unfortunately, to generate high-fidelity images, prior IMLE-based methods require a large number of samples, which is expensive. In this paper, we propose a new method to get around this limitation, which we dub Conditional Hierarchical IMLE (CHIMLE), which can generate high-fidelity images without requiring many samples. We show CHIMLE significantly outperforms the prior best IMLE, GAN and diffusion-based methods in terms of image fidelity and mode coverage across four tasks, namely night-to-day, 16 single image super-resolution, image colourization and image decompression. Quantitatively, our method improves Fréchet Inception Distance (FID) by 36.9% on average compared to the prior best IMLE-based method, and by 27.5% on average compared to the best non-IMLE-based generalpurpose methods. More results and code are available on the project website at https://niopeng.github.io/CHIMLE/.

The objective of this research is to examine how sentiment analysis can be employed to generate trading signals for the Foreign Exchange (Forex) market. The author assessed sentiment in social media posts and news articles pertaining to the United States Dollar (USD) using a combination of methods: lexicon-based analysis and the Naive Bayes machine learning algorithm. The findings indicate that sentiment analysis proves valuable in forecasting market movements and devising trading signals. Notably, its effectiveness is consistent across different market conditions. The author concludes that by analyzing sentiment expressed in news and social media, traders can glean insights into prevailing market sentiments towards the USD and other pertinent countries, thereby aiding trading decision-making. This study underscores the importance of weaving sentiment analysis into trading strategies as a pivotal tool for predicting market dynamics.