Accurate uncertainty quantification in graph neural networks (GNNs) is essential, especially in high-stakes domains where GNNs are frequently employed. Conformal prediction (CP) offers a promising framework for quantifying uncertainty by providing $\textit{valid}$ prediction sets for any black-box model. CP ensures formal probabilistic guarantees that a prediction set contains a true label with a desired probability. However, the size of prediction sets, known as $\textit{inefficiency}$, is influenced by the underlying model and data generating process. On the other hand, Bayesian learning also provides a credible region based on the estimated posterior distribution, but this region is $\textit{well-calibrated}$ only when the model is correctly specified. Building on a recent work that introduced a scaling parameter for constructing valid credible regions from posterior estimate, our study explores the advantages of incorporating a temperature parameter into Bayesian GNNs within CP framework. We empirically demonstrate the existence of temperatures that result in more efficient prediction sets. Furthermore, we conduct an analysis to identify the factors contributing to inefficiency and offer valuable insights into the relationship between CP performance and model calibration.

Learning from noisy labels is an important and long-standing problem in machine learning for real applications. One of the main research lines focuses on learning a label corrector to purify potential noisy labels. However, these methods typically rely on strict assumptions and are limited to certain types of label noise. In this paper, we reformulate the label-noise problem from a generative-model perspective, $\textit{i.e.}$, labels are generated by gradually refining an initial random guess. This new perspective immediately enables existing powerful diffusion models to seamlessly learn the stochastic generative process. Once the generative uncertainty is modeled, we can perform classification inference using maximum likelihood estimation of labels. To mitigate the impact of noisy labels, we propose the $\textbf{L}$abel-$\textbf{R}$etrieval-$\textbf{A}$ugmented (LRA) diffusion model, which leverages neighbor consistency to effectively construct pseudo-clean labels for diffusion training. Our model is flexible and general, allowing easy incorporation of different types of conditional information, $\textit{e.g.}$, use of pre-trained models, to further boost model performance. Extensive experiments are conducted for evaluation. Our model achieves new state-of-the-art (SOTA) results on all the standard real-world benchmark datasets. Remarkably, by incorporating conditional information from the powerful CLIP model, our method can boost the current SOTA accuracy by 10-20 absolute points in many cases.

Retrained large language models (LLMs) have become extensively used across various sub-disciplines of natural language processing (NLP). In NLP, text classification problems have garnered considerable focus, but still faced with some limitations related to expensive computational cost, time consumption, and robust performance to unseen classes. With the proposal of chain of thought prompting (CoT), LLMs can be implemented using zero-shot learning (ZSL) with the step by step reasoning prompts, instead of conventional question and answer formats. The zero-shot LLMs in the text classification problems can alleviate these limitations by directly utilizing pretrained models to predict both seen and unseen classes. Our research primarily validates the capability of GPT models in text classification. We focus on effectively utilizing prompt strategies to various text classification scenarios. Besides, we compare the performance of zero shot LLMs with other state of the art text classification methods, including traditional machine learning methods, deep learning methods, and ZSL methods. Experimental results demonstrate that the performance of LLMs underscores their effectiveness as zero-shot text classifiers in three of the four datasets analyzed. The proficiency is especially advantageous for small businesses or teams that may not have extensive knowledge in text classification.

We present a new algorithm to learn a deep neural network model robust against adversarial attacks. Previous algorithms demonstrate an adversarially trained Bayesian Neural Network (BNN) provides improved robustness. We recognize the adversarial learning approach for approximating the multi-modal posterior distribution of a Bayesian model can lead to mode collapse; consequently, the model's achievements in robustness and performance are sub-optimal. Instead, we first propose preventing mode collapse to better approximate the multi-modal posterior distribution. Second, based on the intuition that a robust model should ignore perturbations and only consider the informative content of the input, we conceptualize and formulate an information gain objective to measure and force the information learned from both benign and adversarial training instances to be similar. Importantly. we prove and demonstrate that minimizing the information gain objective allows the adversarial risk to approach the conventional empirical risk. We believe our efforts provide a step toward a basis for a principled method of adversarially training BNNs. Our model demonstrate significantly improved robustness--up to 20%--compared with adversarial training and Adv-BNN under PGD attacks with 0.035 distortion on both CIFAR-10 and STL-10 datasets.

Knowledge tracing (KT) plays a crucial role in computer-aided education and intelligent tutoring systems, aiming to assess students' knowledge proficiency by predicting their future performance on new questions based on their past response records. While existing deep learning knowledge tracing (DLKT) methods have significantly improved prediction accuracy and achieved state-of-the-art results, they often suffer from a lack of interpretability. To address this limitation, current approaches have explored incorporating psychological influences to achieve more explainable predictions, but they tend to overlook the potential influences of historical responses. In fact, understanding how models make predictions based on response influences can enhance the transparency and trustworthiness of the knowledge tracing process, presenting an opportunity for a new paradigm of interpretable KT. However, measuring unobservable response influences is challenging. In this paper, we resort to counterfactual reasoning that intervenes in each response to answer \textit{what if a student had answered a question incorrectly that he/she actually answered correctly, and vice versa}. Based on this, we propose RCKT, a novel response influence-based counterfactual knowledge tracing framework. RCKT generates response influences by comparing prediction outcomes from factual sequences and constructed counterfactual sequences after interventions. Additionally, we introduce maximization and inference techniques to leverage accumulated influences from different past responses, further improving the model's performance and credibility. Extensive experimental results demonstrate that our RCKT method outperforms state-of-the-art knowledge tracing methods on four datasets against six baselines, and provides credible interpretations of response influences.

We consider the problem of learning causal Directed Acyclic Graphs (DAGs) using combinations of observational and interventional experimental data. Current methods tailored to this setting assume that interventions either destroy parent-child relations of the intervened (target) nodes or only alter such relations without modifying the parent sets, even when the intervention targets are unknown. We relax this assumption by proposing a Bayesian method for causal discovery from general interventions, which allow for modifications of the parent sets of the unknown targets. Even in this framework, DAGs and general interventions may be identifiable only up to some equivalence classes. We provide graphical characterizations of such interventional Markov equivalence and devise compatible priors for Bayesian inference that guarantee score equivalence of indistinguishable structures. We then develop a Markov Chain Monte Carlo (MCMC) scheme to approximate the posterior distribution over DAGs, intervention targets and induced parent sets. Finally, we evaluate the proposed methodology on both simulated and real protein expression data.

Accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, the classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easily interpretable. In this paper, we introduce Bayesian CART models for insurance pricing, with a particular focus on claims frequency modelling. Additionally to the common Poisson and negative binomial (NB) distributions used for claims frequency, we implement Bayesian CART for the zero-inflated Poisson (ZIP) distribution to address the difficulty arising from the imbalanced insurance claims data. To this end, we introduce a general MCMC algorithm using data augmentation methods for posterior tree exploration. We also introduce the deviance information criterion (DIC) for the tree model selection. The proposed models are able to identify trees which can better classify the policy-holders into risk groups. Some simulations and real insurance data will be discussed to illustrate the applicability of these models.

The current paradigm of large-scale pre-training and fine-tuning Transformer large language models has lead to significant improvements across the board in natural language processing. However, such large models are susceptible to overfitting to their training data, and as a result the models perform poorly when the domain changes. Also, due to the model's scale, the cost of fine-tuning the model to the new domain is large. Nonparametric Variational Information Bottleneck (NVIB) has been proposed as a regulariser for training cross-attention in Transformers, potentially addressing the overfitting problem. We extend the NVIB framework to replace all types of attention functions in Transformers, and show that existing pretrained Transformers can be reinterpreted as Nonparametric Variational (NV) models using a proposed identity initialisation. We then show that changing the initialisation introduces a novel, information-theoretic post-training regularisation in the attention mechanism, which improves out-of-domain generalisation without any training. This success supports the hypothesis that pretrained Transformers are implicitly NV Bayesian models.

A prompt is a sequence of symbol or tokens, selected from a vocabulary according to some rule, which is prepended/concatenated to a textual query. A key problem is how to select the sequence of tokens: in this paper we formulate it as a combinatorial optimization problem. The high dimensionality of the token space com-pounded by the length of the prompt sequence requires a very efficient solution. In this paper we propose a Bayesian optimization method, executed in a continuous em-bedding of the combinatorial space. In this paper we focus on hard prompt tuning (HPT) which directly searches for discrete tokens to be added to the text input with-out requiring access to the large language model (LLM) and can be used also when LLM is available only as a black-box. This is critically important if LLMs are made available in the Model as a Service (MaaS) manner as in GPT-4. The current manu-script is focused on the optimization of discrete prompts for classification tasks. The discrete prompts give rise to difficult combinatorial optimization problem which easily become intractable given the dimension of the token space in realistic applications. The optimization method considered in this paper is Bayesian optimization (BO) which has become the dominant approach in black-box optimization for its sample efficiency along with its modular structure and versatility. In this paper we use BoTorch, a library for Bayesian optimization research built on top of pyTorch. Albeit preliminary and obtained using a 'vanilla' version of BO, the experiments on RoB-ERTa on six benchmarks, show a good performance across a variety of tasks and enable an analysis of the tradeoff between size of the search space, accuracy and wall clock time.

We develop an online learning MCMC approach applicable for hierarchical bayesian models and GLMS. We also develop a fat-tailed LTV model that generalizes over several kinds of fat and thin tails. We demonstrate both developments on commercial LTV data from a large mobile app.