One contribution seems to have been in defining a surrogate functional g (line 166) that replaces the \mu(0) term in a denominator term with an arbitrary parameter c and then using a uniform convergence bound over values of c to ensure that estimation does take place even if c is replaced with its actual value of \mu(0). Another contribution seems to be in fine tuning the proof technique used to prove Proposition 5. The main contribution is a proof for obtaining generalization bound for weighted areas under the ROC curve for Lipschitz weight functions.

This is a theoretical paper that has received relatively good reviews. However, two of the reviewers only increased their scores from 5 to 6 in order to reduce the divergence and help form a consensus (in the discussions), but neither was really convinced about the quality of the paper. Unfortunately, the highest scoring reviewer was also the least confident. I read the paper myself and I find that it has some merits --- it seems theoretically solid, but I have a slight tendency towards saying that it may be a better fit at ALT/AISTATS/COLT, and it is unclear if the NeurIPS community will benefit from knowing these results. Nevertheless, regardless of the final outcome, the authors are encouraged to improve the readability of their paper through (it is currently somewhat dense for the average reader).

Weaknesses: Given the paper's current state, I have following major comments: - The proposed method's motivation is to tackle the issue of model-data mismatch by modeling the context representation uncertainty. However the notion of the model-data mismatch is loosely defined. It would be more interesting if the paper's formulation would fomulate this problem in a principled way, e.g. the model-data mismatch problem can be framed in a more principled way, e.g. The combined objective of two models with/without bootstraps is somewhat questionable. The computation of residuals would influence a lot to the input hence the convergence of the full model.

This is an important paper on uncertainty quantification. However as the reviewers noted the main concerns are competitiveness with reespect to GPs and also an analysis (perrhaps with intuitions) of when the method underperforms would be useful. Overall, this paper might pave the way for really interesting follow-ups which will build on top of it.

Facies are the type of rocks with similar characteristics given by geologists and facies classification is of very significance in geological tasks, such as formation evaluation, reservoir characterization. As the geological data accumulates, there are growing interests in facies classification with machine learning methods [1, 2, 3, 4, 5, 6, 7, 8, 9]. There are two issues with the existing works on facies classification. First, the machine learning models are built without variable selection or with only very primary method, such as cross-validation, which makes the classifiers with useless variable as inputs and therefore with low performance. Second, most of the models for facies classification are block-box, such as deep learning [5, 10, 11], Boostings or SVMs[7], which are un-interpretable to geologists. Variable selection is a common task that selects a subset from all the available variables for machine learning models. By this, the accuracy of the predictive models built with the selected variables can be improved compared with those built without selection. The traditional method for variable selection are mainly based on likelihoods, such as AIC, BIC, or accuracy, such as LASSO [12], or correlation, such as HSIC [13], distance correlation [14], and copula entropy [15]. Copula Entropy (CE) is a recently proposed rigorous mathematical concept for measuring multivariate statistical independence and is proved to be equivalent to mutual information in information theory [16].

The dream of achieving a student-teacher ratio of 1:1 is closer than ever thanks to the emergence of large language models (LLMs). One potential application of these models in the educational field would be to provide feedback to students in university introductory programming courses, so that a student struggling to solve a basic implementation problem could seek help from an LLM available 24/7. This article focuses on studying three aspects related to such an application. First, the performance of two well-known models, GPT-3.5T and GPT-4T, in providing feedback to students is evaluated. The empirical results showed that GPT-4T performs much better than GPT-3.5T, however, it is not yet ready for use in a real-world scenario. This is due to the possibility of generating incorrect information that potential users may not always be able to detect. Second, the article proposes a carefully designed prompt using in-context learning techniques that allows automating important parts of the evaluation process, as well as providing a lower bound for the fraction of feedbacks containing incorrect information, saving time and effort. This was possible because the resulting feedback has a programmatically analyzable structure that incorporates diagnostic information about the LLM's performance in solving the requested task. Third, the article also suggests a possible strategy for implementing a practical learning tool based on LLMs, which is rooted on the proposed prompting techniques. This strategy opens up a whole range of interesting possibilities from a pedagogical perspective.

In this paper, we introduce the concept of principal communities and propose a principal graph encoder embedding method that concurrently detects these communities and achieves vertex embedding. Given a graph adjacency matrix with vertex labels, the method computes a sample community score for each community, ranking them to measure community importance and estimate a set of principal communities. The method then produces a vertex embedding by retaining only the dimensions corresponding to these principal communities. Theoretically, we define the population version of the encoder embedding and the community score based on a random Bernoulli graph distribution. We prove that the population principal graph encoder embedding preserves the conditional density of the vertex labels and that the population community score successfully distinguishes the principal communities. We conduct a variety of simulations to demonstrate the finite-sample accuracy in detecting ground-truth principal communities, as well as the advantages in embedding visualization and subsequent vertex classification. The method is further applied to a set of real-world graphs, showcasing its numerical advantages, including robustness to label noise and computational scalability.

We propose a homogeneity test closely related to the concept of linear separability between two samples. Using the test one can answer the question whether a linear classifier is merely ``random'' or effectively captures differences between two classes. We focus on establishing upper bounds for the test's \emph{p}-value when applied to two-dimensional samples. Specifically, for normally distributed samples we experimentally demonstrate that the upper bound is highly accurate. Using this bound, we evaluate classifiers designed to detect ER-positive breast cancer recurrence based on gene pair expression. Our findings confirm significance of IGFBP6 and ELOVL5 genes in this process.

Managing microservice architectures in distributed systems is complex and resource intensive due to the high frequency and dynamic nature of inter service interactions. Accurate prediction of these future interactions can enhance adaptive monitoring, enabling proactive maintenance and resolution of potential performance issues before they escalate. This study introduces a Graph Neural Network GNN based approach, specifically using a Graph Attention Network GAT, for link prediction in microservice Call Graphs. Unlike social networks, where interactions tend to occur sporadically and are often less frequent, microservice Call Graphs involve highly frequent and time sensitive interactions that are essential to operational performance. Our approach leverages temporal segmentation, advanced negative sampling, and GATs attention mechanisms to model these complex interactions accurately. Using real world data, we evaluate our model across performance metrics such as AUC, Precision, Recall, and F1 Score, demonstrating its high accuracy and robustness in predicting microservice interactions. Our findings support the potential of GNNs for proactive monitoring in distributed systems, paving the way for applications in adaptive resource management and performance optimization.

Self-supervised learning (SSL) is an emerging paradigm that exploits supervisory signals generated from the data itself, and many recent studies have leveraged SSL to conduct graph anomaly detection. However, we empirically found that three important factors can substantially impact detection performance across datasets: 1) the specific SSL strategy employed; 2) the tuning of the strategy's hyperparameters; and 3) the allocation of combination weights when using multiple strategies. Most SSL-based graph anomaly detection methods circumvent these issues by arbitrarily or selectively (i.e., guided by label information) choosing SSL strategies, hyperparameter settings, and combination weights. While an arbitrary choice may lead to subpar performance, using label information in an unsupervised setting is label information leakage and leads to severe overestimation of a method's performance. Leakage has been criticized as "one of the top ten data mining mistakes", yet many recent studies on SSL-based graph anomaly detection have been using label information to select hyperparameters. To mitigate this issue, we propose to use an internal evaluation strategy (with theoretical analysis) to select hyperparameters in SSL for unsupervised anomaly detection. We perform extensive experiments using 10 recent SSL-based graph anomaly detection algorithms on various benchmark datasets, demonstrating both the prior issues with hyperparameter selection and the effectiveness of our proposed strategy.