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Generalized estimating equations (GEE) are of great importance in analyzing clustered data without full specification of multivariate distributions. A recent approach jointly models the mean, variance, and correlation coefficients of clustered data through three sets of regressions (Luo and Pan, 2022). We observe that these estimating equations, however, are a special case of those of Yan and Fine (2004) which further allows the variance to depend on the mean through a variance function. The proposed variance estimators may be incorrect for the variance and correlation parameters because of a subtle dependence induced by the nested structure of the estimating equations. We characterize model settings where their variance estimation is invalid and show the variance estimators in Yan and Fine (2004) correctly account for such dependence. In addition, we introduce a novel model selection criterion that enables the simultaneous selection of the mean-scale-correlation model. The sandwich variance estimator and the proposed model selection criterion are tested by several simulation studies and real data analysis, which validate its effectiveness in variance estimation and model selection. Our work also extends the R package geepack with the flexibility to apply different working covariance matrices for the variance and correlation structures.

In the field of neural data compression, the prevailing focus has been on optimizing algorithms for either classical distortion metrics, such as PSNR or SSIM, or human perceptual quality. With increasing amounts of data consumed by machines rather than humans, a new paradigm of machine-oriented compression$\unicode{x2013}$which prioritizes the retention of features salient for machine perception over traditional human-centric criteria$\unicode{x2013}$has emerged, creating several new challenges to the development, evaluation, and deployment of systems utilizing lossy compression. In particular, it is unclear how different approaches to lossy compression will affect the performance of downstream machine perception tasks. To address this under-explored area, we evaluate various perception models$\unicode{x2013}$including image classification, image segmentation, speech recognition, and music source separation$\unicode{x2013}$under severe lossy compression. We utilize several popular codecs spanning conventional, neural, and generative compression architectures. Our results indicate three key findings: (1) using generative compression, it is feasible to leverage highly compressed data while incurring a negligible impact on machine perceptual quality; (2) machine perceptual quality correlates strongly with deep similarity metrics, indicating a crucial role of these metrics in the development of machine-oriented codecs; and (3) using lossy compressed datasets, (e.g. ImageNet) for pre-training can lead to counter-intuitive scenarios where lossy compression increases machine perceptual quality rather than degrading it. To encourage engagement on this growing area of research, our code and experiments are available at: //github.com/danjacobellis/MPQ.

Uncertainty quantification in forecasting represents a topic of great importance in energy trading, as understanding the status of the energy market would enable traders to directly evaluate the impact of their own offers/bids. To this end, we propose a scalable procedure that outputs closed-form simultaneous prediction bands for multivariate functional response variables in a time series setting, which is able to guarantee performance bounds in terms of unconditional coverage and asymptotic exactness, both under some conditions. After evaluating its performance on synthetic data, the method is used to build multivariate prediction bands for daily demand and offer curves in the Italian gas market.

We consider information-theoretic bounds on expected generalization error for statistical learning problems in a networked setting. In this setting, there are $K$ nodes, each with its own independent dataset, and the models from each node have to be aggregated into a final centralized model. We consider both simple averaging of the models as well as more complicated multi-round algorithms. We give upper bounds on the expected generalization error for a variety of problems, such as those with Bregman divergence or Lipschitz continuous losses, that demonstrate an improved dependence of $1/K$ on the number of nodes. These "per node" bounds are in terms of the mutual information between the training dataset and the trained weights at each node, and are therefore useful in describing the generalization properties inherent to having communication or privacy constraints at each node.

Physics-based computer models based on numerical solution of the governing equations generally cannot make rapid predictions, which in turn, limits their applications in the clinic. To address this issue, we developed a physics-informed neural network (PINN) model that encodes the physics of a closed-loop blood circulation system embedding a left ventricle (LV). The PINN model is trained to satisfy a system of ordinary differential equations (ODEs) associated with a lumped parameter description of the circulatory system. The model predictions have a maximum error of less than 5% when compared to those obtained by solving the ODEs numerically. An inverse modeling approach using the PINN model is also developed to rapidly estimate model parameters (in $\sim$ 3 mins) from single-beat LV pressure and volume waveforms. Using synthetic LV pressure and volume waveforms generated by the PINN model with different model parameter values, we show that the inverse modeling approach can recover the corresponding ground truth values, which suggests that the model parameters are unique. The PINN inverse modeling approach is then applied to estimate LV contractility indexed by the end-systolic elastance $E_{es}$ using waveforms acquired from 11 swine models, including waveforms acquired before and after administration of dobutamine (an inotropic agent) in 3 animals. The estimated $E_{es}$ is about 58% to 284% higher for the data associated with dobutamine compared to those without, which implies that this approach can be used to estimate LV contractility using single-beat measurements. The PINN inverse modeling can potentially be used in the clinic to simultaneously estimate LV contractility and other physiological parameters from single-beat measurements.

We study semi-supervised sequence generation tasks where labeled data are too scarce to effectively finetune a model and at the same time few-shot prompting of a large language model (LLM) has suboptimal performance. This happens when a task, such as parsing, is expensive to annotate and also unfamiliar to a pretrained LLM. In this paper, we present a discovery that student models distilled from an in-context learned LLM can often generalize better than their teacher on such tasks. Leveraging this finding, we present a new method -- multistage collaborative knowledge distillation from an LLM (MCKD) -- for such tasks. MCKD first few-shot prompts an LLM to produce pseudolabels for unlabeled data. At each intermediate knowledge distillation (KD) stage, a new pair of students is trained on disjoint partitions of the pseudolabeled data. Each student then produces new and improved pseudolabels for its unseen partition to be used in the next stage of distillation. We demonstrate the advantage of multistage cross-partition labeling on several syntactic and semantic parsing tasks. On CRAFT biomedical parsing, for example, 3-stage MCKD with 50 labeled examples outperforms the prompted LLM and vanilla KD by 7.5% and 3.7% parsing F1, respectively, and matches the performance of supervised finetuning with 500 examples.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.

This paper focuses on two fundamental tasks of graph analysis: community detection and node representation learning, which capture the global and local structures of graphs, respectively. In the current literature, these two tasks are usually independently studied while they are actually highly correlated. We propose a probabilistic generative model called vGraph to learn community membership and node representation collaboratively. Specifically, we assume that each node can be represented as a mixture of communities, and each community is defined as a multinomial distribution over nodes. Both the mixing coefficients and the community distribution are parameterized by the low-dimensional representations of the nodes and communities. We designed an effective variational inference algorithm which regularizes the community membership of neighboring nodes to be similar in the latent space. Experimental results on multiple real-world graphs show that vGraph is very effective in both community detection and node representation learning, outperforming many competitive baselines in both tasks. We show that the framework of vGraph is quite flexible and can be easily extended to detect hierarchical communities.

Recent years have witnessed the enormous success of low-dimensional vector space representations of knowledge graphs to predict missing facts or find erroneous ones. Currently, however, it is not yet well-understood how ontological knowledge, e.g. given as a set of (existential) rules, can be embedded in a principled way. To address this shortcoming, in this paper we introduce a framework based on convex regions, which can faithfully incorporate ontological knowledge into the vector space embedding. Our technical contribution is two-fold. First, we show that some of the most popular existing embedding approaches are not capable of modelling even very simple types of rules. Second, we show that our framework can represent ontologies that are expressed using so-called quasi-chained existential rules in an exact way, such that any set of facts which is induced using that vector space embedding is logically consistent and deductively closed with respect to the input ontology.