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Motivated by classical work of Alon and F\"uredi, we introduce and address the following problem: determine the minimum number of affine hyperplanes in $\mathbb{R}^d$ needed to cover every point of the triangular grid $T_d(n) := \{(x_1,\dots,x_d)\in\mathbb{Z}_{\ge 0}^d\mid x_1+\dots+x_d\le n-1\}$ at least $k$ times. For $d = 2$, we solve the problem exactly for $k \leq 4$, and obtain a partial solution for $k > 4$. We also obtain an asymptotic formula (in $n$) for all $d \geq k - 2$. The proofs rely on combinatorial arguments and linear programming., Comment: 23 pages, 3 figures

We present the final legacy version of stellar photometry for the Panchromatic Hubble Andromeda Treasury (PHAT) survey. We have reprocessed all of the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS) near ultraviolet (F275W, F336W), optical (F475W, F814W), and near infrared (F110W, F160W) imaging from the PHAT survey using an improved method that optimized the survey depth and chip gap coverage by including all overlapping exposures in all bands in the photometry. An additional improvement was gained through the use of charge transfer efficiency (CTE) corrected input images, which provide more complete star finding as well as more reliable photometry for the NUV bands, which had no CTE correction in the previous version of the PHAT photometry. While this method requires significantly more computing resources and time than earlier versions where the photometry was performed on individual pointings, it results in smaller systematic instrumental completeness variations as demonstrated by cleaner maps in stellar density, and it results in optimal constraints on stellar fluxes in all bands from the survey data. Our resulting catalog has 138 million stars, 18% more than the previous catalog, with lower density regions gaining as much as 40% more stars. The new catalog produces nearly seamless population maps which show relatively well-mixed distributions for populations associated with ages older than 1-2 Gyr, and highly structured distributions for the younger populations., Comment: 28 pages, 4 tables, 18 figures, accepted for publication in The Astrophysical Journal Supplement Series

Electrocardiography (ECG) is a non-invasive tool for predicting cardiovascular diseases (CVDs). Current ECG-based diagnosis systems show promising performance owing to the rapid development of deep learning techniques. However, the label scarcity problem, the co-occurrence of multiple CVDs and the poor performance on unseen datasets greatly hinder the widespread application of deep learning-based models. Addressing them in a unified framework remains a significant challenge. To this end, we propose a multi-label semi-supervised model (ECGMatch) to recognize multiple CVDs simultaneously with limited supervision. In the ECGMatch, an ECGAugment module is developed for weak and strong ECG data augmentation, which generates diverse samples for model training. Subsequently, a hyperparameter-efficient framework with neighbor agreement modeling and knowledge distillation is designed for pseudo-label generation and refinement, which mitigates the label scarcity problem. Finally, a label correlation alignment module is proposed to capture the co-occurrence information of different CVDs within labeled samples and propagate this information to unlabeled samples. Extensive experiments on four datasets and three protocols demonstrate the effectiveness and stability of the proposed model, especially on unseen datasets. As such, this model can pave the way for diagnostic systems that achieve robust performance on multi-label CVDs prediction with limited supervision.

Hypernetworks, or hypernets for short, are neural networks that generate weights for another neural network, known as the target network. They have emerged as a powerful deep learning technique that allows for greater flexibility, adaptability, dynamism, faster training, information sharing, and model compression. Hypernets have shown promising results in a variety of deep learning problems, including continual learning, causal inference, transfer learning, weight pruning, uncertainty quantification, zero-shot learning, natural language processing, and reinforcement learning. Despite their success across different problem settings, there is currently no comprehensive review available to inform researchers about the latest developments and to assist in utilizing hypernets. To fill this gap, we review the progress in hypernets. We present an illustrative example of training deep neural networks using hypernets and propose categorizing hypernets based on five design criteria: inputs, outputs, variability of inputs and outputs, and the architecture of hypernets. We also review applications of hypernets across different deep learning problem settings, followed by a discussion of general scenarios where hypernets can be effectively employed. Finally, we discuss the challenges and future directions that remain underexplored in the field of hypernets. We believe that hypernetworks have the potential to revolutionize the field of deep learning. They offer a new way to design and train neural networks, and they have the potential to improve the performance of deep learning models on a variety of tasks. Through this review, we aim to inspire further advancements in deep learning through hypernetworks., Comment: 2 figures and 2 tables -- Accepted to Artificial Intelligence Review

Estimation of individualized treatment effects (ITE) from observational studies is a fundamental problem in causal inference and holds significant importance across domains, including healthcare. However, limited observational datasets pose challenges in reliable ITE estimation as data have to be split among treatment groups to train an ITE learner. While information sharing among treatment groups can partially alleviate the problem, there is currently no general framework for end-to-end information sharing in ITE estimation. To tackle this problem, we propose a deep learning framework based on `\textit{soft weight sharing}' to train ITE learners, enabling \textit{dynamic end-to-end} information sharing among treatment groups. The proposed framework complements existing ITE learners, and introduces a new class of ITE learners, referred to as \textit{HyperITE}. We extend state-of-the-art ITE learners with \textit{HyperITE} versions and evaluate them on IHDP, ACIC-2016, and Twins benchmarks. Our experimental results show that the proposed framework improves ITE estimation error, with increasing effectiveness for smaller datasets., Comment: accepted to The 27th International Conference on Artificial Intelligence and Statistics (AISTATS) 2024

By September, 2022, more than 600 million cases of SARS-CoV-2 infection have been reported globally, resulting in over 6.5 million deaths. COVID-19 mortality risk estimators are often, however, developed with small unrepresentative samples and with methodological limitations. It is highly important to develop predictive tools for pulmonary embolism (PE) in COVID-19 patients as one of the most severe preventable complications of COVID-19. Using a dataset of more than 800,000 COVID-19 patients from an international cohort, we propose a cost-sensitive gradient-boosted machine learning model that predicts occurrence of PE and death at admission. Logistic regression, Cox proportional hazards models, and Shapley values were used to identify key predictors for PE and death. Our prediction model had a test AUROC of 75.9% and 74.2%, and sensitivities of 67.5% and 72.7% for PE and all-cause mortality respectively on a highly diverse and held-out test set. The PE prediction model was also evaluated on patients in UK and Spain separately with test results of 74.5% AUROC, 63.5% sensitivity and 78.9% AUROC, 95.7% sensitivity. Age, sex, region of admission, comorbidities (chronic cardiac and pulmonary disease, dementia, diabetes, hypertension, cancer, obesity, smoking), and symptoms (any, confusion, chest pain, fatigue, headache, fever, muscle or joint pain, shortness of breath) were the most important clinical predictors at admission. Our machine learning model developed from an international cohort can serve to better regulate hospital risk prioritisation of at-risk patients.

The lack of data democratization and information leakage from trained models hinder the development and acceptance of robust deep learning-based healthcare solutions. This paper argues that irreversible data encoding can provide an effective solution to achieve data democratization without violating the privacy constraints imposed on healthcare data and clinical models. An ideal encoding framework transforms the data into a new space where it is imperceptible to a manual or computational inspection. However, encoded data should preserve the semantics of the original data such that deep learning models can be trained effectively. This paper hypothesizes the characteristics of the desired encoding framework and then exploits random projections and random quantum encoding to realize this framework for dense and longitudinal or time-series data. Experimental evaluation highlights that models trained on encoded time-series data effectively uphold the information bottleneck principle and hence, exhibit lesser information leakage from trained models.

The prevalence of artificial intelligence (AI) has envisioned an era of healthcare democratisation that promises every stakeholder a new and better way of life. However, the advancement of clinical AI research is significantly hurdled by the dearth of data democratisation in healthcare. To truly democratise data for AI studies, challenges are two-fold: 1. the sensitive information in clinical data should be anonymised appropriately, and 2. AI-oriented clinical knowledge should flow freely across organisations. This paper considers a recent deep-learning advent, dataset condensation (DC), as a stone that kills two birds in democratising healthcare data. The condensed data after DC, which can be viewed as statistical metadata, abstracts original clinical records and irreversibly conceals sensitive information at individual levels; nevertheless, it still preserves adequate knowledge for learning deep neural networks (DNNs). More favourably, the compressed volumes and the accelerated model learnings of condensed data portray a more efficient clinical knowledge sharing and flowing system, as necessitated by data democratisation. We underline DC's prospects for democratising clinical data, specifically electrical healthcare records (EHRs), for AI research through experimental results and analysis across three healthcare datasets of varying data types.

We use young clusters and giant molecular clouds (GMCs) in the galaxies M33 and M31 to constrain temporal and spatial scales in the star formation process. In M33, we compare the PHATTER catalogue of 1214 clusters with ages measured via colour-magnitude diagram (CMD) fitting to 444 GMCs identified from a new 35 pc resolution ALMA $^{12}$CO(2-1) survey. In M31, we compare the PHAT catalogue of 1249 clusters to 251 GMCs measured from a CARMA $^{12}$CO(1-0) survey with 20 pc resolution. Through two-point correlation analysis, we find that young clusters have a high probability of being near other young clusters, but correlation between GMCs is suppressed by the cloud identification algorithm. By comparing the positions, we find that younger clusters are closer to GMCs than older clusters. Through cross-correlation analysis of the M33 cluster data, we find that clusters are statistically associated when they are $\leq$10 Myr old. Utilizing the high precision ages of the clusters, we find that clusters older than $\approx 18$ Myr are uncorrelated with the molecular ISM. Using the spatial coincidence of the youngest clusters and GMCs in M33, we estimate that clusters spend $\approx$4-6 Myr inside their parent GMC. Through similar analysis, we find that the GMCs in M33 have a total lifetime of $\approx 11$-15 Myr. We also develop a drift model and show that the above correlations can be explained if the clusters in M33 have a 5-10 km s$^{-1}$ velocity dispersion relative to the molecular ISM., Comment: 14 pages, 13 figures, 1 tables, accepted for publication at MNRAS

External validation is often recommended to ensure the generalizability of ML models. However, it neither guarantees generalizability nor equates to a model's clinical usefulness (the ultimate goal of any clinical decision-support tool). External validation is misaligned with current healthcare ML needs. First, patient data changes across time, geography, and facilities. These changes create significant volatility in the performance of a single fixed model (especially for deep learning models, which dominate clinical ML). Second, newer ML techniques, current market forces, and updated regulatory frameworks are enabling frequent updating and monitoring of individual deployed model instances. We submit that external validation is insufficient to establish ML models' safety or utility. Proposals to fix the external validation paradigm do not go far enough. Continued reliance on it as the ultimate test is likely to lead us astray. We propose the MLOps-inspired paradigm of recurring local validation as an alternative that ensures the validity of models while protecting against performance-disruptive data variability. This paradigm relies on site-specific reliability tests before every deployment, followed by regular and recurrent checks throughout the life cycle of the deployed algorithm. Initial and recurrent reliability tests protect against performance-disruptive distribution shifts, and concept drifts that jeopardize patient safety.

We present analysis using a citizen science campaign to improve the cosmological measures from the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX). The goal of HETDEX is to measure the Hubble expansion rate, $H(z)$, and angular diameter distance, $D_A(z)$, at $z =$ 2.4, each to percent-level accuracy. This accuracy is determined primarily from the total number of detected Lyman-$\alpha$ emitters (LAEs), the false positive rate due to noise, and the contamination due to [O II] emitting galaxies. This paper presents the citizen science project, Dark Energy Explorers, with the goal of increasing the number of LAEs, decreasing the number of false positives due to noise and the [O II] galaxies. Initial analysis shows that citizen science is an efficient and effective tool for classification most accurately done by the human eye, especially in combination with unsupervised machine learning. Three aspects from the citizen science campaign that have the most impact are 1) identifying individual problems with detections, 2) providing a clean sample with 100% visual identification above a signal-to-noise cut, and 3) providing labels for machine learning efforts. Since the end of 2022, Dark Energy Explorers has collected over three and a half million classifications by 11,000 volunteers in over 85 different countries around the world. By incorporating the results of the Dark Energy Explorers we expect to improve the accuracy on the $D_A(z)$ and $H(z)$ parameters at $z =$ 2.4 by 10 - 30%. While the primary goal is to improve on HETDEX, Dark Energy Explorers has already proven to be a uniquely powerful tool for science advancement and increasing accessibility to science worldwide., Comment: 14 pages, 6 figures, accepted for publication in The Astrophysical Journal