Estimating Unknown Population Sizes Using the Hypergeometric Distribution

The multivariate hypergeometric distribution describes sampling without replacement from a discrete population of elements divided into multiple categories. Addressing a gap in the literature, we tackle the challenge of estimating discrete distributions when both the total population size and the sizes of its constituent categories are unknown. Here, we propose a novel solution using the hypergeometric likelihood to solve this estimation challenge, even in the presence of severe under-sampling. We develop our approach to account for a data generating process where the ground-truth is a mixture of distributions conditional on a continuous latent variable, such as with collaborative filtering, using the variational autoencoder framework. Empirical data simulation demonstrates that our method outperforms other likelihood functions used to model count data, both in terms of accuracy of population size estimate and in its ability to learn an informative latent space. We demonstrate our method's versatility through applications in NLP, by inferring and estimating the complexity of latent vocabularies in text excerpts, and in biology, by accurately recovering the true number of gene transcripts from sparse single-cell genomics data.

The Uncanny Valley: A Comprehensive Analysis of Diffusion Models

Through Diffusion Models (DMs), we have made significant advances in generating high-quality images. Our exploration of these models delves deeply into their core operational principles by systematically investigating key aspects across various DM architectures: i) noise schedules, ii) samplers, and iii) guidance. Our comprehensive examination of these models sheds light on their hidden fundamental mechanisms, revealing the concealed foundational elements that are essential for their effectiveness. Our analyses emphasize the hidden key factors that determine model performance, offering insights that contribute to the advancement of DMs. Past findings show that the configuration of noise schedules, samplers, and guidance is vital to the quality of generated images; however, models reach a stable level of quality across different configurations at a remarkably similar point, revealing that the decisive factors for optimal performance predominantly reside in the diffusion process dynamics and the structural design of the model's network, rather than the specifics of configuration details. Our comparative analysis reveals that Denoising Diffusion Probabilistic Model (DDPM)-based diffusion dynamics consistently outperform the Noise Conditioned Score Network (NCSN)-based ones, not only when evaluated in their original forms but also when continuous through Stochastic Differential Equation (SDE)-based implementations.

Representational Ethical Model Calibration

Equity is widely held to be fundamental to the ethics of healthcare. In the context of clinical decision-making, it rests on the comparative fidelity of the intelligence -- evidence-based or intuitive -- guiding the management of each individual patient. Though brought to recent attention by the individuating power of contemporary machine learning, such epistemic equity arises in the context of any decision guidance, whether traditional or innovative. Yet no general framework for its quantification, let alone assurance, currently exists. Here we formulate epistemic equity in terms of model fidelity evaluated over learnt multi-dimensional representations of identity crafted to maximise the captured diversity of the population, introducing a comprehensive framework for Representational Ethical Model Calibration. We demonstrate use of the framework on large-scale multimodal data from UK Biobank to derive diverse representations of the population, quantify model performance, and institute responsive remediation. We offer our approach as a principled solution to quantifying and assuring epistemic equity in healthcare, with applications across the research, clinical, and regulatory domains.

Orientation and Context Entangled Network for Retinal Vessel Segmentation

Most of the existing deep learning based methods for vessel segmentation neglect two important aspects of retinal vessels, one is the orientation information of vessels, and the other is the contextual information of the whole fundus region. In this paper, we propose a robust Orientation and Context Entangled Network (denoted as OCE-Net), which has the capability of extracting complex orientation and context information of the blood vessels. To achieve complex orientation aware, a Dynamic Complex Orientation Aware Convolution (DCOA Conv) is proposed to extract complex vessels with multiple orientations for improving the vessel continuity. To simultaneously capture the global context information and emphasize the important local information, a Global and Local Fusion Module (GLFM) is developed to simultaneously model the long-range dependency of vessels and focus sufficient attention on local thin vessels. A novel Orientation and Context Entangled Non-local (OCE-NL) module is proposed to entangle the orientation and context information together. In addition, an Unbalanced Attention Refining Module (UARM) is proposed to deal with the unbalanced pixel numbers of background, thick and thin vessels. Extensive experiments were performed on several commonly used datasets (DRIVE, STARE and CHASEDB1) and some more challenging datasets (AV-WIDE, UoA-DR, RFMiD and UK Biobank). The ablation study shows that the proposed method achieves promising performance on maintaining the continuity of thin vessels and the comparative experiments demonstrate that our OCE-Net can achieve state-of-the-art performance on retinal vessel segmentation.

Label scarcity in biomedicine: Data-rich latent factor discovery enhances phenotype prediction

High-quality data accumulation is now becoming ubiquitous in the health domain. There is increasing opportunity to exploit rich data from normal subjects to improve supervised estimators in specific diseases with notorious data scarcity. We demonstrate that low-dimensional embedding spaces can be derived from the UK Biobank population dataset and used to enhance data-scarce prediction of health indicators, lifestyle and demographic characteristics. Phenotype predictions facilitated by Variational Autoencoder manifolds typically scaled better with increasing unlabeled data than dimensionality reduction by PCA or Isomap. Performances gains from semisupervison approaches will probably become an important ingredient for various medical data science applications.

Clusters in Explanation Space: Inferring disease subtypes from model explanations

Identification of disease subtypes and corresponding biomarkers can substantially improve clinical diagnosis and treatment selection. Discovering these subtypes in noisy, high dimensional biomedical data is often impossible for humans and challenging for machines. We introduce a new approach to facilitate the discovery of disease subtypes: Instead of analyzing the original data, we train a diagnostic classifier (healthy vs. diseased) and extract instance-wise explanations for the classifier's decisions. The distribution of instances in the explanation space of our diagnostic classifier amplifies the different reasons for belonging to the same class - resulting in a representation that is uniquely useful for discovering latent subtypes. We compare our ability to recover subtypes via cluster analysis on model explanations to classical cluster analysis on the original data. In multiple datasets with known ground-truth subclasses, most compellingly on UK Biobank brain imaging data and transcriptome data from the Cancer Genome Atlas, we show that cluster analysis on model explanations substantially outperforms the classical approach. While we believe clustering in explanation space to be particularly valuable for inferring disease subtypes, the method is more general and applicable to any kind of sub-type identification.

Finding the needle in high-dimensional haystack: A tutorial on canonical correlation analysis

Since the beginning of the 21st century, the size, breadth, and granularity of data in biology and medicine has grown rapidly. In the example of neuroscience, studies with thousands of subjects are becoming more common, which provide extensive phenotyping on the behavioral, neural, and genomic level with hundreds of variables. The complexity of such big data repositories offer new opportunities and pose new challenges to investigate brain, cognition, and disease. Canonical correlation analysis (CCA) is a prototypical family of methods for wrestling with and harvesting insight from such rich datasets. This doubly-multivariate tool can simultaneously consider two variable sets from different modalities to uncover essential hidden associations. Our primer discusses the rationale, promises, and pitfalls of CCA in biomedicine.

Learning Neural Representations of Human Cognition across Many fMRI Studies

Cognitive neuroscience is enjoying rapid increase in extensive public brain-imaging datasets. It opens the door to large-scale statistical models. Finding a unified perspective for all available data calls for scalable and automated solutions to an old challenge: how to aggregate heterogeneous information on brain function into a universal cognitive system that relates mental operations/cognitive processes/psychological tasks to brain networks? We cast this challenge in a machine-learning approach to predict conditions from statistical brain maps across different studies. For this, we leverage multi-task learning and multi-scale dimension reduction to learn low-dimensional representations of brain images that carry cognitive information and can be robustly associated with psychological stimuli. Our multi-dataset classification model achieves the best prediction performance on several large reference datasets, compared to models without cognitive-aware low-dimension representations, it brings a substantial performance boost to the analysis of small datasets, and can be introspected to identify universal template cognitive concepts.

The Future of Data Analysis in the Neurosciences

Neuroscience is undergoing faster changes than ever before. Over 100 years our field qualitatively described and invasively manipulated single or few organisms to gain anatomical, physiological, and pharmacological insights. In the last 10 years neuroscience spawned quantitative big-sample datasets on microanatomy, synaptic connections, optogenetic brain-behavior assays, and high-level cognition. While growing data availability and information granularity have been amply discussed, we direct attention to a routinely neglected question: How will the unprecedented data richness shape data analysis practices? Statistical reasoning is becoming more central to distill neurobiological knowledge from healthy and pathological brain recordings. We believe that large-scale data analysis will use more models that are non-parametric, generative, mixing frequentist and Bayesian aspects, and grounded in different statistical inferences.

Classical Statistics and Statistical Learning in Imaging Neuroscience

Neuroimaging research has predominantly drawn conclusions based on classical statistics, including null-hypothesis testing, t-tests, and ANOVA. Throughout recent years, statistical learning methods enjoy increasing popularity, including cross-validation, pattern classification, and sparsity-inducing regression. These two methodological families used for neuroimaging data analysis can be viewed as two extremes of a continuum. Yet, they originated from different historical contexts, build on different theories, rest on different assumptions, evaluate different outcome metrics, and permit different conclusions. This paper portrays commonalities and differences between classical statistics and statistical learning with their relation to neuroimaging research. The conceptual implications are illustrated in three common analysis scenarios. It is thus tried to resolve possible confusion between classical hypothesis testing and data-guided model estimation by discussing their ramifications for the neuroimaging access to neurobiology.