Density-Calibrated Conformal Quantile Regression

This paper introduces the Density-Calibrated Conformal Quantile Regression (CQR-d) method, a novel approach for constructing prediction intervals that adapts to varying uncertainty across the feature space. Building upon conformal quantile regression, CQR-d incorporates local information through a weighted combination of local and global conformity scores, where the weights are determined by local data density. We prove that CQR-d provides valid marginal coverage at level $1 - \alpha - \epsilon$, where $\epsilon$ represents a small tolerance from numerical optimization. Through extensive simulation studies and an application to the a heteroscedastic dataset available in R, we demonstrate that CQR-d maintains the desired coverage while producing substantially narrower prediction intervals compared to standard conformal quantile regression (CQR). The method's effectiveness is particularly pronounced in settings with clear local uncertainty patterns, making it a valuable tool for prediction tasks in heterogeneous data environments.

Electrocardiogram-Language Model for Few-Shot Question Answering with Meta Learning

Electrocardiogram (ECG) interpretation requires specialized expertise, often involving synthesizing insights from ECG signals with complex clinical queries posed in natural language. The scarcity of labeled ECG data coupled with the diverse nature of clinical inquiries presents a significant challenge for developing robust and adaptable ECG diagnostic systems. This work introduces a novel multimodal meta-learning method for few-shot ECG question answering, addressing the challenge of limited labeled data while leveraging the rich knowledge encoded within large language models (LLMs). Our LLM-agnostic approach integrates a pre-trained ECG encoder with a frozen LLM (e.g., LLaMA and Gemma) via a trainable fusion module, enabling the language model to reason about ECG data and generate clinically meaningful answers. Extensive experiments demonstrate superior generalization to unseen diagnostic tasks compared to supervised baselines, achieving notable performance even with limited ECG leads. For instance, in a 5-way 5-shot setting, our method using LLaMA-3.1-8B achieves accuracy of 84.6%, 77.3%, and 69.6% on single verify, choose and query question types, respectively. These results highlight the potential of our method to enhance clinical ECG interpretation by combining signal processing with the nuanced language understanding capabilities of LLMs, particularly in data-constrained scenarios.

Electrocardiogram Report Generation and Question Answering via Retrieval-Augmented Self-Supervised Modeling

Interpreting electrocardiograms (ECGs) and generating comprehensive reports remain challenging tasks in cardiology, often requiring specialized expertise and significant time investment. To address these critical issues, we propose ECG-ReGen, a retrieval-based approach for ECG-to-text report generation and question answering. Our method leverages a self-supervised learning for the ECG encoder, enabling efficient similarity searches and report retrieval. By combining pre-training with dynamic retrieval and Large Language Model (LLM)-based refinement, ECG-ReGen effectively analyzes ECG data and answers related queries, with the potential of improving patient care. Experiments conducted on the PTB-XL and MIMIC-IV-ECG datasets demonstrate superior performance in both in-domain and cross-domain scenarios for report generation. Furthermore, our approach exhibits competitive performance on ECG-QA dataset compared to fully supervised methods when utilizing off-the-shelf LLMs for zero-shot question answering. This approach, effectively combining self-supervised encoder and LLMs, offers a scalable and efficient solution for accurate ECG interpretation, holding significant potential to enhance clinical decision-making.

AMES: A Differentiable Embedding Space Selection Framework for Latent Graph Inference

In real-world scenarios, although data entities may possess inherent relationships, the specific graph illustrating their connections might not be directly accessible. Latent graph inference addresses this issue by enabling Graph Neural Networks (GNNs) to operate on point cloud data, dynamically learning the necessary graph structure. These graphs are often derived from a latent embedding space, which can be modeled using Euclidean, hyperbolic, spherical, or product spaces. However, currently, there is no principled differentiable method for determining the optimal embedding space. In this work, we introduce the Attentional Multi-Embedding Selection (AMES) framework, a differentiable method for selecting the best embedding space for latent graph inference through backpropagation, considering a downstream task. Our framework consistently achieves comparable or superior results compared to previous methods for latent graph inference across five benchmark datasets. Importantly, our approach eliminates the need for conducting multiple experiments to identify the optimal embedding space. Furthermore, we explore interpretability techniques that track the gradient contributions of different latent graphs, shedding light on how our attention-based, fully differentiable approach learns to choose the appropriate latent space. In line with previous works, our experiments emphasize the advantages of hyperbolic spaces in enhancing performance. More importantly, our interpretability framework provides a general approach for quantitatively comparing embedding spaces across different tasks based on their contributions, a dimension that has been overlooked in previous literature on latent graph inference.

Notes on Low-rank Matrix Factorization

Low-rank matrix factorization (MF) is an important technique in data science. The key idea of MF is that there exists latent structures in the data, by uncovering which we could obtain a compressed representation of the data. By factorizing an original matrix to low-rank matrices, MF provides a unified method for dimension reduction, clustering, and matrix completion. In this article we review several important variants of MF, including: Basic MF, Non-negative MF, Orthogonal non-negative MF. As can be told from their names, non-negative MF and orthogonal non-negative MF are variants of basic MF with non-negativity and/or orthogonality constraints. Such constraints are useful in specific senarios. In the first part of this article, we introduce, for each of these models, the application scenarios, the distinctive properties, and the optimizing method. By properly adapting MF, we can go beyond the problem of clustering and matrix completion. In the second part of this article, we will extend MF to sparse matrix compeletion, enhance matrix compeletion using various regularization methods, and make use of MF for (semi-)supervised learning by introducing latent space reinforcement and transformation. We will see that MF is not only a useful model but also as a flexible framework that is applicable for various prediction problems.