💻 bioinformatics

POME: Graph-based embeddings for partially observed mixed-type data

The paper introduces POME, a self-supervised graph-based embedding model designed to generate low-dimensional representations for partially observed mixed-type biomedical data, achieving state-of-the-art imputation performance and enabling effective downstream tasks such as patient subgroup discovery, predictive modeling, and therapy recommendation.

Original authors: Woller, F., Arend, L., Kist, A. M., List, M., Rahimi, F., Sirocchi, C., Blumenthal, D. B.

Published 2026-09-15

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CC BY 4.0

Original authors: Woller, F., Arend, L., Kist, A. M., List, M., Rahimi, F., Sirocchi, C., Blumenthal, D. B.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

In the vast landscape of modern medicine, data is the primary tool for understanding disease and guiding treatment. Doctors and researchers collect immense amounts of information about patients, ranging from the specific types of cells found in a tumor to the results of blood tests and the history of past illnesses. This information is rarely uniform; it is a chaotic mix of numbers, categories, and text, often referred to as mixed-type data. Furthermore, this data is almost never complete. Patients miss appointments, certain tests are not ordered for everyone, and records are lost, leaving behind gaps that look like empty spaces in a spreadsheet. For decades, these gaps and the messy variety of data types have forced scientists to either throw away incomplete records or use statistical tricks to fill them in, both of which can distort the true picture of a patient's health and lead to flawed conclusions.

A team of researchers has now developed a new way to handle this messy reality, turning the gaps and the variety into features rather than flaws. They created a tool called POME, which stands for partially observed mixed-type data embeddings. Instead of trying to force all the different kinds of medical data into a single, rigid format or simply deleting the missing pieces, POME treats the entire dataset as a map of connections. Imagine a network where patients are one set of points and every possible piece of information about them is another set of points. When a patient has a blood test result, a line connects them to that result. When a piece of data is missing, the line simply isn't drawn. This approach allows the computer to learn the relationships between patients and their symptoms, even when the data is incomplete and jumbled together.

The researchers tested this approach on three large, real-world collections of medical records involving thousands of patients with lung cancer, head and neck cancer, and various other conditions treated with chemotherapy. They found that POME could fill in the missing information with a level of accuracy that matched or exceeded the best existing methods. More importantly, the tool created a new kind of "fingerprint" for each patient. These fingerprints were not just simple summaries but rich, low-dimensional representations that captured the complex interplay of a patient's diverse health markers. When the researchers used these fingerprints to group patients together without telling the computer what to look for, the groups that formed were medically meaningful. For instance, the tool naturally separated patients based on whether their tumors were linked to a specific virus, a factor known to influence survival rates, or grouped them by the density of immune cells in their tumors, which is a sign of how the body is fighting the disease.

The power of these fingerprints extended beyond just sorting patients. The researchers used them to look back at historical treatment decisions and see if they made sense. By comparing a new patient's fingerprint to those of past patients, the system could suggest which treatment strategy had worked best for similar individuals in the past. In one test involving head and neck cancer patients, those whose actual treatment matched the system's recommendation based on these fingerprints had significantly better five-year survival rates than those whose treatment did not match. This suggests that the tool can identify subtle patterns in how different combinations of symptoms and history respond to specific therapies, offering a way to support doctors in making more informed choices.

The study also showed that these fingerprints could be used to predict future outcomes, such as whether a patient would develop a specific side effect from chemotherapy, often outperforming other standard methods for handling mixed data. The researchers even looked inside the tool to see what it had learned about the variables themselves. They found that the tool had correctly grouped together medical terms that are biologically related, such as different types of white blood cells, demonstrating that it had learned the underlying logic of the medical data rather than just memorizing numbers.

While the tool is currently optimized to run on powerful computer hardware and requires significant memory for very large datasets, the researchers demonstrated that it is fast enough to be useful in real-world workflows. They made the software available to the public so that other scientists can test it on their own data. The work does not claim to solve every problem in medical data analysis, but it offers a robust new way to turn the messy, incomplete, and varied records of clinical practice into clear, actionable insights. By respecting the natural structure of the data, including its missing parts, POME allows researchers to see the patient more clearly, potentially leading to better diagnoses and more effective treatments.

Technical Summary: POME – Graph-based Embeddings for Partially Observed Mixed-type Data

Problem Statement

Biomedical research frequently relies on Partially Observed Mixed-type (POM) datasets, which combine heterogeneous feature types (numeric, binary, and multi-class categorical) with substantial fractions of missing values. Traditional analytical workflows face significant challenges with such data:

Heterogeneity: Standard methods like Principal Component Analysis (PCA) are limited to numeric data, while others like Factor Analysis of Mixed Data (FAMD) or t-SNE struggle to integrate missing values or combine different variable types without ad-hoc preprocessing.
Missingness: Common strategies to handle missing data, such as complete-case analysis or pairwise deletion, introduce systematic bias. Conversely, standard imputation techniques often fail to capture the complex joint structure of mixed-type data or require specific strategies for each variable type.
Gap in Representation Learning: Existing embedding methods (e.g., UMAP, scVI, MOFA) either do not natively support mixed-type data with missing values or lack ready-to-use implementations that handle the specific constraints of POM datasets (e.g., multi-class categorical variables with missingness).

Methodology: The POME Model

The authors propose POME (Partially Observed Mixed-type data Embeddings), a self-supervised model designed to generate low-dimensional vector representations for both samples and variables. POME treats the dataset as a bipartite graph where missingness is naturally encoded as absent edges.

1. Graph Representation

The dataset $X$ is modeled as a bipartite graph $G = (S \cup R, E)$ :

Nodes:
- Sample Nodes ( $S$ ): Represent individual observations.
- Value Nodes ( $R$ ): Represent variable values.
  - For categorical variables, value nodes correspond to specific classes.
  - For numeric variables, values are discretized into bins ( $B$ ) via a binning strategy (default: z-score binning with $B=15$ ). Value nodes represent these bins.
Edges: An edge exists between a sample node $i$ and a value node $r$ if the sample has an observed value corresponding to that class or bin. Missing values are represented by the absence of an edge.
Shared Concept Learning:
- Variable Encodings ( $e_j$ ): Shared across all value nodes of a specific variable.
- Bin Encodings ( $e_b$ ): Shared across all numeric variables for the same bin index, allowing the model to learn a unified semantic for numeric ranges (e.g., "high value").
- Class Encodings ( $e_c$ ): Specific to the variable, as categories of different variables are not semantically comparable.

2. Architecture

POME employs a Graph Neural Network (GNN) framework:

Encoder: A two-layer Graph Attention Network (GAT) learns embeddings ( $z_u$ ) for all nodes. The attention mechanism allows the model to weigh the contribution of different variables non-uniformly.
Decoder: A two-layer Multi-Layer Perceptron (MLP) performs link prediction, reconstructing the graph by predicting the probability of an edge between a sample and a value node.
Loss Function: A binary cross-entropy loss is minimized to distinguish observed edges (positive) from randomly sampled non-edges (negative).

3. Inductive Reasoning

To handle new, unseen samples (inductive setting), POME initializes new sample nodes with zero encodings. Crucially, during inference, edges are directed only from value nodes to the new sample node. This ensures the new sample aggregates information from its observed values without perturbing the learned representations of existing nodes or other new samples, allowing for efficient batch embedding of new data.

4. Downstream Applications

Imputation: Categorical values are imputed by selecting the value node with the highest link prediction score. Numeric values are imputed using a lightweight regression head trained on the learned sample and variable encodings.
Stratification & Visualization: Sample embeddings ( $z_i$ ) are used for clustering (e.g., Leiden) and visualization (e.g., t-SNE).
Predictive Modeling: Embeddings serve as input features for supervised tasks (linear probing).
Variable Semantics: Variable encodings ( $e_j$ ) are analyzed to understand learned semantic relationships.

Key Results

The authors evaluated POME on three real-world biomedical datasets: TCGA-LUAD (lung adenocarcinoma), HANCOCK (head and neck cancer), and MIMIC-IV (chemotherapy side effects).

Imputation Performance:
- POME achieved state-of-the-art performance on categorical variables across all datasets and missingness ratios (1%–50%), significantly outperforming k-NN, MissForest, and AutoComplete.
- On numeric variables, POME performed comparably to MissForest and significantly better than k-NN and AutoComplete on two of the three datasets.
Unsupervised Sample Stratification:
- POME embeddings yielded superior clustering quality (higher Silhouette scores, lower Davies-Bouldin indices) compared to UMAP, particularly at lower embedding dimensions (16 and 32).
- Clusters identified in the HANCOCK dataset were clinically meaningful, recovering known prognostic markers (e.g., HPV status, tumor site, CD3+ cell density) and showing significant differences in overall survival.
Predictive Modeling (Linear Probing):
- Logistic regression models trained on POME embeddings outperformed those trained on UMAP embeddings on 7 out of 8 binary target variables across the datasets.
- POME demonstrated superior utility in jointly representing numeric and categorical data, whereas UMAP required separate models that were combined post-hoc.
Adjuvant Therapy Recommendation:
- In a retrospective study using the HANCOCK dataset, POME-based similarity queries were used to recommend adjuvant therapy modalities.
- Patients whose actual treatment matched the POME-based recommendation ("POME-consistent") showed significantly higher 5-year overall survival fractions compared to those whose treatment did not match, even in subgroups where no therapy was administered.
Variable Semantics:
- Exploratory analysis of variable encodings on MIMIC-IV revealed that the learned semantic space aligned with biomedical knowledge. For instance, the embedding for "aplasia" clustered closely with white blood cell-related variables (neutrophils, monocytes), consistent with known immunosuppression markers.

Significance and Claims

The paper positions POME as a versatile, ready-to-use solution for the specific challenges of POM data in biomedical research.

Unified Framework: POME eliminates the need for separate strategies to handle missing data and variable integration, learning a joint representation that inherently respects the graph structure of observed data.
Practical Utility: The model is fast (training on 10,000 samples takes <2 minutes on GPU) and supports inductive reasoning, making it suitable for iterative analysis workflows and real-world deployment.
Clinical Relevance: The study demonstrates that POME embeddings are not just mathematical abstractions but capture clinically actionable information, enabling the discovery of patient subgroups, improved predictive modeling, and data-driven therapy recommendations.
Accessibility: The authors provide a fully documented Python package (pome-py) available on PyPI and GitHub to facilitate adoption.

The authors maintain a modest tone regarding future improvements, suggesting that while architectural enhancements (e.g., attention blocks, transformer-based decoders) could boost performance, the core value of POME lies in its successful application of bipartite graph learning to POM data. They acknowledge current limitations in memory consumption for very large datasets and the optimization for GPU hardware.