# HI-PMK: A Data-Dependent Kernel for Incomplete Heterogeneous Data Representation

arXiv: https://arxiv.org/abs/2501.04300 · HTML: https://mlsanity.com/paper/2501.04300/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 49 references that are in the map.
- First posted on arXiv 8 Jan 2025.

## Builds on (most cited first, 11 of 11)

- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [GCNet: Graph Completion Network for Incomplete Multimodal Learning in Conversation](https://mlsanity.com/paper/2203.02177/) (2022)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [Cold Brew: Distilling Graph Node Representations with Incomplete or Missing Neighborhoods](https://mlsanity.com/paper/2111.04840/) (2021)
- [Processing of missing data by neural networks](https://mlsanity.com/paper/1805.07405/) (2018)
- [Conformalized matrix completion](https://mlsanity.com/paper/2305.10637/) (2023)
- [Isolation Kernel: The X Factor in Efficient and Effective Large Scale Online Kernel Learning](https://mlsanity.com/paper/1907.01104/) (2019)

## Built on by (most cited first, 2 of 2)

- [MissDDIM: Deterministic and Efficient Conditional Diffusion for Tabular Data Imputation](https://mlsanity.com/paper/2508.03083/) (2025)
- [MissMecha: An All-in-One Python Package for Studying Missing Data Mechanisms](https://mlsanity.com/paper/2508.04740/) (2025)

## Abstract (arXiv)

Handling incomplete and heterogeneous data remains a central challenge in real-world machine learning, where missing values may follow complex mechanisms (MCAR, MAR, MNAR) and features can be of mixed types (numerical and categorical). Existing methods often rely on imputation, which may introduce bias or privacy risks, or fail to jointly address data heterogeneity and structured missingness. We propose the Heterogeneous Incomplete Probability Mass Kernel (HI-PMK), a novel data-dependent representation learning approach that eliminates the need for imputation. HI-PMK introduces two key innovations: (1) a probability mass-based dissimilarity measure that adapts to local data distributions across heterogeneous features (numerical, ordinal, nominal), and (2) a missingness-aware uncertainty strategy (MaxU) that conservatively handles all three missingness mechanisms by assigning maximal plausible dissimilarity to unobserved entries. Our approach is privacy-preserving, scalable, and readily applicable to downstream tasks such as classification and clustering. Extensive experiments on over 15 benchmark datasets demonstrate that HI-PMK consistently outperforms traditional imputation-based pipelines and kernel methods across a wide range of missing data settings. Code is available at: https://github.com/echoid/Incomplete-Heter-Kernel