# Learning Sample-Specific Models with Low-Rank Personalized Regression

arXiv: https://arxiv.org/abs/1910.06939 · HTML: https://mlsanity.com/paper/1910.06939/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2019.

## Built on by (most cited first, 5 of 5)

- [Contextualized Machine Learning](https://mlsanity.com/paper/2310.11340/) (2023)
- [NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters](https://mlsanity.com/paper/2111.01104/) (2021)
- [Retrieval-Augmented Interpretable Learning: Towards Task-Specific Zero-Shot Models in Healthcare](https://mlsanity.com/paper/2607.17508/) (2026)
- [Patient-Specific Models of Treatment Effects Explain Heterogeneity in Tuberculosis](https://mlsanity.com/paper/2411.10645/) (2024)
- [Predicting and Understanding College Student Mental Health with Interpretable Machine Learning](https://mlsanity.com/paper/2503.08002/) (2025)

## Abstract (arXiv)

Modern applications of machine learning (ML) deal with increasingly heterogeneous datasets comprised of data collected from overlapping latent subpopulations. As a result, traditional models trained over large datasets may fail to recognize highly predictive localized effects in favour of weakly predictive global patterns. This is a problem because localized effects are critical to developing individualized policies and treatment plans in applications ranging from precision medicine to advertising. To address this challenge, we propose to estimate sample-specific models that tailor inference and prediction at the individual level. In contrast to classical ML models that estimate a single, complex model (or only a few complex models), our approach produces a model personalized to each sample. These sample-specific models can be studied to understand subgroup dynamics that go beyond coarse-grained class labels. Crucially, our approach does not assume that relationships between samples (e.g. a similarity network) are known a priori. Instead, we use unmodeled covariates to learn a latent distance metric over the samples. We apply this approach to financial, biomedical, and electoral data as well as simulated data and show that sample-specific models provide fine-grained interpretations of complicated phenomena without sacrificing predictive accuracy compared to state-of-the-art models such as deep neural networks.