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Modern applications of machine learning (ML) deal with increasinglyheterogeneous datasets comprised of data collected from overlapping latentsubpopulations. As a result, traditional models trained over large datasets mayfail to recognize highly predictive localized effects in favour of weaklypredictive global patterns. This is a problem because localized effects arecritical to developing individualized policies and treatment plans inapplications ranging from precision medicine to advertising. To address thischallenge, we propose to estimate sample-specific models that tailor inferenceand prediction at the individual level. In contrast to classical ML models thatestimate a single, complex model (or only a few complex models), our approachproduces a model personalized to each sample. These sample-specific models canbe studied to understand subgroup dynamics that go beyond coarse-grained classlabels. Crucially, our approach does not assume that relationships betweensamples (e.g. a similarity network) are known a priori. Instead, we useunmodeled covariates to learn a latent distance metric over the samples. Weapply this approach to financial, biomedical, and electoral data as well assimulated data and show that sample-specific models provide fine-grainedinterpretations of complicated phenomena without sacrificing predictiveaccuracy compared to state-of-the-art models such as deep neural networks.

Learning Sample-Specific Models with Low-Rank Personalized Regression