This paper develops a machine learning approach to estimate internationally-and-intertemporally comparable, decomposable, structural asset poverty measures. These measures are founded in theory, link directly to official poverty lines, and are amenable to ML-based prediction using Earth Observation data. Using household survey data from Tanzania, Uganda, and Malawi, we model the relationship between household consumption expenditures and productive assets, directly linking flow-based poverty measures with asset-based structural poverty measures. The poverty measures we construct can serve as new, improved dependent variables for ML poverty prediction. We also assess whether our poverty estimates vary from readily available poverty estimates and whether this difference in poverty measures matters.