Accurate forecasting of lithium-ion battery performance is important for easing consumer concerns about the safety and reliability of electric vehicles. Most research on battery health prognostics focuses on the R&D setting where cells are subjected to the same usage patterns, yet in practice there is great variability in use across cells and cycles, making forecasting much more challenging. Here, we address this challenge by combining electrochemical impedance spectroscopy (EIS), a non-invasive measurement of battery state, with probabilistic machine learning. We generated a dataset of 40 commercial lithium-ion coin cells cycled under multistage constant current charging/discharging, with currents randomly changed between cycles to emulate realistic use patterns. We show that future discharge capacities can be predicted with calibrated uncertainties, given the future cycling protocol and a single EIS measurement made just before charging, and without any knowledge of usage history. Our method is data-efficient, requiring just eight cells to achieve a test error of less than 10%, and robust to dataset shifts. Our model can forecast well into the future, attaining a test error of less than 10% when projecting 32 cycles ahead. Further, we find that model performance can be boosted by 25% by augmenting EIS with additional features derived from historical capacity-voltage curves. Our results suggest that battery health is better quantified by a multidimensional vector rather than a scalar State of Health, thus deriving informative electrochemical `biomarkers' in tandem with machine learning is key to predictive battery management and control.