Inflation has been rising during the pandemic against supply chain disruptions and a multi-year boom in global owner-occupied house prices. We present some stylized facts pointing to house prices as a leading indicator of headline inflation in the U.S. and eight other major economies with fast-rising house prices. We then apply machine learning methods to forecast inflation in two housing components (rent and owner-occupied housing cost) of the headline inflation and draw tentative inferences about inflationary impact. Our results suggest that for most of these countries, the housing components could have a relatively large and sustained contribution to headline inflation, as inflation is just starting to reflect the higher house prices. Methodologically, for the vast majority of countries we analyze, machine-learning models outperform the VAR model, suggesting some potential value for incorporating such models into inflation forecasting.