Accurate assessment of pulmonary emphysema is crucial to assess disease severity and subtype, to monitor disease progression, and to predict lung cancer risk. However, visual assessment is time-consuming and subject to substantial inter-rater variability while standard densitometry approaches to quantify emphysema remain inferior to visual scoring. We explore if machine learning methods that learn from a large dataset of visually assessed CT scans can provide accurate estimates of emphysema extent and if methods that learn from emphysema extent scoring can outperform algorithms that learn only from emphysema presence scoring. Four Multiple Instance Learning classifiers, trained on emphysema presence labels, and five Learning with Label Proportions classifiers, trained on emphysema extent labels, are compared. Performance is evaluated on 600 low-dose CT scans from the Danish Lung Cancer Screening Trial and we find that learning from emphysema presence labels, which are much easier to obtain, gives equally good performance to learning from emphysema extent labels. The best performing Multiple Instance Learning and Learning with Label Proportions classifiers, achieve intra-class correlation coefficients around 0.90 and average overall agreement with raters of 78% and 79% compared to an inter-rater agreement of 83.