Elevated pulmonary artery pressure (PAP) is a significant healthcare risk. Continuous monitoring for patients with elevated PAP is crucial for effective treatment, yet the most accurate method is invasive and expensive, and cannot be performed repeatedly. Noninvasive methods exist but are inaccurate, expensive, and cannot be used for continuous monitoring. We present a machine learning model based on heart sounds that estimates pulmonary artery pressure with enough accuracy to exclude an invasive diagnostic operation, allowing for consistent monitoring of heart condition in suspect patients without the cost and risk of invasive monitoring. We conduct a greedy search through 38 possible features using a 109-patient cross-validation to find the most predictive features. Our best general model has a standard estimate of error (SEE) of 8.28 mmHg, which outperforms the previous best performance in the literature on a general set of unseen patient data.