Dr. Brett Addison's Data Science Projects & Blog

Predicting the Orbital Obliquities of Exoplanets Using Machine Learning

Part 4: Random Forest Classification to Predict Orbital Obliquities

Posted by Brett Addison on 1 February 2025 • Topics: Machine Learning, Random Forest Classification, Python, Exoplanets • 5-minute read

Illustration of a decision tree (in this case the first tree in the forest) with a depth of three branches from the random forest classifier model produced using the training dataset. Image credit: Brett Addison.

In my previous posts (Parts 2 and 3), I discussed using a random forest regression model to predict exoplanet orbital obliquities based on stellar and planetary parameters. However, its predictive accuracy was limited. In this post, I shift to a classification approach using Scikit-learn's RandomForestClassifier, categorizing obliquities into aligned (λ < 22.5°), misaligned (22.5° ≤ λ < 67.5°), and highly misaligned (λ ≥ 67.5°)—following how they are defined in Addison et al. (2013).

Data Preparation and Feature Engineering

The dataset is compiled using the same preprocessing steps as before, including replacing missing values using physically derived estimates instead of median imputation as well as using the same engineered features—planet-to-star mass ratio (pl_ratmom) and planet density (pl_density), as discussed in Part 3). To account for uncertainties, I again augment the dataset by simulating 100 additional data points per row based on the 1 σ errors.

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Part 3: Improving the Random Forest Regression Model

Posted by Brett Addison on 25 January 2025 • Topics: Machine Learning, Random Forest Regression, Feature Engineering, Python, Exoplanets • 5-minute read

As discussed in part 2 of this blog series, the current random forest model struggles to predict the orbital obliquities of exoplanets accurately. This may be due to factors such as the small sample size, imbalanced dataset, reliance on median imputation for missing data, insufficiently relevant features, and/or the random forest method being unsuitable for this problem. In part 3, I address these challenges with two enhancements: physically derived imputation and feature engineering.

1. Physically Derived Imputation: Instead of median-based imputation (replacement), missing values are calculated using established relationships between features. For example, the mass of a star can be derived from its effective temperature and radius, assuming it is on the main sequence. This approach produces more accurate and physically meaningful values compared to median replacement.

 

2. Feature Engineering: Orbital obliquity may depend more on combinations of features than individual ones. To test this, I created two new features: the planet-to-star mass ratio (M_p/M_*) and planetary density. These features aim to better capture the dependencies related to obliquity.

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Part 2: Obtaining & Cleaning Datasets & Fitting First Random Forest Regression Model

Posted by Brett Addison on 10 January 2025 • Topics: Machine Learning, Random Forest Regression, Python, Visualization, Exoplanets • 5-minute read

Illustration of a random forest model consisting of N number of decision trees, with each tree consisting of M number of branches (or nodes), similar to how a forest consists of many trees and each tree consists of many branches. The nodes within each decision tree are used to make a prediction, and all of the predictions are averaged together to produce a final result. The red path taken in each decision tree is where specific criteria are met that result in a prediction. Image credit: Brett Addison.

In this project, I applied machine learning to explore an interesting question in astronomy: Can we predict the orbital obliquities of exoplanets using their host stars' properties and planetary system features? Orbital obliquity—the angle between a planet's orbital plane and the equator of its host star—offers crucial insights into planetary formation and evolution. Here's how I approached this challenge using a random forest regression model.

Data Collection and Pre-processing

The first step involved obtaining data from two databases: the catalog of the physical properties of transiting planetary systems (TEPCat) and the NASA Exoplanet Archive. These sources provided the required properties of the exoplanets and their host star's to build a machine learning model, including, for example, the masses, radii, orbital distances, and orbital obliquities. However, the sample size of planets with measured orbital obliquities was small and the measurements came with significant uncertainties. Additionally, the dataset is somewhat imbalanced, there are more than double the number of planets on low obliquity orbits compared to high obliquity orbits as shown in the figure below.

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