The exoplanet archive is an incredible resource of information on the properties of discovered extrasolar planets, but statistical analysis has been limited by the number of missing values. One of the most informative bulk properties is planet mass, which is particularly challenging to measure with more than 70\% of discovered planets with no measured value. We compare the capabilities of five different machine learning algorithms that can utilize multidimensional incomplete datasets to estimate missing properties for imputing planet mass. The results are compared when using a partial subset of the archive with a complete set of six planet properties, and where all planet discoveries are leveraged in an incomplete set of six and eight planet properties. We find that imputation results improve with more data even when the additional data is incomplete, and allows a mass prediction for any planet regardless of which properties are known. Our favored algorithm is the newly developed $k$NN$\times$KDE, which can return a probability distribution for the imputed properties. The shape of this distribution can indicate the algorithm's level of confidence, and also inform on the underlying demographics of the exoplanet population. We demonstrate how the distributions can be interpreted with a series of examples for planets where the discovery was made with either the transit method, or radial velocity method. Finally, we test the generative capability of the $k$NN$\times$KDE to create a large synthetic population of planets based on the archive, and identify potential categories of planets from groups of properties in the multidimensional space. All codes are Open Source.

Symbolic Regression (SR) searches for mathematical expressions which best describe numerical datasets. This allows to circumvent interpretation issues inherent to artificial neural networks, but SR algorithms are often computationally expensive. This work proposes a new Transformer model aiming at Symbolic Regression particularly focused on its application for Scientific Discovery. We propose three encoder architectures with increasing flexibility but at the cost of column-permutation equivariance violation. Training results indicate that the most flexible architecture is required to prevent from overfitting. Once trained, we apply our best model to the SRSD datasets (Symbolic Regression for Scientific Discovery datasets) which yields state-of-the-art results using the normalized tree-based edit distance, at no extra computational cost.

Numerical data imputation algorithms replace missing values by estimates to leverage incomplete data sets. Current imputation methods seek to minimize the error between the unobserved ground truth and the imputed values. But this strategy can create artifacts leading to poor imputation in the presence of multimodal or complex distributions. To tackle this problem, we introduce the $k$NN$\times$KDE algorithm: a data imputation method combining nearest neighbor estimation ($k$NN) and density estimation with Gaussian kernels (KDE). We compare our method with previous data imputation methods using artificial and real-world data with different data missing scenarios and various data missing rates, and show that our method can cope with complex original data structure, yields lower data imputation errors, and provides probabilistic estimates with higher likelihood than current methods. We release the code in open-source for the community: https://github.com/DeltaFloflo/knnxkde