Parameterized Manifold Learning and Sparse Tensor Train Regression for Cosmological Parameter Inference from Merger Trees

Abstract: Inferring cosmological parameters like Omega\_m and sigma\_8 from the complex, hierarchical structures of merger trees presents a significant challenge for understanding galaxy formation and evolution. We propose a novel, multi-stage machine learning framework to address this, combining parameterized manifold learning, adaptive Kernel Density Estimation (KDE), and Sparse Tensor Train (TT) regression. Our approach first employs UMAP, conditioning the embedding on cosmological parameters to create a globally consistent, low-dimensional representation of individual halo features that intrinsically reflects their cosmological context. Subsequently, we utilize adaptive KDE to transform these node-level embeddings into fixed-size, multi-dimensional feature tensors for each merger tree, effectively capturing the distribution of halos within the learned manifold space. Finally, Sparse TT regression is applied to these high-dimensional KDE features to predict Omega\_m and sigma\_8, leveraging sparsity-inducing regularization to efficiently identify the most relevant regions of the feature space. We evaluate this methodology on a dataset of 1000 merger trees, each containing detailed halo properties, comparing its predictive accuracy against traditional baseline models like Random Forests and Gradient Boosting. Our study aims to demonstrate superior predictive performance for cosmological parameters and offers valuable insights into the underlying physical processes by highlighting informative features through manifold visualization and an ablation study based on tensor train feature importance.

Subjects:	gr-qc; hep-th; astro-ph.CO
Cite as:	PX:2508.00075