Sam Patterson | Searcharxiv

arXiv2026

Mapping the z>=5 SiIV Column Density Distribution onto the Galaxy Stellar Mass Function Using the Cumulative Absorption Cross Section

Efforts to constrain directly the activity in low-mass galaxies confront sensitivity limits even in the JWST era. Metal absorbers offer a complementary probe and are easier to detect, but leveraging them requires a known relationship between absorber strength and host mass. To this end, many studies assume a simple monotonic relationship between absorber strength and host mass. This ansatz ignores evidence that galaxies at fixed luminosity host absorbers spanning a variety of strengths. We address this issue by deriving a six-parameter model for the cumulative absorption cross section from cosmological simulations that combines with the galaxy stellar mass function to predict the absorber column density distribution (CDD). A maximum-likelihood analysis confirms that this approach reconciles the observed galaxy stellar mass function with the observed SiIV CDD at z=5-6. The extrapolated CDD grows uncertain outside the observed range and the resulting constraints contain degeneracies, highlighting the need for improved measurements. Galaxies of all masses host absorbers of all strengths, but a weak empirical association between massive galaxies and strong absorbers is indicated. Faint galaxies (M* < 10^8 Msun) host the majority of weak SiIV absorbers (log N < 13), emphasizing emission/absorber complementarity. The assumption of a power-law relationship between absorbers' geometric cross sections and host galaxy masses is empirically disfavored. The model may be applied to any combination of ion and redshift if the galaxy stellar mass function is well-constrained. Future observational tests incorporating improved host statistics will extend the model's range.

astro-ph.GA↗

arXiv2012

Conditional mean embeddings as regressors - supplementary

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings minimise, providing an intuitive understanding of the embeddings and a justification for their use. Furthermore, the equivalence allows the application of vector-valued regression methods and results to the problem of learning conditional distributions. Using this link we derive a sparse version of the embedding by considering alternative formulations. Further, by applying convergence results for vector-valued regression to the embedding problem we derive minimax convergence rates which are O(\log(n)/n) -- compared to current state of the art rates of O(n^{-1/4}) -- and are valid under milder and more intuitive assumptions. These minimax upper rates coincide with lower rates up to a logarithmic factor, showing that the embedding method achieves nearly optimal rates. We study our sparse embedding algorithm in a reinforcement learning task where the algorithm shows significant improvement in sparsity over an incomplete Cholesky decomposition.

cs.LG↗