Conditional Density Estimation Tools in Python and R with Applications to Photometric Redshifts and Likelihood-Free Cosmological Inference

It is well known in astronomy that propagating non-Gaussian prediction uncertainty in photometric redshift estimates is key to reducing bias in downstream cosmological analyses. Similarly, likelihood-free inference approaches, which are beginning to emerge as a tool for cosmological analysis, require the full uncertainty landscape of the parameters of interest given observed data. However, most machine learning (ML) based methods with open-source software target point prediction or classification, and hence fall short in quantifying uncertainty in complex regression and parameter inference settings such as the applications mentioned above. As an alternative to methods that focus on predicting the response (or parameters) $\mathbf{y}$ from features $\mathbf{x}$, we provide nonparametric conditional density estimation (CDE) tools for approximating and validating the entire probability density $\mathrm{p}(\mathbf{y} \mid \mathbf{x})$ given training data for $\mathbf{x}$ and $\mathbf{y}$. As there is no one-size-fits-all CDE method, the goal of this work is to provide a comprehensive range of statistical tools and open-source software for nonparametric CDE and method assessment which can accommodate different types of settings and which in addition can easily be fit to the problem at hand. Specifically, we introduce CDE software packages in $\texttt{Python}$ and $\texttt{R}$ based on four ML prediction methods adapted and optimized for CDE: $\texttt{NNKCDE}$, $\texttt{RFCDE}$, $\texttt{FlexCode}$, and $\texttt{DeepCDE}$. Furthermore, we present the $\texttt{cdetools}$ package, which includes functions for computing a CDE loss function for model selection and tuning of parameters, together with diagnostics functions. We provide sample code in $\texttt{Python}$ and $\texttt{R}$ as well as examples of applications to photometric redshift estimation and likelihood-free cosmology via CDE.