Nonparametric Statistics

We show how a nonparametric conditional density estimation (CDE) framework helps address three nontrivial challenges in ABC. (i) how to efficiently estimate the posterior distribution with limited simulations and different types of data, (ii) how to tune and compare the performance of ABC and related methods in estimating the posterior itself, rather than just certain properties of the density, and (iii) how to efficiently choose among a large set of summary statistics based on a CDE surrogate loss.

Most machine learning tools aim at creating good predictions for new samples. However, obtaining 100% is not feasible in most problems, …

Here we propose a fully nonparametric approach to conditional density estimation that reformulates CDE as a non-parametric orthogonal series problem where the expansion coefficients are estimated by regression. By taking such an approach, one can efficiently estimate conditional densities and not just expectations in high dimensions by drawing upon the success in high-dimensional regression. We show applications to photometric galaxy data, Twitter data, and line-of-sight velocities in a galaxy cluster.

Photometric redshift estimation is an indispensable tool of precision cosmology. One problem that plagues the use of this tool in the …

We describe a general framework for properly constructing and assessing nonparametric conditional density estimators under selection bias, and for combining two or more estimators for optimal performance. This leads to new improved photo-z estimators. We illustrate our methods on data from the Sloan Data Sky Survey and an application to galaxy-galaxy lensing.

In some applications (e.g., in cosmology and economics), the regression E[Z|x] is not adequate to represent the association between a …

A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has …

The ratio between two probability density functions is an important component of various tasks, including selection bias correction, …