This project addresses fundamental challenges in statistical modeling, to develop more accurate and reliable methods for analyzing complex data. As data becomes increasingly central to scientific discovery, economic prosperity, and national security, the need for advanced statistical tools is paramount. This research will create new techniques in nonparametric regression, a field of statistics focused on fitting models to data without pre-supposing the relationship's form. It confronts three recurrent obstacles in analyzing large datasets -- curse of dimensionality, ad-hoc tuning choices, and the tension between flexibility and interpretability -- by developing principled regression and density-estimation tools, thereby improving our ability to interpret complex information. The work forges new links between shape-constrained nonparametric methods and neural networks, adapts ideas from image processing to statistics, and also unites frequentist and Bayesian thinking through simple, intuitive priors. The development of these methods will have wide-ranging benefits in many applied fields. Furthermore, this project will contribute to the education and training of the next generation of statisticians and data scientists, ensuring that the nation remains at the forefront of this critical field. The investigator will develop a suite of novel approaches to nonparametric regression. One area of focus is a new shape-constrained method for multi-index convex re