Welcome to Tidy Modeling with R! This book is a guide to using a collection of software in the R programming language for model building called tidymodels, and it has two main goals: First and foremost, this book provides a practical introduction to how to use these specific R packages to create models. We focus on a dialect of R called the tidyverse that is designed with a consistent, human-centered philosophy, and demonstrate how the tidyverse and the tidymodels packages can be used to produce high quality statistical and machine learning models. Second, this book will show you how to develop good methodology and statistical practices. Whenever possible, our software, documentation, and other materials attempt to prevent common pitfalls. In Chapter 1, we outline a taxonomy for models and highlight what good software for modeling is like.

One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it. However, to date, analyses of this approach crucially rely on the convexity and smoothness of the objective function. We give two algorithms that extend this approach substantially. The first algorithm requires nothing except boundedness of the loss function, and operates over a discrete domain. Its privacy and accuracy guarantees hold even without assuming convexity. The second algorithm operates over a continuous domain and requires only that the loss function be bounded and Lipschitz in its continuous parameter. Its privacy analysis does not even require convexity. Its accuracy analysis does require convexity, but does not require second order conditions like smoothness. We complement our theoretical results with an empirical evaluation of the non-convex case, in which we use an integer program solver as our optimization oracle. We find that for the problem of learning linear classifiers, directly optimizing for 0/1 loss using our approach can out-perform the more standard approach of privately optimizing a convex-surrogate loss function on the Adult dataset.