SAM aims to find a perturbed model within the vicinity of a current model that maximizes the loss over a training set.

Stein discrepancies have emerged as a powerful statistical tool, being applied to fundamental statistical problems including parameter inference, goodness-of-fit testing, and sampling. The canonical Stein discrepancies require the derivatives of a statistical model to be computed, and in return provide theoretical guarantees of convergence detection and control. However, for complex statistical models, the stable numerical computation of derivatives can require bespoke algorithmic development and render Stein discrepancies impractical. This paper focuses on posterior approximation using Stein discrepancies, and introduces a collection of non-canonical Stein discrepancies that are gradient-free, meaning that derivatives of the statistical model are not required. Sufficient conditions for convergence detection and control are established, and applications to sampling and variational inference are presented.

Work done as a master's student at the University of Chicago. One way to compute this optimum is to use EM. We then get the following (see e.g., Sec 4.2.4 of Murphy [2022] In this section we discuss the datasets in more detail. B.1 Colored MNIST We show some sample images in Figure 1. We show some sample images in Figure 2. We list all the target attributes in Table 1.

In this section, we first summarize frequently used notations in the following table. Table 4: Frequently used notations.Notation Description C Lemma 7. Let d = 1 . Combining the cases above completes the proof. Subsection B.2 proves several convergence rate lemmas. Subsection B.3 gives some technical We are now ready to prove Theorem 1. Proof of Theorem 1.

And, conversely, the minimum-norm interpolator is the solution to adversarial training with a given radius.