Finally, we provide experiments on real data comparing NTK and the Laplace kernel, along with a larger class ofγ-exponential kernels. We show that these perform almost identically.

We first prove the direction Z T SI(Z;T) = 0, which is equivalent to prove I(Z;T) = 0 SI(Z;T) = 0. We prove the contrapositive, i.e. rather than show LHS = RHS, we show that RHS = LHS. Now assume that supwi,vj ρ(w i Z i,v j T j) > ϵ for some i,j. Then by setting those elements in w,v unrelated to Z i,T j to zero, and those related to Z i,T j exactlythesameaswi,vj,weknowthatsupw,vρ(w Z,v T) > ϵ. All neural networks are trained by Adam with its default settings and a learning rate η = 0.001. Early stopping is an useful technique for avoiding overfitting, however it needs to be carefully considered when applied to adversarial methods.

Inthis paper,wefirst clarify themathematical connection between the SW distance and the Radon transform. We then utilize the generalized Radon transform to define a new family of distances for probability measures, which we call generalized sliced-Wasserstein (GSW) distances.

Fitting a linear subspace to a dataset corrupted by outliers is a fundamental problem in machine learning and statistics, primarily known as(Robust) Principal Component Analysis (PCA)[10,2].

In practice,θ is typically chosen as a neural network, for which it is often impossible to evaluate the induced densityµθ.

Wedevisetheoretical convergenceguarantees and extensively evaluate our method on synthetic and real benchmarks.

Evidencesuggests that this problem can be circumvented by the use of alarge number of parameters in DL models.

This appendix contains additional material for the paper "Optimistic tree search strategies forblack-box combinatorial optimization".

Computing statistics of large, complex high-dimensional datasets under privacy constraints is a fundamental challenge in modern data science.

By Eq. (103) and Condition 2, we have