To conclude, we present two natural open problems:

There were several topics that I hoped to cover that we didn’t have time to cover. Here is a summary of the most important.

This paper explores only one aspect of the connection between manifold learning and linear smoothing, namely the analysis of manifold learning methods and ways to use that analysis to improve existing NLDR methods.

We thank the following speakers at the workshop for bringing insights to the policies and practices faced by journals in striving for openness in scientific research and research reporting. By framing the issues, both philosophical and practical, th…

We thank Prof. M. E. Vares for drawing our attention to articles [6] and [26]. We are also grateful to the anonymous referee for an extremely helpful review which significantly improved the quality of the paper, including pointing out references [7]…

In this section, we turn to studying a nonparametric statistical problem in which the effects of local differential privacy turn out to be somewhat more severe. We show that for the problem of density estimation, instead of just multiplicative loss …

It is our pleasure to thank Omer Tamuz for several motivating discussions that served as a starting point of the project. We would also like to thank Franck Barthe, Lawrence Craig Evans, Steven N. Evans and Gil Kalai for helpful suggestions. We also…

In what follows, we provide proofs of the results mentioned in the previous two sections.

The aim of this section is to provide formal definitions of entire monotonicity and HK0 variation for the convenience of the reader. We roughly follow the notation of aistleitner2014functions and owen2005multidimensional.

The results of Raghavendra (2008) show that assuming Khot's Unique Games Conjecture (2002), for every constraint satisfaction problem there exists a generic semi-definite program that achieves the optimal approximation factor. This result is existen…