### 10th World Congress in Probability and Statistics

## Invited Session (live Q&A at Track 1, 11:30AM KST)

## Recent Advances in Shape Constrained Inference (Organizer: Bodhisattva Sen)

### Global rates of convergence in mixture density estimation

Arlene Kyoung Hee Kim (Korea University)

### Convex regression in multidimensions

Adityanand Guntuboyina (University of California Berkeley)

This is joint work with Gil Kur, Frank Fuchang Gao and Bodhisattva Sen.

### Multiple isotonic regression: limit distribution theory and confidence intervals

Qiyang Han (Rutgers University)

In the second part of the talk, we demonstrate how to use this limiting distribution to construct tuning-free pointwise nonparametric confidence intervals in this model, despite the existence of an infinite-dimensional nuisance parameter in the limit distribution that involves multiple unknown partial derivatives of the true regression function. We show that this difficult nuisance parameter can be effectively eliminated by taking advantage of information beyond point estimates in the block max-min and min-max estimators through random weighting. Notably, the construction of the confidence intervals, even new in the univariate setting, requires no more efforts than performing an isotonic regression for once using the block max-min and min-max estimators, and can be easily adapted to other common monotone models.

This talk is based on joint work with Hang Deng and Cun-Hui Zhang.

### Q&A for Invited Session 05

###### Session Chair

Bodhisattva Sen (Columbia University)

## Optimization in Statistical Learning (Organizer: Garvesh Raskutti)

### Statistical inference on latent network growth processes using the PAPER model

Min Xu (Rutgers University)

### Adversarial classification, optimal transport, and geometric flows

Nicolas Garcia Trillos (University of Wisconsin-Madison)

### Capturing network effect via fused lasso penalty with application on shared-bike data

Yunjin Choi (University of Seoul)

### Q&A for Invited Session 06

###### Session Chair

Garvesh Raskutti (University of Wisconsin-Madison)