# Events

Friday, October 25, 2019 — 10:30 AM EDT

## Department seminar by Fabio Bellini, Università degli Studi di Milano-Bicocca

On the properties of Lambda-quantiles

We present a systematic treatment of Lambda-quantiles, a family of generalized quantiles introduced in Frittelli et al. (2014) under the name of Lambda Value at Risk. We consider various possible definitions and derive their fundamental properties, mainly working under the assumption that the threshold function Lambda is nonincreasing. We refine some of the weak continuity results derived in Burzoni et al. (2017), showing that the weak continuity properties of Lambda-quantiles are essentially similar to those of the usual quantiles. Further, we provide an axiomatic foundation for Lambda-quantiles based on a locality property that generalizes a similar axiomatization of the usual quantiles based on the ordinal covariance property given in Chambers (2009). We study scoring functions consistent with Lambda-quantiles and as an extension of the usual quantile regression we introduce Lambda-quantile regression, of which we provide two financial applications.

(joint work with Ilaria Peri).

Thursday, October 31, 2019 — 4:00 PM EDT

## Department seminar by Qi Long, University of Pennsylvania

#### Variable selection for structured high-dimensional data using known and novel graph information

Variable selection for structured high-dimensional covariates lying on an underlying graph has drawn considerable interest. However, most of the existing methods may not be scalable to high dimensional settings involving tens of thousands of variables lying on known pathways such as the case in genomics studies, and they assume that the graph information is fully known. This talk will focus on addressing these two challenges. In the first part, I will present an adaptive Bayesian shrinkage approach which incorporates known graph information through shrinkage parameters and is scalable to high dimensional settings (e.g., p~100,000 or millions). We also establish theoretical properties of the proposed approach for fixed and diverging p. In the second part, I will tackle the issue that graph information is not fully known. For example, the role of miRNAs in regulating gene expression is not well-understood and the miRNA regulatory network is often not validated. We propose an approach that treats unknown graph information as missing data (i.e. missing edges), introduce the idea of imputing the unknown graph information, and define the imputed information as the novel graph information.  In addition, we propose a hierarchical group penalty to encourage sparsity at both the pathway level and the within-pathway level, which, combined with the imputation step, allows for incorporation of known and novel graph information. The methods are assessed via simulation studies and are applied to analyses of cancer data.

Thursday, November 7, 2019 — 4:00 PM EST

## Department seminar by Yang Ning, Cornell University

#### Nonregular and Minimax Estimation of Individualized Thresholds in High Dimension with Binary Responses

Given a large number of covariates $\bZ$, we consider the estimation of a high-dimensional parameter $\btheta$ in an individualized linear threshold $\btheta^T\bZ$ for a continuous variable $X$, which minimizes the disagreement between $\sign{X-\btheta^T\bZ}$ and a binary response $Y$. While the problem can be formulated into the M-estimation framework, minimizing the corresponding empirical risk function is computationally intractable due to discontinuity of the sign function. Moreover, estimating $\btheta$ even in the fixed-dimensional setting is known as a nonregular problem leading to nonstandard asymptotic theory. To tackle the computational and theoretical challenges in the estimation of the high-dimensional parameter $\btheta$, we propose an empirical risk minimization approach based on a regularized smoothed non-convex loss function. The Fisher consistency of the proposed method is guaranteed as the bandwidth of the smoothed loss is shrunk to 0. Statistically, we show that the finite sample error bound for estimating $\btheta$ in $\ell_2$ norm is $(s\log d/n)^{\beta/(2\beta+1)}$, where $d$ is the dimension of $\btheta$, $s$ is the sparsity level, $n$ is the sample size and $\beta$ is the smoothness of the conditional density of $X$ given the response $Y$ and the covariates $\bZ$. The convergence rate is nonstandard and slower than that in the classical Lasso problems. Furthermore, we prove that the resulting estimator is minimax rate optimal up to a logarithmic factor. The Lepski's method is developed to achieve the adaption to the unknown sparsity $s$ and smoothness $\beta$. Computationally, an efficient path-following algorithm is proposed to compute the solution path. We show that this algorithm achieves geometric rate of convergence for computing the whole path. Finally, we evaluate the finite sample performance of the proposed estimator in simulation studies and a real data analysis from the ChAMP (Chondral Lesions And Meniscus Procedures) Trial.

Thursday, November 14, 2019 — 4:00 PM EST

## Department seminar by Adam Kashlak, University of Alberta

#### On Khintchine's Inequality for Statistics

In complex estimation and hypothesis testing settings, it may be impossible to compute p-values or construct confidence intervals using classical analytic approaches like asymptotic normality.  Instead, one often relies on randomization and resampling procedures such as the bootstrap or permutation test.  But these approaches suffer from the computational burden of large scale Monte Carlo runs.  To remove this burden, we develop analytic methods for hypothesis testing and confidence intervals by specifically considering the discrete finite sample distributions of the randomized test statistic.  The primary tool we use to achieve such results is Khintchine's inequality and its extensions and generalizations.

Friday, November 15, 2019 — 10:30 AM EST

## Department seminar by Arthur Charpentier, Université du Québec à Montréal

Thursday, November 21, 2019 — 4:00 PM EST

## Department seminar by Linglong Kong, University of Alberta

Friday, November 22, 2019 — 10:30 AM EST

## Department seminar by Mathieu Boudreault, Université du Québec à Montréal

Thursday, November 28, 2019 — 4:00 PM EST

## Department seminar by Shihao Yang, Georgia Institute of Technology

Friday, November 29, 2019 — 10:30 AM EST

## Department seminar by Yang Lu, Paris Dauphine University

### October 2019

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