Department of Mathematics and Statistics

Friday, January 12th, 2018

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Yifan Cui, University of North Carolina at Chapel Hill

Title: Tree-based Survival Models and Precision Medicine

Abstract: In the first part, we develop a theoretical framework for survival tree and forest models. We first investigate the method from the aspect of splitting rules. We show that existing approaches lead to a potentially biased estimation of the within-node survival and cause non-optimal selection of the splitting rules. Based on this observation, we develop an adaptive concentration bound result which quantifies the variance component for survival forest models. Furthermore, we show with three specific examples how these concentration bounds, combined with properly designed splitting rules, yield consistency results. In the second part, we focus on one application of survival trees in precision medicine which estimates individualized treatment rules nonparametrically under right censoring. We extend the outcome weighted learning to right censored data without requiring either inverse probability of censoring weighting or semi-parametric modeling of the censoring and failure times. To accomplish this, we take advantage of the tree-based approach to nonparametrically impute the survival time in two different ways. In simulation studies, our estimators demonstrate improved performance compared to existing methods. We also illustrate the proposed method on a phase III clinical trial of non-small cell lung cancer.

Yifan Cui (University of North Carolina at Chapel Hill): Yifan Cui is a PhD candidate in the Department of Statistics and Operations Research at the University of North Carolina at Chapel Hill. He works under the co-supervision of Professors Michael Kosorok and Jian Hannig. His research interest include machine learning, tree-based methods, high-dimensional data, personalized medicine, fiducial inference, bayesian inference, causal inference, and survival analysis.

Friday, December 1st, 2017

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Bob Ross Barmish, University of Wisconsin-Madison

Title: When the expected value is not expected

Abstract: Our motivation for the research to be described is derived from the following fact: The expected value of a random variable~$X$, denoted~$\mathbb{E}(X)$, is often inconsistent with what human beings may actually expect based on psychological considerations. This is particularly important when predictions involving life-threatening situations arise. To bring this issue into sharp focus, this seminar begins with a set of questions related to the recent rampage of Hurricane Irma in the State of Florida. When the use of empirical data leads to an expected value forecast of storm surge wave height which is unduly pessimistic, will the "boy who cried wolf" effect be in play the next time a hurricane approaches the mainland? On the other hand, if the formally calculated expected wave height is too optimistic, might it be the case that many will take inadequate protective measures? Based on such considerations, we define a new alternative to~$\mathbb{E}(X)$ which we believe is quite useful for "mission critical" situations with downside risk being of paramount concern. We call this new metric the {\it Conservative Expected Value} and denote it by~$\mathbb{CEV}(X)$. In this talk, we provide the technical definition of the $\mathbb{CEV}$, compare it with the classical expected value and describe some aspects of the rich mathematical theory which accompanies it. We also include a description of some of the studies we have conducted using the~$\mathbb{CEV}$ to evaluate historical data.

Bob Ross Barmish (University of Wisconsin): B. Ross Barmish received his Ph.D. degree in electrical engineering from Cornell University in 1975. From 1975 to 1978, he was an Assistant Professor of Engineering and Applied Science at Yale University. From 1978 to 1984, he was as an Associate Professor of Electrical Engineering at the University of Rochester. He joined the University of Wisconsin{Madison in 1984, where he is currently a Professor ofelectrical and computer engineering. His research interests include robustness of dynamical systems, building a bridge between feedback control theory, and trading in complex financial markets. Prof. Barmish was a recipient of the Best Paper Award (1986-1989 and 1990-1992) from the International Federation of Automatic Control, and the 2013 Bode Prize by the IEEE Control Systems Society.

Wednesday, November 29th, 2017

Time: 3:30 p.m.  Place: Jeffery Hall 234

Speaker: Jason Klusowski

Title: Counting motifs and connected components of large graphs via subgraph sampling

Abstract: Learning properties of large graphs from samples is an important problem in statistical network analysis. We revisit the problem of estimating the numbers of connected components in a graph of $N$ vertices based on the subgraph sampling model, where we observe the subgraph induced by $n$ vertices drawn uniformly at random. The key question is whether it is possible to achieve accurate estimation, i.e., vanishing normalized mean-square error, by sampling a vanishing fraction of the vertices. We show that it is possible by accessing only sublinear number of samples if the graph does not contains high-degree vertices or long induced cycles; otherwise it is impossible. Optimal sample complexity bounds are obtained for several classes of graphs including forests, cliques, and chordal graphs. The methodology relies on topological identities of graph homomorphism numbers, which, in turn, also play a key role proving minimax lower bounds based on constructing random instances of graphs with matching structures of small subgraphs. We will also discuss results for the neighborhood sampling model, where we observe the edges between the sampled vertices and their neighbors.

Jason Klusowski (Yale University): Jason M. Klusowski obtained his B.Sc. in Mathematics and Statistics in 2013 from the University of Manitoba, receiving the Robert Ross McLaughlin Scholarship in Mathematics, the Faculty of Science Medal in B.Sc., and the Governor General's Silver Medal. In 2013 he was received the NSERC Alexander Graham Bell Canada Graduate Scholarship and joined Yale University where he is currently a Ph.D. candidate in Statistics and Data Science, under the supervision of Prof. Andrew Barron. Jason Klusowski's research interests include the theoretical and computational aspects of neural networks, approximation algorithms for networks, high-dimensional function estimation, mixture models, and shape constrained estimation.

Friday, November 24th, 2017

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Jeffery Rosenthal, University of Toronto

Title: Adaptive MCMC for Everyone

Abstract: Markov chain Monte Carlo (MCMC) algorithms, such as the Metropolis Algorithm and the Gibbs Sampler, are an extremely useful and popular method of approximately sampling from complicated probability distributions. Adaptive MCMC attempts to automatically modify the algorithm while it runs, to improve its performance on the fly. However, such adaptation often destroys the ergodicity properties necessary for the algorithm to be valid. In this talk, we first illustrate MCMC algorithms using simple graphical Java applets. We then discuss adaptive MCMC, and present examples and theorems concerning its ergodicity and efficiency. We close with some recent ideas which make adaptive MCMC more widely applicable in broader contexts.

Wednesday, November 22nd, 2017

Time: 1:30 p.m.  Place: Jeffery Hall 319

Speaker: Jung-Jo Lee

Title: Cyclotomic units, values of the Riemann zeta function and p-adic measures

Abstract:  I would explain the connection between the cyclotomic units and the values of complex Riemann zeta function via higher logarithmic derivative maps. We can use Mahler transform to construct a p-adic zeta function.

Note: I consider a series of talks, each "hopefully" self-contained.

Talk 2 : Euler system of cyclotomic units and Iwasawa's main conjecture

Talk 3 : Euler system of Heegner points and Birch and Swinnerton-Dyer conjecture