Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, January 22, 2020.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, January 22, 2020

12:00 pm in 141 Altgeld Hall,Wednesday, January 22, 2020

Predictive Actuarial Analystics Using Tree-Based Models

Zhiyu Quan (University of Connecticut)

Abstract: Because of its many advantages, the use of tree-based models has become an increasingly popular alternative predictive tool for building classification and regression models. Innovations to the original methods, such as random forests and gradient boosting, have further improved the capabilities of using tree-based models as a predictive model. Quan et al. (2018) examined the performance of tree-based models for the valuation of the guarantees embedded in variable annuities. We found that tree-based models are generally very efficient in producing more accurate predictions and the gradient boosting ensemble method is considered the most superior. Quan and Valdez (2018) applied multivariate tree-based models to multi-line insurance claims data with correlated responses drawn from the Wisconsin Local Government Property Insurance Fund (LGPIF). We were able to capture the inherent relationship among the response variables and improved marginal predictive accuracy. Quan et al. (2019) propose to use tree-based models with a hybrid structure as an alternative approach to the Tweedie Generalized Linear Model (GLM). This hybrid structure captures the benefits of tuning hyperparameters at each step of the algorithm thereby allowing for an improved prediction accuracy. We examined the performance of this model vis-\`a-vis the Tweedie GLM using the LGPIF and simulated datasets. Our empirical results indicate that this hybrid tree-based model produces more accurate predictions without loss of intuitive interpretation.

2:00 pm in 447 Altgeld Hall,Wednesday, January 22, 2020

Organizational Meeting

Sungwoo Nam (Illinois Math)

Abstract: We will have an organizational meeting for this semester. This involves making a plan for this semester and possibly choose a topic for a reading seminar. If you want to speak this semester, or are interested in a reading seminar, please join us and make a suggestion.

3:00 pm in 243 Altgeld Hall,Wednesday, January 22, 2020

How do mathematicians believe?

Brian P Katz (Smith College)

Abstract: Love it or hate it, many people believe that mathematics gives humans access to a kind of truth that is more absolute and universal than other disciplines. If this claim is true, we must ask: what makes the origins and processes of mathematics special and how can our messy, biological brains connect to the absolute? If the claim is false, then what becomes of truth in mathematics? In this session, we will consider beliefs about truth and how they play out in the mathematics classroom, trying to understand a little about identity, authority, and the Liberal Arts.

3:30 pm in 341 Altgeld Hall,Wednesday, January 22, 2020

Organizational meeting

4:00 pm in 245 Altgeld Hall,Wednesday, January 22, 2020

Statistical reduced models and rigorous analysis for uncertainty quantification of turbulent dynamical systems

Di Qi   [email] (Courant Institute of Mathematical Sciences)

Abstract: The capability of using imperfect statistical reduced-order models to capture crucial statistics in turbulent flows is investigated. Much simpler and more tractable block-diagonal models are proposed to approximate the complex and high-dimensional turbulent flow equations. A rigorous statistical bound for the total statistical uncertainty is derived based on a statistical energy conservation principle. The systematic framework of correcting model errors is introduced using statistical response and empirical information theory, and optimal model parameters under this unbiased information measure are achieved in a training phase before the prediction. It is demonstrated that crucial principal statistical quantities in the most important large scales can be captured efficiently with accuracy using the reduced-order model in various dynamical regimes with distinct statistical structures.