Schedule for: 22w5144 - Dynamics and Data Assimilation, Physiology and Bioinformatics: Mathematics at the Interface of Theory and Clinical Application

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

We will present vignettes from our modeling work on diabetes, insulin secretion, and reproductive hormones to illustrate why and how mechanistic models of physiology are developed and tested and the sorts of physiological insight they provide.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

We will present vignettes from our modeling work on diabetes, insulin secretion, and reproductive hormones to illustrate why and how mechanistic models of physiology are developed and tested and the sorts of physiological insight they provide.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

We will discuss adapting our longitudinal model for diabetes progression to a model for obtaining snapshots of glucose tolerance status. We set the slow variables that govern progression to constants and fit glucose and insulin from a five-point OGTT to obtain estimates for insulin sensitivity and beta-cell function. Correlation and agreement with estimates obtained from MINMOD and clamp will be shown, along with estimates of precision of parameter estimates.

This talk will discuss how optimal transport-inspired techniques can help make individualized predictions, taking into account not only quantifiable factors but also idiosyncratic ones. Examples of quantifiable factors are a patient’s age and the amount of carbohydrates in a meal, while idiosyncratic factors may characterize for instance how a particular individual or group responds to treatment or the differential effect on glucose level of food of a particular origin. In an optimal transport framework, quantifiable factors appear as parameters of a transportation map, while idiosyncratic factors are addressed through a unique form of sub-sampling.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Characterizing the evolution of female hormonal dynamics is a challenging task, but a critical one to improve general understanding of the menstrual cycle. The goal is to reconstruct and forecast individual daily hormone levels over time, while accommodating pragmatic and minimally invasive measurement settings. To that end, we present an end-to-end statistical framework for personalized and accurate modeling of female reproductive hormonal patterns. Our approach combines the power of probabilistic generative models (i.e., multi-task Gaussian processes) with the flexibility of neural networks (i.e., a dilated convolutional architecture) to learn complex temporal mappings. The framework provides accurate predictive performance across different realistic sampling budgets.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Reinforcement learning (RL) methods for estimating an optimal policy are traditionally categorized as being model-based or model-free. Model-based methods ex- tract an estimated optimal policy from estimated system dynamics. In contrast, model-free methods estimate only a portion of the dynamics model which is sufficient to identify the optimal policy, e.g., a state-action value function. Model-based RL is efficient when there is strong domain knowledge to inform a high-quality and parsimonious system dynamics model; however, if the posited system dynamics model is misspecified the resulting policy can perform poorly. In contrast, model-free methods impose less structure and are thus less prone to misspecification; however, they are less efficient and can be unstable when data are scarce. The strengths and weaknesses of model-based and model-free estima- tors dovetail. It is therefore natural to try and combine them to obtain the strengths of both approaches and the weaknesses of neither. We propose a model-assisted estimator that uses a model of the system dynamics model to increase efficiency and robustness of model-based methods. We show the proposed estimator is: (i) consistent if the model-free method is derived from a unbiased estimating equation; (ii) optimizes the projection of the value function onto the model-class if the estimating equation is biased but the dynamics model is correctly specified; and (iii) asymptotically efficient if the estimating equations are unbiased and the system dynamics model is correctly specified. In simulation experi- ments, the model-assisted estimator performs favorably to state-of-the-art model-free and model-based methods in terms of expected cumulative utility.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.