Owning Your Research: Things I wish I knew for graduate study
Pursuing graduate study is a courageous decision for life that takes time, effort, and commitment. Graduate study can be mysterious at the beginning, miserable in the process, and marvelous at the end. As a recent grad, I am going to share some of my graduate study experiences in this presentation. In particular, I hope to give some advice to current graduate students to make their graduate study easier, faster, and happier. Among other recommendations, I will provide some tricks and tips on coding that can improve research productivity.
Challenges in Developing Learning Algorithms to Personalize Treatment in Real Time
A formidable challenge in designing sequential treatments is to determine when and in which context it is best to deliver treatments. Consider treatment for individuals struggling with chronic health conditions. Operationally designing the sequential treatments involves the construction of decision rules that input current context of an individual and output a recommended treatment. That is, the treatment is adapted to the individual's context; the context may include current health status, current level of social support and current level of adherence for example. Data sets on individuals with records of time-varying context and treatment delivery can be used to inform the construction of the decision rules. There is much interest in personalizing the decision rules, particularly in real time as the individual experiences sequences of treatment. Here we discuss our work in designing online "bandit" learning algorithms for use in personalizing mobile health interventions.
Statistically and Numerically Efficient Independence Test
We study how to generate a statistical inference procedure that is both computational efficient and having theoretical guarantee on its statistical performance. Test of independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation based hypotheses testing for independence) have numerous advantages, comparing with many other alternatives. A known limitation of the distance-based method is that its computational complexity can be high. In general, when the sample size is n, the order of computational complexity of a distance-based method, which typically requires computing of all pairwise distances, can be O(n^2). Recent advances have discovered that in the univariate cases, a fast method with O(n log n) computational complexity and O(n) memory requirement exists. In this talk, I introduce a test of independence method based on random projection and distance correlation, which achieves nearly the same power as the state-of-the-art distance-based approach, works in the multivariate cases, and enjoys the O(n K log n) computational complexity and O(max{n,K}) memory requirement, where K is the number of random projections. Note that saving is achieved when K < n/ log n. We name our method a Randomly Projected Distance Covariance (RPDC). The statistical theoretical analysis takes advantage of some techniques on random projection, which are rooted in contemporary machine learning. Numerical experiments demonstrate the efficiency of the proposed method, in relative to several competitors.
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Estimation of the expected shortfall given an extreme component under conditional extreme value model
For two risks, $X$, and $Y$ , the Marginal Expected Shortfall (MES) is defined as $E[Y \mid X > x]$, where $x$ is large. MES is an important factor when measuring the systemic risk of financial institutions. In this talk we will discuss consistency and asymptotic normality of an estimator of MES on assuming that $(X, Y)$ follows a Conditional Extreme Value (CEV) model. The theoretical findings are supported by simulation studies. Our procedure is applied to some financial data. This is a joint work with Kevin Tong (Bank of Montreal).
Analysis of Clinical Trials with Multiple Outcomes
In order to obtain better overall knowledge of a treatment effect, investigators in clinical trials often collect many medically related outcomes, which are commonly called as endpoints. It is fundamental to understand the objectives of a particular analysis before applying any adjustment for multiplicity. For example, multiplicity does not always lead to error rate inflation, or multiplicity may be introduced for purpose other than making an efficacy or safety claim such as in sensitivity assessments. Sometimes, the multiple endpoints in clinical trials can be hierarchically ordered and logically related. In this talk, we will discuss the methods to analyze multiple outcomes in clinical trials with different objectives: all or none approach, global approach, composite endpoint, at-least-one approach.
