Current graduate students

Censoring Unbiased Regression Trees and Ensembles

Tree-based methods are useful tools to identify risk groups and conduct prediction by employing recursive partitioning to separate subjects into different risk groups. We propose a novel paradigm of building regression trees for censored data in survival analysis. We prudently construct the censored-data loss function through an extension of the theory of censoring unbiased transformations. With the construction, we can conveniently implement the proposed regression trees algorithm using existing software for the Classification and Regression Trees algorithm (e.g., rpart package in R) and extend it for ensemble learning. Simulations and real data examples demonstrate that our methods either improve upon or remain competitive with existing tree-based algorithms for censored data.

Detecting the Signal Among Noise and Contamination in High Dimensions

Improvements in biomedical technology and a surge in other data-driven sciences lead to the collection of increasingly large amounts of data. In this affluence of data, contamination is ubiquitous but often neglected, creating substantial risk of spurious scientific discoveries. Especially in applications with high-dimensional data, for instance proteomic biomarker discovery, the impact of contamination on methods for variable selection and estimation can be profound yet difficult to diagnose.

In this talk I present a method for variable selection and estimation in high-dimensional linear regression models, leveraging the elastic-net penalty for complex data structures. The method is capable of harnessing the collected information even in the presence of arbitrary contamination in the response and the predictors. I showcase the method’s theoretical and practical advantages, specifically in applications with heavy-tailed errors and limited control over the data. I outline efficient algorithms to tackle computational challenges posed by inherently non-convex objective functions of robust estimators and practical strategies for hyper-parameter selection, ensuring scalability of the method and applicability to a wide range of problems.

Batch-mode active learning for regression and its application to the valuation of large variable annuity portfolios

Supervised learning algorithms require a sufficient amount of labeled data to construct an accurate predictive model. In practice, collecting labeled data may be extremely time-consuming while unlabeled data can be easily accessed. In a situation where labeled data are insufficient for a prediction model to perform well and the budget for an additional data collection is limited, it is important to effectively select objects to be labeled based on whether they contribute to a great improvement in the model's performance. In this talk, I will focus on the idea of active learning that aims to train an accurate prediction model with minimum labeling cost. In particular, I will present batch-mode active learning for regression problems. Based on random forest, I will propose two effective random sampling algorithms that consider the prediction ambiguities and diversities of unlabeled objects as measures of their informativeness. Empirical results on an insurance data set demonstrate the effectiveness of the proposed approaches in valuing large variable annuity portfolios (which is a practical problem in the actuarial field). Additionally, comparisons with the existing framework that relies on a sequential combination of unsupervised and supervised learning algorithms are also investigated.

Clustering and Classification of Three-Way Data

Clustering and classification is the process of finding and analyzing underlying group structure in heterogenous data and is fundamental to computational statistics and machine learning. In the past, relatively simple techniques could be used for clustering; however, with data becoming increasingly complex, these methods are oftentimes not advisable, and in some cases not possible. One such such example is the analysis of three-way data where each data point is represented as a matrix instead of a traditional vector. Examples of three-way include greyscale images and multivariate longitudinal data. In this talk, recent methods for clustering three-way data will be presented including high-dimensional and skewed three-way data. Both simulated and real data will be used for illustration and future directions and extensions will be discussed.

The possibility of nearly assumption-free inference in causal inference

In causal effect estimation, the state-of-the-art is the so-called double machine learning (DML) estimators, which combine the benefit of doubly robust estimation, sample splitting and using machine learning methods to estimate nuisance parameters. The validity of the confidence interval associated with a DML estimator, in most part, relies on the complexity of nuisance parameters and how close the machine learning estimators are to the nuisance parameters. Before we have a complete understanding of the theory of many machine learning methods including deep neural networks, even a DML estimator may have a bias so large that prohibits valid inference. In this talk, we describe a nearly assumption-free procedure that can either criticize the invalidity of the Wald confidence interval associated with the DML estimators of some causal effect of interest or falsify the certificates (i.e. the mathematical conditions) that, if true, could ensure valid inference. Essentially, we are testing the null hypothesis that if the bias of an estimator is smaller than a fraction $\rho$ its standard error. Our test is valid under the null without requiring any complexity (smoothness or sparsity) assumptions on the nuisance parameters or the properties of machine learning estimators and may have power to inform the analysts that they have to do something else than DML estimators or Wald confidence intervals for inference purposes. This talk is based on joint work with Rajarshi Mukherjee and James M. Robins.

Diagnostics for Regression Models with Discrete Outcomes

Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard residuals such as Pearson and deviance residuals for such outcomes often show a large discrepancy from the hypothesized pattern even under the true model and are not informative especially when data are highly discrete. To fill this gap, we propose a surrogate empirical residual distribution function for general discrete (e.g. ordinal and count) outcomes that serves as an alternative to the empirical Cox-Snell residual distribution function. When at least one continuous covariate is available, we show asymptotically that the proposed function converges uniformly to the identity function under the correctly specified model, even with highly discrete (e.g. binary) outcomes. Through simulation studies, we demonstrate empirically that the proposed surrogate empirical residual distribution function is highly effective for various diagnostic tasks, since it is close to the hypothesized pattern under the true model and significantly departs from this pattern under model misspecification.

Sufficient Dimension Reduction for Populations with Structured Heterogeneity

Risk modeling has become a crucial component in the effective delivery of health care. A key challenge in building effective risk models is accounting for patient heterogeneity among the diverse populations present in health systems. Incorporating heterogeneity based on the presence of various comorbidities into risk models is crucial for the development of tailored care strategies, as it can provide patient-centered information and can result in more accurate risk prediction. Yet, in the presence of high dimensional covariates, accounting for this type of heterogeneity can exacerbate estimation difficulties even with large sample sizes. Towards this aim, we propose a flexible and interpretable risk modeling approach based on semiparametric sufficient dimension reduction. The approach accounts for patient heterogeneity, borrows strength in estimation across related subpopulations to improve both estimation efficiency and interpretability, and can serve as a useful exploratory tool or as a powerful predictive model. In simulated examples, we show that our approach can improve estimation performance in the presence of heterogeneity and is quite robust to deviations from its key underlying assumption. We demonstrate the utility of our approach in the prediction of hospital admission risk for a large health system when tested on further follow-up data.

A Machine Learning Approach to Portfolio Risk Management

Risk measurement, valuation and hedging form an integral task in portfolio risk management for insurance companies and other financial institutions. Portfolio risk arises because the values of constituent assets and liabilities change over time in response to changes in the underlying risk factors. The quantification of this risk requires modeling the dynamic portfolio value process. This boils down to compute conditional expectations of future cash flows over long time horizons, e.g., up to 40 years and beyond, which is computationally challenging. 

This lecture presents a framework for dynamic portfolio risk management in discrete time building on machine learning theory. We learn the replicating martingale of the portfolio from a finite sample of its terminal cumulative cash flow. The learned replicating martingale is in closed form thanks to a suitable choice of the reproducing kernel Hilbert space. We develop an asymptotic theory and prove
convergence and a central limit theorem. We also derive finite sample error bounds and concentration inequalities. As application we compute the value at risk and expected shortfall of the one-year loss of some stylized portfolios.

Uncovering the Mechanisms of General Anesthesia: Where Neuroscience Meets Statistics

General anesthesia is a drug-induced, reversible condition involving unconsciousness, amnesia (loss of memory), analgesia (loss of pain sensation), akinesia (immobility), and hemodynamic stability. I will describe a primary mechanism through which anesthetics create these altered states of arousal. Our studies have allowed us to give a detailed characterization of the neurophysiology of loss and recovery of consciousness​, in the case of propofol, and we have demonstrated ​​ that the state of general anesthesia can be rapidly reversed by activating specific brain circuits. The success of our research has depended critically on tight coupling of experiments, ​statistical signal processing​​ and mathematical modeling.