Peter Hall and optimality and efficiency issues in smoothing in nonparametric and semiparametric estimation

Peter Hall and optimality and efficiency issues in smoothing in nonparametric and semiparametric estimation

Abstract: Smoothing techniques for data on (subsets of) the real line are well developed. The development of smoothing techniques (such as kernel and local polynomial methods) for directional data has taken large steps forward in the last decades. Peter made seminal contributions in this area too, and research today builds further on these. Many challenging questions regarding statistical inference for directional data (and more generally data in non-Euclidean settings), need to get attention. Some selected topics will be discussed during this talk, ranging from kernel density estimation, to methods for high-dimensional data.

Deep Learning for Censored Survival Data

Deep Learning for Censored Survival Data

Abstract: Unlike standard tasks, survival analysis requires modeling incomplete data, such as right-censored data, which must be treated with care. While deep neural networks excel in traditional supervised learning, it remains unclear how to best utilize these models in survival analysis. A key question asks which data-generating assumptions of traditional survival models should be retained and which should be made more flexible via the function-approximating capabilities of neural networks. In addition, most of these methods are difficult to interpret and mathematical understanding of them is lacking. In this talk, we explore these issues from two directions. First, we study the partially linear Cox model, where the nonlinear component of the model is implemented using a deep neural network. The proposed approach is flexible and able to circumvent the curse of dimensionality, yet it facilitates interpretability of the effects of treatment covariates on survival. Next, we introduce a Deep Extended Hazard (DeepEH) model to provide a flexible and general framework for deep survival analysis. The extended hazard model includes the conventional Cox proportional hazards and accelerated failure time models as special cases, so DeepEH subsumes the popular Deep Cox proportional hazard (DeepSurv) and Deep Accelerated Failure Time (DeepAFT) models. We provide theoretical support for the proposed models, which underscores the attractive feature that deep learning is able to detect low-dimensional structure of data in high-dimensional space. Numerical experiments further provide evidence that the proposed methods outperform existing statistical and deep learning approaches to survival analysis. Time permitting, we will explore how to perform hypothesis testing for survival data.

Bootstrapping out-of-sample predictability tests with real-time data

Bootstrapping out-of-sample predictability tests with real-time data

Abstract: In this paper we develop a block bootstrap approach to out-of-sample inference when real-time data are used to produce forecasts. In particular, we establish its first-order asymptotic validity for West-type (1996) tests of predictive ability in the presence of regular data revisions. This allows the user to conduct asymptotically valid inference without having to estimate the asymptotic variances derived in Clark and McCracken's (2009) extension of West (1996) when data are subject to revision. Monte Carlo experiments indicate that the bootstrap can provide satisfactory finite sample size and power even in modest sample sizes. We conclude with an application to inflation forecasting that adapts the results in Ang et al. (2007) to the presence of real-time data. This is joint work with Michael McCracken and Yongxu Yao
References:
Ang, A., Bekaert, G., and M. Wei (2007), ❝Do Macro Variables, Asset Markets, or Surveys Forecast Inflation Better?,❞ Journal of Monetary Economics, 54, 1163-1212.
Clark, T.E., and M.W. McCracken (2009), ❝Tests of Equal Predictive Ability with Real-Time Data,❞ Journal of Business and Economic Statistics 27, 441-54.
West, K.D. (1996), ❝Asymptotic Inference about Predictive Ability,❞ Econometrica, 64, 1067-1084.

Causality-inspired Statistical Machine Learning

Causality-inspired Statistical Machine Learning

Abstract: Reliable, robust and interpretable machine learning is a big emerging theme in data science and statistics, complementing the development of pure black box prediction algorithms. New connections between distributional robustness, external validity and causality provide methodological paths for improving the reliability and understanding of machine learning algorithms, with wide-ranging prospects for various applications.

Common atoms mixture models in two biostatistical inference problems

Common atoms mixture models in two biostatistical inference problems

Abstract: We consider two examples of statistical inference for two related populations. In one example we characterize two patient populations that are relevant in the construction of a clinical study design, and propose a method to adjust for detected differences. The second example is about characterizing immune cell populations under two biologic conditions of interest and identify shared versus condition-specific homogeneous cell subpopulations. Bayesian inference in both applications requires prior probability models for two or more related distributions. We build on extensive literature on such models based on Dirichlet process priors. Models are commonly known as dependent Dirichlet processes (DDP), with many variations and extensions beyond the Dirichlet process model. The special feature in the two motivating applications is the focus on differences in the heterogeneity of the related populations, with one application aiming to adjust for such differences, and the other application aiming to identify and understand immune cell subtypes that are characteristic for one or the other condition. We briefly review the extensive literature on DDP models and then introduce variations of DDP priors suitable for these inference goals. The common structure are common atoms mixture models with highly structured priors on the weights.

Specification tests for statistical models with recent results and applications

Specification tests for statistical models with recent results and applications

Abstract: Specification tests in statistical models refer to the assertion or rejection of some assumption about the statistical model structure. These cover well studied topics as for example the goodness-of-fit for distributions, densities or regression models between others. The objectives, in general, can be different: Testing if one regression model belongs to some parametric family, the comparison of the structure of k populations, testing the significance of covariates in one high dimensional regression model…etc. In this talk we will revise the different methodologies developed in the last 25 years (of my academic life) with recent results in complex models with some different applications.

Provably Fast and Accurate Estimation of Neural Nets

Provably Fast and Accurate Estimation of Neural Nets

Abstract: Recent developments in fast algorithms for relaxed greedy training of artificial neural networks are presented. Both guaranteed optimization procedures and greedy Bayes sampling procedures with rapid mixing are explored. Along with these algorithmic developments we present corresponding bounds for statistical risk and for online learning regret for predictions based on these neural network fits. This is based on joint work with Curtis McDonald of Yale University and Jason Klusowski of Princeton University.