Motivated by the empirical power law of the distributions of credits (e.g., the number of "likes") of viral posts in social media, we introduce the high-dimensional tail index regression and methods of estimation and inference for its parameters. We propose a regularized estimator, establish its consistency, and derive its convergence rate. To conduct inference, we propose to debias the regularized estimate, and establish the asymptotic normality of the debiased estimator. Simulation studies support our theory. These methods are applied to text analyses of viral posts in X (formerly Twitter) concerning LGBTQ+.

In this post, we summarise the final two invited talks from the International Conference on Machine Learning (ICML 2022). These presentations covered estimation and inference for causal effects, and machine learning for drug discovery and development. Guido's talk covered the topic of estimation and inference for causal effects in panel data settings, in particular focussing on synthetic control methods and difference-in-difference methods. These methods are very popular in the empirical literature in economics, but many questions remain concerning causal effects in these settings. There has been a lot of recent theoretical work trying to improve practices in this field.

The estimation of Average Treatment Effect (ATE) as a causal parameter is carried out in two steps, wherein the first step, the treatment, and outcome are modeled to incorporate the potential confounders, and in the second step, the predictions are inserted into the ATE estimators such as the Augmented Inverse Probability Weighting (AIPW) estimator. Due to the concerns regarding the nonlinear or unknown relationships between confounders and the treatment and outcome, there has been an interest in applying non-parametric methods such as Machine Learning (ML) algorithms instead. \cite{farrell2018deep} proposed to use two separate Neural Networks (NNs) where there's no regularization on the network's parameters except the Stochastic Gradient Descent (SGD) in the NN's optimization. Our simulations indicate that the AIPW estimator suffers extensively if no regularization is utilized. We propose the normalization of AIPW (referred to as nAIPW) which can be helpful in some scenarios. nAIPW, provably, has the same properties as AIPW, that is double-robustness and orthogonality \citep{chernozhukov2018double}. Further, if the first step algorithms converge fast enough, under regulatory conditions \citep{chernozhukov2018double}, nAIPW will be asymptotically normal.

Many privacy mechanisms reveal high-level information about a data distribution through noisy measurements. It is common to use this information to estimate the answers to new queries. In this work, we provide an approach to solve this estimation problem efficiently using graphical models, which is particularly effective when the distribution is high-dimensional but the measurements are over low-dimensional marginals. We show that our approach is far more efficient than existing estimation techniques from the privacy literature and that it can improve the accuracy and scalability of many state-of-the-art mechanisms.

The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite strong motivation from biostatistics applications, high-dimensional Fine-Gray model has attracted relatively little attention among the methodological or theoretical literatures. We fill in this blank by proposing first a consistent regularized estimator and then the confidence intervals based on the one-step bias-correcting estimator. We are able to generalize the partial likelihood approach for the Fine-Gray model under random censoring despite many technical difficulties. We lay down a methodological and theoretical framework for the one-step bias-correcting estimator with the partial likelihood, which does not have independent and identically distributed entries. We also handle for our theory the approximation error from the inverse probability weighting (IPW), proposing novel concentration results for time dependent processes. In addition to the theoretical results and algorithms, we present extensive numerical experiments and an application to a study of non-cancer mortality among prostate cancer patients using the linked Medicare-SEER data.