Related papers: Beyond Consistency: Inference for the Relative ris…
We study the flexible piecewise exponential model in a high dimensional setting where the number of covariates $p$ grows proportionally to the number of observations $n$ and under the hypothesis of random uncorrelated Gaussian designs. We…
We study the estimation of distributional treatment effects in randomized experiments with imperfect compliance. When participants do not adhere to their assigned treatments, we leverage treatment assignment as an instrumental variable to…
The proportional hazards model has been extensively used in many fields such as biomedicine to estimate and perform statistical significance testing on the effects of covariates influencing the survival time of patients. The classical…
In this paper we address the challenges posed by non-proportional hazards and informative censoring, offering a path toward more meaningful causal inference conclusions. We start from the marginal structural Cox model, which has been widely…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
The Cox proportional hazards model (Cox model) is a popular model for survival data analysis. When the sample size is small relative to the dimension of the model, the standard maximum partial likelihood inference is often problematic. In…
Cox's proportional hazards model is one of the most popular statistical models to evaluate associations of exposure with a censored failure time outcome. When confounding factors are not fully observed, the exposure hazard ratio estimated…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
This paper investigates the partial linear model by Least Absolute Deviation (LAD) regression. We parameterize the nonparametric term using Deep Neural Networks (DNNs) and formulate a penalized LAD problem for estimation. Specifically, our…
Weighted empirical risk minimization is a common approach to prediction under distribution drift. This article studies its out-of-sample prediction error under nonstationarity. We provide a general decomposition of the excess risk into a…
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…
Establishing a theoretical analysis that explains why deep learning can outperform shallow learning such as kernel methods is one of the biggest issues in the deep learning literature. Towards answering this question, we evaluate excess…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
Regularization in fitting regression models has been a highly active topic of research in the past few decades, but most of the existing methods are designed for particular situations, e.g. for the case of a sparse coefficient vector. We…
We consider the problem of model selection type aggregation in the context of density estimation. We first show that empirical risk minimization is sub-optimal for this problem and it shares this property with the exponential weights…
The Cox proportional hazards model is a canonical method in survival analysis for prediction of the life expectancy of a patient given clinical or genetic covariates -- it is a linear model in its original form. In recent years, several…
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…
Risk estimation is at the core of many learning systems. The importance of this problem has motivated researchers to propose different schemes, such as cross validation, generalized cross validation, and Bootstrap. The theoretical…