Related papers: Dealing with Logs and Zeros in Regression Models
We consider a general statistical linear inverse problem, where the solution is represented via a known (possibly overcomplete) dictionary that allows its sparse representation. We propose two different approaches. A model selection…
We study the estimation of average effects in nonlinear panel data models with fixed effects when the time dimension $T$ is only moderately large. Our approach, called approximate operator inversion (AOI), offers a new perspective on bias…
Adaptive experiments, including efficient average treatment effect estimation and multi-armed bandit algorithms, have garnered attention in various applications, such as social experiments, clinical trials, and online advertisement…
We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized 'labeled' data, and (ii) a much larger sized 'unlabeled' data. Such data arises…
Regression analysis is a central topic in statistical modeling, aimed at estimating the relationships between a dependent variable, commonly referred to as the response variable, and one or more independent variables, i.e., explanatory…
Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis…
We propose a rate optimal estimator for the linear regression model on network data with interacted (unobservable) individual effects. The estimator achieves a faster rate of convergence $N$ compared to the standard estimators' $\sqrt{N}$…
The statistical essence of the Transformer architecture has long remained elusive: Is it a universal approximator, or a neural network version of known computational algorithms? Through rigorous algebraic proof, we show that the latter…
Deep learning models, especially convolutional neural networks, have achieved impressive results in medical image classification. However, these models often produce overconfident predictions, which can undermine their reliability in…
We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of $K$ unknown linear models. In practical applications, the proportions of the $K$ components are often imbalanced. Unfortunately, most MLR…
Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately.…
Contingency tables are a fundamental representation of multivariate categorical data. As the size of the contingency table grows exponentially with the number of variables, even a moderate number of variables, each with a moderate number of…
Induced order statistics (IOS) arise when sample units are reordered according to the value of an auxiliary variable, and the associated responses are analyzed in that induced order. IOS play a central role in applications where the goal is…
In Generalized Linear Models (GLMs) it is assumed that there is a linear effect of the predictor variables on the outcome. However, this assumption is often too strict, because in many applications predictors have a nonlinear relation with…
Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. The conventional approach of model building…
Missing data are inevitable in clinical trials, and trials that produce categorical ordinal responses are not exempted from this. Typically, missing values in the data occur due to different missing mechanisms, such as missing completely at…
The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…
This paper investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…
Predicting simple function classes has been widely used as a testbed for developing theory and understanding of the trained Transformer's in-context learning (ICL) ability. In this paper, we revisit the training of Transformers on linear…
Orthogonal least square (OLS) is an important sparse signal recovery algorithm for compressive sensing, which enjoys superior probability of success over other well-known recovery algorithms under conditions of correlated measurement…