Related papers: Variable Screenings in Binary Response Regressions…
Traditionally, the least squares regression is mainly concerned with studying the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects.…
Shuffled regression concerns settings in which covariates and responses are observed without their correct pairing. In dependent-data problems, a second form of missing correspondence can arise when responses are also detached from the…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
For the binary regression, the use of symmetrical link functions are not appropriate when we have evidence that the probability of success increases at a different rate than decreases. In these cases, the use of link functions based on the…
Conformal inference has played a pivotal role in providing uncertainty quantification for black-box ML prediction algorithms with finite sample guarantees. Traditionally, conformal prediction inference requires a data-independent…
We develop a framework for post model selection inference, via marginal screening, in linear regression. At the core of this framework is a result that characterizes the exact distribution of linear functions of the response $y$,…
Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…
We introduce a quantile-adaptive framework for nonlinear variable screening with high-dimensional heterogeneous data. This framework has two distinctive features: (1) it allows the set of active variables to vary across quantiles, thus…
Structured prediction involves learning to predict complex structures rather than simple scalar values. The main challenge arises from the non-Euclidean nature of the output space, which generally requires relaxing the problem formulation.…
Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we…
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…
Peer prediction mechanisms incentivize agents to truthfully report their signals even in the absence of verification by comparing agents' reports with those of their peers. In the detail-free multi-task setting, agents respond to multiple…
Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…
In the classical setting of self-selection, the goal is to learn $k$ models, simultaneously from observations $(x^{(i)}, y^{(i)})$ where $y^{(i)}$ is the output of one of $k$ underlying models on input $x^{(i)}$. In contrast to mixture…
Fan and Lv (2008) proposed the path-breaking theory of sure independence screening (SIS) and an iterative algorithm (ISIS) to effectively reduce the predictor dimension for further variable selection approaches. Fan et al. (2009) extended…
Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semiparametric efficiency theory for more…
The evaluation and post-training of large language models (LLMs) rely on supervision, but strong supervision for difficult tasks is often unavailable, especially when evaluating frontier models. In such cases, models are demonstrated to…
Ultrahigh dimensional data sets are becoming increasingly prevalent in areas such as bioinformatics, medical imaging, and social network analysis. Sure independent screening of such data is commonly used to analyze such data. Nevertheless,…
For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…