Related papers: Wasserstein Regression with Empirical Measures and…
Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies,…
Distributionally robust stochastic optimization (DRSO) is an approach to optimization under uncertainty in which, instead of assuming that there is a known true underlying probability distribution, one hedges against a chosen set of…
The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the…
Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons:…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…
In real-world regression tasks, datasets frequently exhibit imbalanced distributions, characterized by a scarcity of data in high-complexity regions and an abundance in low-complexity areas. This imbalance presents significant challenges…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional…
We develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
We revisit Markowitz's mean-variance portfolio selection model by considering a distributionally robust version, where the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures…
Classical regression models do not cover non-Euclidean data that reside in a general metric space, while the current literature on non-Euclidean regression by and large has focused on scenarios where either predictors or responses are…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distribution with local probability weights satisfying the conditions of Stone's theorem provide…
Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…