Related papers: Isotonic Distributional Regression
Isotonic regression is a standard problem in shape-constrained estimation where the goal is to estimate an unknown nondecreasing regression function $f$ from independent pairs $(x_i, y_i)$ where $\mathbb{E}[y_i]=f(x_i), i=1, \ldots n$.…
Prediction, in regression and classification, is one of the main aims in modern data science. When the number of predictors is large, a common first step is to reduce the dimension of the data. Sufficient dimension reduction (SDR) is a well…
The sample-based Gibbs sampler has been the dominant method for approximating joint distribution from a collection of compatible full-conditional distributions. However for conditionally specified model, mixtures of incompatible full and…
For modeling the serial dependence in time series of counts, various approaches have been proposed in the literature. In particular, models based on a recursive, autoregressive-type structure such as the well-known integer-valued…
Synthesizing information from multiple data sources is crucial for constructing accurate individualized treatment rules (ITRs). However, privacy concerns often present significant barriers to the integrative analysis of such multi-source…
We investigate nonparametric estimation of sliced inverse regression (SIR) via the $k$-nearest neighbors approach with a kernel. An estimator of the covariance matrix of the conditional expectation of the explanatory random vector given the…
Regression trees are a popular machine learning algorithm that fit piecewise constant models by recursively partitioning the predictor space. This paper focuses on statistical inference for a data-dependent model obtained from a fitted…
In many real-world regression tasks, the data distribution is heavily skewed, and models learn predominantly from abundant majority samples while failing to predict minority labels accurately. While imbalanced classification has been…
Out-Of-Distribution (OOD) generalization is an essential topic in machine learning. However, recent research is only focusing on the corresponding methods for neural networks. This paper introduces a novel and effective solution for OOD…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
Artificial intelligence has advanced quantitative remote sensing, yet its effectiveness is constrained by imbalanced label distribution. This imbalance leads conventionally trained models to favor common samples, which in turn degrades…
Statistical depth, a useful tool to measure the center-outward rank of multivariate and functional data, is still under-explored in temporal point processes. Recent studies on point process depth proposed a weighted product of two terms -…
A major family of sufficient dimension reduction (SDR) methods, called inverse regression, commonly require the distribution of the predictor $X$ to have a linear $E(X|\beta^\mathsf{T}X)$ and a degenerate $\mathrm{var}(X|\beta^\mathsf{T}X)$…
Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…
Divergence From Randomness (DFR) ranking models assume that informative terms are distributed in a corpus differently than non-informative terms. Different statistical models (e.g. Poisson, geometric) are used to model the distribution of…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
In many real-world applications of machine learning classifiers, it is essential to predict the probability of an example belonging to a particular class. This paper proposes a simple technique for predicting probabilities based on…
We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…
Sliced inverse regression (SIR) is the most widely-used sufficient dimension reduction method due to its simplicity, generality and computational efficiency. However, when the distribution of the covariates deviates from the multivariate…
In this paper, we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed. We propose a correspondent mini-max problem for nonlinear regression and give a numerical…