相关论文: A dimensional R2 regression metric

In this study, we explore the effects of including noise predictors and noise observations when fitting linear regression models. We present empirical and theoretical results that show that double descent occurs in both cases, albeit with…

In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the…

Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…

This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…

We revisit the classical problem of comparing regression functions, a fundamental question in statistical inference with broad relevance to modern applications such as data integration, transfer learning, and causal inference. Existing…

The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are…

Doubly robust (DR) estimators guard against model misspecification but remain sensitive to weak covariate overlap. We show that trimming propensity scores reduces variance but eliminates double robustness. We introduce DR estimators that…

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the…

There are several ways to measure the compressibility of a random measure; they include general approaches such as using the rate-distortion curve, as well as more specific notions, such as the Renyi information dimension (RID). The RID…

We construct confidence sets for the regression function in nonparametric binary regression with an unknown design density. These confidence sets are adaptive in $L^2$ loss over a continuous class of Sobolev type spaces. Adaptation holds in…

In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…

This paper introduces a novel deep metric learning-based semi-supervised regression (DML-S2R) method for parameter estimation problems. The proposed DML-S2R method aims to mitigate the problems of insufficient amount of labeled samples…

Minimax $L_2$ risks for high-dimensional nonparametric regression are derived under two sparsity assumptions: (1) the true regression surface is a sparse function that depends only on $d=O(\log n)$ important predictors among a list of $p$…

We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…

Our study introduces ResNet-L2 (RL2), a novel metric for evaluating generative models and image quality in histopathology, addressing limitations of traditional metrics, such as Frechet inception distance (FID), when the data is scarce. RL2…

This paper presents a novel self-supervised two-frame multi-camera metric depth estimation network, termed M${^2}$Depth, which is designed to predict reliable scale-aware surrounding depth in autonomous driving. Unlike the previous works…

Regression plays an essential role in many medical imaging applications for estimating various clinical risk or measurement scores. While training strategies and loss functions have been studied for the deep neural networks in medical image…

Deep Metric Learning (DML) plays a critical role in various machine learning tasks. However, most existing deep metric learning methods with binary similarity are sensitive to noisy labels, which are widely present in real-world data. Since…

Detecting uncertainty in large language models (LLMs) is essential for building reliable systems, yet many existing approaches are overly complex and depend on brittle semantic clustering or access to model internals. We introduce Radial…