相关论文: Depth induced regression medians and uniqueness

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity…

We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…

Unsupervised deep learning is one of the most powerful representation learning techniques. Restricted Boltzman machine, sparse coding, regularized auto-encoders, and convolutional neural networks are pioneering building blocks of deep…

Deep neural networks have achieved tremendous success due to their representation power and adaptation to low-dimensional structures. Their potential for estimating structured regression functions has been recently established in the…

Ridge regression with random coefficients provides an important alternative to fixed coefficients regression in high dimensional setting when the effects are expected to be small but not zeros. This paper considers estimation and prediction…

Depth estimation plays a pivotal role in advancing human-robot interactions, especially in indoor environments where accurate 3D scene reconstruction is essential for tasks like navigation and object handling. Monocular depth estimation,…

We propose a robust method for averaging numbers contaminated by a large proportion of outliers. Our method, dubbed RODIAN, is inspired by the key idea of MINPRAN [1]: We assume that the outliers are uniformly distributed within the range…

In this article, we propose a class of semiparametric mixture regression models with single-index. We argue that many recently proposed semiparametric/nonparametric mixture regression models can be considered special cases of the proposed…

This work examines risk bounds for nonparametric distributional regression estimators. For convex-constrained distributional regression, general upper bounds are established for the continuous ranked probability score (CRPS) and the…

In this Element and its accompanying Element, Matias D. Cattaneo, Nicolas Idrobo, and Rocio Titiunik provide an accessible and practical guide for the analysis and interpretation of Regression Discontinuity (RD) designs that encourages the…

There have been numerous recently proposed methods for monocular depth prediction (MDP) coupled with the equally rapid evolution of benchmarking tools. However, we argue that MDP is currently witnessing benchmark over-fitting and relying on…

The issue of spatial confounding between the spatial random effect and the fixed effects in regression analyses has been identified as a concern in the statistical literature. Multiple authors have offered perspectives and potential…

This paper proposes an extension of Random Projection Depth (RPD) to cope with multiple modalities and non-convexity on data clouds. In the framework of the proposed method, the RPD is computed in a reproducing kernel Hilbert space. With…

Most data sets comprise of measurements on continuous and categorical variables. In regression and classification Statistics literature, modeling high-dimensional mixed predictors has received limited attention. In this paper we study the…

Autoencoders have achieved great success in various computer vision applications. The autoencoder learns appropriate low dimensional image representations through the self-supervised paradigm, i.e., reconstruction. Existing studies mainly…

For non-randomized studies, the regression discontinuity design (RDD) can be used to identify and estimate causal effects from a "locally-randomized" subgroup of subjects, under relatively mild conditions. However, current models focus…

We propose a new estimation method for heterogeneous causal effects which utilizes a regression discontinuity (RD) design for multiple datasets with different thresholds. The standard RD design is frequently used in applied researches, but…

Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…

This work investigates the ways in which deep learning methods can benefit from random projection (RP), a classic linear dimensionality reduction method. We focus on two areas where, as we have found, employing RP techniques can improve…

We develop $(\epsilon,\delta)$-differentially private projection-depth-based medians using the propose-test-release (PTR) and exponential mechanisms. Under general conditions on the input parameters and the population measure, (e.g. we do…