相关论文: Depth induced regression medians and uniqueness

Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures how good of a regression hyperplane a given query hyperplane is with respect to a set of data points. Under projective duality, this can be interpreted…

This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…

Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…

Users of a personalised recommendation system face a dilemma: recommendations can be improved by learning from data, but only if the other users are willing to share their private information. Good personalised predictions are vitally…

In general, Deep Neural Networks (DNNs) are evaluated by the generalization performance measured on unseen data excluded from the training phase. Along with the development of DNNs, the generalization performance converges to the…

We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and…

Prompting has become an important mechanism by which users can more effectively interact with many flavors of foundation model. Indeed, the last several years have shown that well-honed prompts can sometimes unlock emergent capabilities…

In this paper, we study the properties of robust nonparametric estimation using deep neural networks for regression models with heavy tailed error distributions. We establish the non-asymptotic error bounds for a class of robust…

In the conventional regression-discontinuity (RD) design, the probability that units receive a treatment changes discontinuously as a function of one covariate exceeding a threshold or cutoff point. This paper studies an extended RD design…

Accurate monocular metric depth estimation (MMDE) is crucial to solving downstream tasks in 3D perception and modeling. However, the remarkable accuracy of recent MMDE methods is confined to their training domains. These methods fail to…

Estimating depth from RGB images can facilitate many computer vision tasks, such as indoor localization, height estimation, and simultaneous localization and mapping (SLAM). Recently, monocular depth estimation has obtained great progress…

The concept of median/consensus has been widely investigated in order to provide a statistical summary of ranking data, i.e. realizations of a random permutation $\Sigma$ of a finite set, $\{1,\; \ldots,\; n\}$ with $n\geq 1$ say. As it…

We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…

The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…

This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…

Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large…

Randomized coordinate descent (RCD) methods are state-of-the-art algorithms for training linear predictors via minimizing regularized empirical risk. When the number of examples ($n$) is much larger than the number of features ($d$), a…

In machine learning and statistical data analysis, we often run into objective function that is a summation: the number of terms in the summation possibly is equal to the sample size, which can be enormous. In such a setting, the stochastic…

Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…

The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…