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pro vyhledávání: '"Tian, Songtao"'
Autor:
Tian, Songtao, Yu, Zixiong
Deep Residual Neural Networks (ResNets) have demonstrated remarkable success across a wide range of real-world applications. In this paper, we identify a suitable scaling factor (denoted by $\alpha$) on the residual branch of deep wide ResNets to ach
Externí odkaz:
http://arxiv.org/abs/2403.04545
Functional sliced inverse regression (FSIR) is one of the most popular algorithms for functional sufficient dimension reduction (FSDR). However, the choice of slice scheme in FSIR is critical but challenging. In this paper, we propose a new method ca
Externí odkaz:
http://arxiv.org/abs/2307.12537
In this paper, we prove that functional sliced inverse regression (FSIR) achieves the optimal (minimax) rate for estimating the central space in functional sufficient dimension reduction problems. First, we provide a concentration inequality for the
Externí odkaz:
http://arxiv.org/abs/2307.02777
In this paper, we study the generalization ability of the wide residual network on $\mathbb{S}^{d-1}$ with the ReLU activation function. We first show that as the width $m\rightarrow\infty$, the residual network kernel (RNK) uniformly converges to th
Externí odkaz:
http://arxiv.org/abs/2305.18506
In this work, we address the longstanding puzzle that Sliced Inverse Regression (SIR) often performs poorly for sufficient dimension reduction when the structural dimension $d$ (the dimension of the central space) exceeds 4. We first show that in the
Externí odkaz:
http://arxiv.org/abs/2305.04340
Autor:
Luo, Saidi, Tian, Songtao
State equations (SEs) were firstly introduced in the approximate message passing (AMP) to describe the mean square error (MSE) in compressed sensing. Since then a set of state equations have appeared in studies of logistic regression, robust estimato
Externí odkaz:
http://arxiv.org/abs/2209.12156
Akademický článek
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Autor:
Tian, Songtao, Liu, Zhirong
Publikováno v:
In Physica A: Statistical Mechanics and its Applications 1 January 2020 537
The central space of a joint distribution $(\vX,Y)$ is the minimal subspace $\mathcal S$ such that $Y\perp\hspace{-2mm}\perp \vX \mid P_{\mathcal S}\vX$ where $P_{\mathcal S}$ is the projection onto $\mathcal S$. Sliced inverse regression (SIR), one
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c2856e1ccb710311daaa42f732e6563