Question
Q. 隨時有效矩陣迴歸所需的相關文獻?
Q. 隨時有效矩陣迴歸所需的相關文獻?
Literature
Reduced rank regression
🤔 2013: Reduced rank regression via adaptive nuclear norm penalization :
- (a) reduced-rank estimation method for the general high-dimensional multivariate regression problems.
- (b) low-rank matrix approximation problem. 低rank矩陣逼近.
- (c) its low-rank approximation for denoising, which can be achieved by various methods, e.g., rank penalization or nuclear norm penalization. 核範數懲罰.
😍 2018: Generalized high-dimensional trace regression via nuclear norm regularization Journal Version :
- (a) reduced-rank regression, matrix regression that accommodates a panel of regressors, matrix completion, among others 有矩陣填充.
- (b) 我們是always-valid的statistical error rate of $\hat{\Theta}$.
- (c) 我們的版本match 最小化negative log-likelihood plus nuclear norm penalty.
- (d) One-bit matrix completion: Related to our work is the matrix completion problem with binary entry, i.e., 1-bit matrix completion, which is a specific example of our generalized trace regression and has direct application in predicting aforementioned P2P microfinance.
- 引用情況
先用這篇文章來幫忙Revise.
1@article{chen2013reduced,
2 title={Reduced rank regression via adaptive nuclear norm penalization},
3 author={Chen, Kun and Dong, Hongbo and Chan, Kung-Sik},
4 journal={Biometrika},
5 volume={100},
6 number={4},
7 pages={901--920},
8 year={2013},
9 publisher={Oxford University Press}
10}
11@article{fan2019generalized,
12 title={Generalized high-dimensional trace regression via nuclear norm regularization},
13 author={Fan, Jianqing and Gong, Wenyan and Zhu, Ziwei},
14 journal={Journal of econometrics},
15 volume={212},
16 number={1},
17 pages={177--202},
18 year={2019},
19 publisher={Elsevier}
20}
Low-Rank bandit
- Low-rank generalized linear bandit problems : 裡面regret的關鍵, 是否是estimation error?
Matrix Game
🤩 UAI2021: sMatrix games with bandit feedback
- (a) Payment of two players: $r_{t}=A_{i_{t} j_{t}}+\eta_{t}$. 與我們的模型$y_{t}=g\left(\Theta_{\pi_{t}}^{*}\right)+\epsilon_{t}$比較, 這模型幾乎一樣！只是它是linear, 我們可以是GLM.
- (b) 如何探索? 使用UCB for matrix games.
- (c) 也可以使用Thompson sampling for matrix games
- (d) 還可以做Entropy based的探索
在我們的框架中, 好的Statistical error對regret有幫助嗎? 感覺技術難點是怎麼讓sample足夠, 使其good event有好結果. 所以, 套路是, 我們可以用不同的「探索機制」來組合我們的「隨時有效統計誤差結果」. 這個蠻酷的, 均衡探索與剝削.
評論