Conditional Uncorrelation and Efficient Non-approximate Subset Selection in Sparse Regression

• URL: http://arxiv.org/abs/2009.03986v2
• Date: Tue, 24 Nov 2020 10:00:18 GMT
• Title: Conditional Uncorrelation and Efficient Non-approximate Subset Selection in Sparse Regression
• Authors: Jianji Wang, Qi Liu, Shupei Zhang, Nanning Zheng, Fei-Yue Wang
• Abstract summary: We consider sparse regression from the view of correlation, and propose the formula of conditional uncorrelation. By the proposed method, the computational complexity is reduced from $O(frac16k3+mk2+mkd)$ to $O(frac16k3+frac12mk2)$ for each candidate subset in sparse regression.
• Score: 72.84177488527398
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Given $m$ $d$-dimensional responsors and $n$ $d$-dimensional predictors, sparse regression finds at most $k$ predictors for each responsor for linear approximation, $1\leq k \leq d-1$. The key problem in sparse regression is subset selection, which usually suffers from high computational cost. Recent years, many improved approximate methods of subset selection have been published. However, less attention has been paid on the non-approximate method of subset selection, which is very necessary for many questions in data analysis. Here we consider sparse regression from the view of correlation, and propose the formula of conditional uncorrelation. Then an efficient non-approximate method of subset selection is proposed in which we do not need to calculate any coefficients in regression equation for candidate predictors. By the proposed method, the computational complexity is reduced from $O(\frac{1}{6}{k^3}+mk^2+mkd)$ to $O(\frac{1}{6}{k^3}+\frac{1}{2}mk^2)$ for each candidate subset in sparse regression. Because the dimension $d$ is generally the number of observations or experiments and large enough, the proposed method can greatly improve the efficiency of non-approximate subset selection.

Related papers

• Optimal level set estimation for non-parametric tournament and crowdsourcing problems [49.75262185577198]
  Motivated by crowdsourcing, we consider a problem where we partially observe the correctness of the answers of $n$ experts on $d$ questions. In this paper, we assume that the matrix $M$ containing the probability that expert $i$ answers correctly to question $j$ is bi-isotonic up to a permutation of it rows and columns. We construct an efficient-time algorithm that turns out to be minimax optimal for this classification problem.
  arXiv  Detail & Related papers  (2024-08-27T18:28:31Z)
• An Oblivious Stochastic Composite Optimization Algorithm for Eigenvalue Optimization Problems [76.2042837251496]
  We introduce two oblivious mirror descent algorithms based on a complementary composite setting. Remarkably, both algorithms work without prior knowledge of the Lipschitz constant or smoothness of the objective function. We show how to extend our framework to scale and demonstrate the efficiency and robustness of our methods on large scale semidefinite programs.
  arXiv  Detail & Related papers  (2023-06-30T08:34:29Z)
• Retire: Robust Expectile Regression in High Dimensions [3.9391041278203978]
  Penalized quantile and expectile regression methods offer useful tools to detect heteroscedasticity in high-dimensional data. We propose and study (penalized) robust expectile regression (retire) We show that the proposed procedure can be efficiently solved by a semismooth Newton coordinate descent algorithm.
  arXiv  Detail & Related papers  (2022-12-11T18:03:12Z)
• Dimension free ridge regression [10.434481202633458]
  We revisit ridge regression on i.i.d. data in terms of the bias and variance of ridge regression in terms of the bias and variance of an equivalent' sequence model. As a new application, we obtain a completely explicit and sharp characterization of ridge regression for Hilbert covariates with regularly varying spectrum.
  arXiv  Detail & Related papers  (2022-10-16T16:01:05Z)
• Permuted and Unlinked Monotone Regression in $\mathbb{R}^d$: an approach based on mixture modeling and optimal transport [4.924126492174802]
  We show that the notion of cyclical monotonicity of the regression function is sufficient for identification and estimation in the permuted/unlinked regression model. We develop a computationally efficient and easy-to-use algorithm for denoising based on the Kiefer-Wolfowitz.
  arXiv  Detail & Related papers  (2022-01-10T18:37:59Z)
• Efficient and robust high-dimensional sparse logistic regression via nonlinear primal-dual hybrid gradient algorithms [0.0]
  We propose an iterative algorithm that provably computes a solution to a logistic regression problem regularized by an elastic net penalty. This result improves on the known complexity bound of $O(min(m2n,mn2)log (1/epsilon))$ for first-order optimization methods.
  arXiv  Detail & Related papers  (2021-11-30T14:16:48Z)
• Clustering Mixture Models in Almost-Linear Time via List-Decodable Mean Estimation [58.24280149662003]
  We study the problem of list-decodable mean estimation, where an adversary can corrupt a majority of the dataset. We develop new algorithms for list-decodable mean estimation, achieving nearly-optimal statistical guarantees.
  arXiv  Detail & Related papers  (2021-06-16T03:34:14Z)
• List-Decodable Mean Estimation in Nearly-PCA Time [50.79691056481693]
  We study the fundamental task of list-decodable mean estimation in high dimensions. Our algorithm runs in time $widetildeO(ndk)$ for all $k = O(sqrtd) cup Omega(d)$, where $n$ is the size of the dataset. A variant of our algorithm has runtime $widetildeO(ndk)$ for all $k$, at the expense of an $O(sqrtlog k)$ factor in the recovery guarantee
  arXiv  Detail & Related papers  (2020-11-19T17:21:37Z)
• Truncated Linear Regression in High Dimensions [26.41623833920794]
  In truncated linear regression, $(A_i, y_i)_i$ whose dependent variable equals $y_i= A_irm T cdot x* + eta_i$ is some fixed unknown vector of interest. The goal is to recover $x*$ under some favorable conditions on the $A_i$'s and the noise distribution. We prove that there exists a computationally and statistically efficient method for recovering $k$-sparse $n$-dimensional vectors $x*$ from $m$ truncated samples.
  arXiv  Detail & Related papers  (2020-07-29T00:31:34Z)
• Optimal Robust Linear Regression in Nearly Linear Time [97.11565882347772]
  We study the problem of high-dimensional robust linear regression where a learner is given access to $n$ samples from the generative model $Y = langle X,w* rangle + epsilon$ We propose estimators for this problem under two settings: (i) $X$ is L4-L2 hypercontractive, $mathbbE [XXtop]$ has bounded condition number and $epsilon$ has bounded variance and (ii) $X$ is sub-Gaussian with identity second moment and $epsilon$ is
  arXiv  Detail & Related papers  (2020-07-16T06:44:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.