Summary of Variable Selection in Convex Piecewise Linear Regression, by Haitham Kanj et al.
Variable Selection in Convex Piecewise Linear Regression
by Haitham Kanj, Seonho Kim, Kiryung Lee
First submitted to arxiv on: 4 Nov 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Information Theory (cs.IT); Machine Learning (cs.LG); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper presents a novel approach to variable selection in convex piecewise linear regression using Sparse Gradient Descent (Sp-GD). The model is given as max(a_j^* ⋅ x) + b_j^* for j = 1,⋅⋅⋅,k, where x is the covariate vector. A non-asymptotic local convergence analysis is provided for Sp-GD under sub-Gaussian noise, assuming the covariate distribution satisfies sub-Gaussianity and anti-concentration property. When the model order and parameters are fixed, Sp-GD provides an ε-accurate estimate given O(max(ε(-2)σ_z2,1)slog(d/s)) observations. This also implies exact parameter recovery by Sp-GD from O(slog(d/s)) noise-free observations. The paper also proposes an initialization scheme to provide a suitable initial estimate within the basin of attraction for Sp-GD, using sparse principal component analysis and r-covering search. A non-asymptotic analysis is presented for this initialization scheme when the covariates and noise samples follow Gaussian distributions. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand how to select important variables in complex models. It uses a new approach called Sparse Gradient Descent, which can accurately estimate model parameters even when there’s noise. The method works by analyzing how well the model fits the data and adjusting its variables accordingly. The authors also provide an initialization scheme that helps get the algorithm started on the right track. |
Keywords
» Artificial intelligence » Gradient descent » Linear regression » Principal component analysis
