Chang Ho Yu

Shuang Xu, Chang Yu, Jiangjun Peng et al.

Remote sensing image restoration aims to reconstruct missing or corrupted areas within images. To date, low-rank based models have garnered significant interest in this field. This paper proposes a novel low-rank regularization term, named the Haar nuclear norm (HNN), for efficient and effective remote sensing image restoration. It leverages the low-rank properties of wavelet coefficients derived from the 2-D frontal slice-wise Haar discrete wavelet transform, effectively modeling the low-rank prior for separated coarse-grained structure and fine-grained textures in the image. Experimental evaluations conducted on hyperspectral image inpainting, multi-temporal image cloud removal, and hyperspectral image denoising have revealed the HNN's potential. Typically, HNN achieves a performance improvement of 1-4 dB and a speedup of 10-28x compared to some state-of-the-art methods (e.g., tensor correlated total variation, and fully-connected tensor network) for inpainting tasks.

Xin Chen, Jason M. Klusowski, Yan Shuo Tan et al.

Combining randomized estimators in an ensemble, such as via random forests, has become a fundamental technique in modern data science, but can be computationally expensive. Furthermore, the mechanism by which this improves predictive performance is poorly understood. We address these issues in the context of sparse linear regression by proposing and analyzing an ensemble of greedy forward selection estimators that are randomized by feature subsampling -- at each iteration, the best feature is selected from within a random subset. We design a novel implementation based on dynamic programming that greatly improves its computational efficiency. Furthermore, we show via careful numerical experiments that our method can outperform popular methods such as lasso and elastic net across a wide range of settings. Next, contrary to prevailing belief that randomized ensembling is analogous to shrinkage, we show via numerical experiments that it can simultaneously reduce training error and degrees of freedom, thereby shifting the entire bias-variance trade-off curve of the base estimator. We prove this fact rigorously in the setting of orthogonal features, in which case, the ensemble estimator rescales the ordinary least squares coefficients with a two-parameter family of logistic weights, thereby enlarging the model search space. These results enhance our understanding of random forests and suggest that implicit regularization in general may have more complicated effects than explicit regularization.