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In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated as low-rank semi-definite programming (SDP) problems. Traditional formulations use the square loss, which is notorious for being sensitive to outliers. We propose to replace this with more robust noise models, including the $\ell _1$ ℓ 1 -loss and other nonconvex losses. However, the resultant optimization problem becomes difficult as the objective is no longer convex or smooth. To alleviate this problem, we design an efficient algorithm based on majorization-minimization. The crux is on constructing a good optimization surrogate, and we show that this surrogate can be efficiently obtained by the alternating direction method of multipliers (ADMM). By properly monitoring ADMM's convergence, the proposed algorithm is empirically efficient and also theoretically guaranteed to converge to a critical point. Extensive experiments are performed on four machine learning applications using both synthetic and real-world data sets. Results show that the proposed algorithm is not only fast but also has better performance than the state-of-the-arts. [ABSTRACT FROM AUTHOR]

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) restoration, which includes the tasks of denoising, compressed HSI reconstruction and inpainting. Unfortunately, while its restoration performance benefits from more spectral bands, its runtime also substantially increases. In this paper, we claim that the HSI lies in a global spectral low-rank subspace, and the spectral subspaces of each full band patch group should lie in this global low-rank subspace. This motivates us to propose a unified paradigm combining the spatial and spectral properties for HSI restoration. The proposed paradigm enjoys performance superiority from the non-local spatial denoising and light computation complexity from the low-rank orthogonal basis exploration. An efficient alternating minimization algorithm with rank adaptation is developed. It is done by first solving a fidelity term-related problem for the update of a latent input image, and then learning a low-dimensional orthogonal basis and the related reduced image from the latent input image. Subsequently, non-local low-rank denoising is developed to refine the reduced image and orthogonal basis iteratively. Finally, the experiments on HSI denoising, compressed reconstruction, and inpainting tasks, with both simulated and real datasets, demonstrate its superiority with respect to state-of-the-art HSI restoration methods. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses articles in the issue on topics including cutting edge AutoML research; tree-structured covariance function; and comprehensive study on predicting run time performance under different AutoML.

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical performance. However, the resulting optimization problem is much more challenging. Recent state-of-the-art requires an expensive full SVD in each iteration. In this paper, we show that for many commonly-used nonconvex low-rank regularizers, the singular values obtained from the proximal operator can be automatically threshold. This allows the proximal operator to be efficiently approximated by the power method. We then develop a fast proximal algorithm and its accelerated variant with inexact proximal step. It can be guaranteed that the squared distance between consecutive iterates converges at a rate of $O(1/T)$O(1/T), where $T$T is the number of iterations. Furthermore, we show the proposed algorithm can be parallelized, and the resultant algorithm achieves nearly linear speedup w.r.t. the number of threads. Extensive experiments are performed on matrix completion and robust principal component analysis. Significant speedup over the state-of-the-art is observed. [ABSTRACT FROM AUTHOR]

Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion algorithm is Soft-Impute, which exploits the special "sparse plus low-rank" structure of the matrix iterates to allow efficient SVD in each iteration. Though Soft-Impute is a proximal algorithm, it is generally believed that acceleration destroys the special structure and is thus not useful. In this paper, we show that Soft-Impute can indeed be accelerated without comprising this structure. To further reduce the iteration time complexity, we propose an approximate singular value thresholding scheme based on the power method. Theoretical analysis shows that the proposed algorithm still enjoys the fast $O(1/T^2)$O(1/T2) convergence rate of accelerated proximal algorithms. We also extend the proposed algorithm to tensor completion with the scaled latent nuclear norm regularizer. We show that a similar "sparse plus low-rank" structure also exists, leading to low iteration complexity and fast $O(1/T^2)$O(1/T2) convergence rate. Besides, the proposed algorithm can be further extended to nonconvex low-rank regularizers, which have better empirical performance than the convex nuclear norm regularizer. Extensive experiments demonstrate that the proposed algorithm is much faster than Soft-Impute and other state-of-the-art matrix and tensor completion algorithms. [ABSTRACT FROM AUTHOR]

Modern machine learning is migrating to the era of complex models, which requires a plethora of well-annotated data. While crowdsourcing is a promising tool to achieve this goal, existing crowdsourcing approaches barely acquire a sufficient amount of high-quality labels. In this paper, motivated by the "Guess-with-Hints" answer strategy from the Millionaire game show, we introduce the hint-guided approach into crowdsourcing to deal with this challenge. Our approach encourages workers to get help from hints when they are unsure of questions. Specifically, we propose a hybrid-stage setting, consisting of the main stage and the hint stage. When workers face any uncertain question on the main stage, they are allowed to enter the hint stage and look up hints before making any answer. A unique payment mechanism that meets two important design principles for crowdsourcing is developed. Besides, the proposed mechanism further encourages high-quality workers less using hints, which helps identify and assigns larger possible payment to them. Experiments are performed on Amazon Mechanical Turk, which show that our approach ensures a sufficient number of high-quality labels with low expenditure and detects high-quality workers. [ABSTRACT FROM AUTHOR]