The Entire Regularization Path for the Support Vector Machine

By Trevor J. Hastie, Saharon Rosset, Robert Tibshirani, Ji Zhu. 2004

745 citations recorded by the source corpus.

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In Optimization & Training

Citations in the corpus

Minding the Gaps for Block Frank-Wolfe Optimization of Structured SVMs (2016, methodology): “Hastie et al. (2004) proposed the path following method to compute the exact regularization path for the binary SVM with L2-regularization.”
Geometric GAN (2017, neutral): “…the true samples versus fake samples, the primal form of soft-margin SVM can be formulated by Equivalently, the primal form of the soft-margin SVM can be represented using loss + penalty form [17, 14]: where The goal of the SVM optimization (13) is to maximize the margin between the two classes.”
Regularization Paths for Generalized Linear Models via Coordinate Descent (2010, methodology): “Regularization paths for the support-vector machine (Hastie et al. 2004).”
Methods and Models for Interpretable Linear Classification (2014, methodology): “To illustrate these points, consider a state-of-the-art approach for producing sparse linear models using `1-regularization, such as LARS [20, 37, 40, 29].”
A Least-squares Approach to Direct Importance Estimation (2009, methodology): “Theℓ2-r gularization method will be used for theoretical analysis in Section 3.3.”
An Exponential Lower Bound on the Complexity of Regularization Paths (2009, methodology): “This conjecture was repeatedly stated for the related models in [14, 13, 3, 26, 21, 28, 29, 25].”
Design of the 2015 ChaLearn AutoML challenge (2015, methodology): “Other authors have devised methods to produce all values of J2(θ) given only a few key samples [50], [51].”
A Robust Regularization Path Algorithm for $\nu $ -Support Vector Classification (2017, background): “However, most solution algorithms [4]–[7], [9] mainly depend on Assumption 1.”
Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment (2017, methodology): “For a linear regression, the SVR model can be written as f̂ ðxÞ ¼ ŶðxÞ ¼ hW xi þ b ð79Þ where ŶðxÞ, W and b denote the approximate value of the objective function at x, vector of weights and the bias term, respectively while h i indicates the inner product.”
CHARACTERIZING THE SOLUTION PATH OF MULTICATEGORY SUPPORT VECTOR MACHINES (2006, methodology): “Moreover, Hastie et al. (2004) empirically demonstrated that the computational cost of obtaining the entire regularization path could be almost the same as getting a single solution by other methods, while misspecification of the tuning parameter can be readily avoided through the SVM path. Motivate”
Clustering via Mode Seeking by Direct Estimation of the Gradient of a Log-Density (2014, methodology): “, the solutions for all λ ≥ 0) can also be computed efficiently, based on the piece-wise linearity of the solution path with respect to λ [12].”