Support Vector Machines with the Ramp Loss and the Hard Margin Loss

By J. Paul Brooks. 2011

154 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Civil and Structural Engineering, Control and Systems Engineering

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Civil and Structural Engineering

In Control and Systems Engineering

Citations in the corpus

Strongly agree or strongly disagree?: Rating features in Support Vector Machines (2016, background): “See Carrizosa and Romero Morales (2013) for a recent review on Mathematical Optimization and the SVM, and Bertsimas et al. (2008), Brooks (2011), Cecchini et al. (2010), Chaovalitwongse et al. (2008), Guyon et al. (2002), Martens et al. (2007), Romero Morales and Wang (2010) for successful…”
Supersparse linear integer models for optimized medical scoring systems (2015, methodology): “Accordingly, the effectiveness of this approach may be improved using techniques that narrow the integrality gap – specifically by using higher quality feasible solutions and/or strengthening SLIM’s LP relaxation (e.g., by using the cutting planes of Brooks, 2011).”
Methods and Models for Interpretable Linear Classification (2014, background): “Accordingly, a large body of work has focused on improving the scalability of misclassification minimization by modifying formulations [20], applying heuristics [95, 118, 4], and designing specialized algorithms [100, 96, 85].”
Supervised classification and mathematical optimization (2013, methodology): “Discontinuous loss functions gi have been proposed in [38, 148, 186].”
On handling indicator constraints in mixed integer programming (2016, methodology): “Although such an internal computation is not responsible for the higher effectiveness of Couenne (typically Couenne is more conservative than the static values of M used in the literature and especially by [8]) this is, in practice, not a negligible issue because a safe value of M is not trivial to ”
L_DMI: An Information-theoretic Noise-robust Loss Function (2019, unknown): “, 0-1 loss [22], ramp loss [3], unhinged loss [40], savage loss [23]) have been proved to be robust to uniform or symmetric noise and Natarajan et al.”
Are all training examples equally valuable? (2013, background): “For SVMs, the loss function can be changed to become more robust to outliers and bad training examples [20, 5].”
Integer optimization methods for machine learning (2012, unknown): “Still, MIO has already been shown to be effective in feature selection, as well as in classification and regression [Nguyen et al., 2009, Bertsimas and Shioda, 2007, Brooks, 2010].”
Direct Learning to Rank and Rerank (2018, methodology): “The methods of Ataman et al (2006), Brooks (2010), and Tan et al (2013) have used linear relaxations or greedy methods for learning to rank, rather than exact reranking, which will have similar issues; if one optimizes the wrong rank statistic, one may not achieve the correct answer.”
Fairness in Machine Learning: A Survey (2020, background): “Note that sufficient data is required for each subgroup for this method of sampling to not negatively affect performance and fairness, as shown by [9], and that outliers can be problematic [45, 211].”
EEG-Based Emotion Recognition Using Regularized Graph Neural Networks (2019, background): “A few studies tackle noisy labels by using noise-tolerant robust loss functions, such as unhinged loss [51] and ramp loss [52].”
Joint Optimization Framework for Learning with Noisy Labels (2018, background): “Robust loss function: A few studies achieve noiserobust classification by using a noise-tolerant loss functions, such as ramp loss [3] and unhinged loss [20].”
Functional-bandwidth kernel for Support Vector Machine with Functional Data: An alternating optimization algorithm (2019, unknown): “Our approach might also be adapted to other loss functions, such as the so-called ramp loss, [9], by replacing (2) with the corresponding SVM problem.”
NLNL: Negative Learning for Noisy Labels (2019, methodology): “Some methods attempted to create noise-robust losses [1, 32, 23, 4, 3, 39].”
Clustering Categories in Support Vector Machines (2017, methodology): “See [4, 9, 13, 17, 21] for successful applications of the SVM and [8] for a recent review on Mathematical Optimization and the SVM.”
Fairness without Harm: Decoupled Classifiers with Preference Guarantees (2019, background): “Such violations can stem from a lack of data for some groups, or the fact that surrogate losses may not be robust to outliers (e.g., points belonging to a heterogeneous subpopulation; Brooks, 2011; Nguyen & Sanner, 2013).”
A nested heuristic for parameter tuning in Support Vector Machines (2014, methodology): “models, such as those analyzed in [7], Support Vector Regression as well as other kernel models, [27].”