Introduction to Statistical Learning Theory

By Olivier Bousquet, Stéphane Boucheron, Gábor Lugosi. 2004

683 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

To Drop or Not to Drop: Robustness, Consistency and Differential Privacy Properties of Dropout (2015, methodology): “Using standard Rademacher complexity bounds Bousquet et al. [2004, Theorem 5], for any θ ∈ C , the following holds (w.p. ≥ 1 − γ over the randomness in selection of dataset H ): Here R refers to the Rademacher complexity of the hypothesis class.”
Supersparse linear integer models for optimized medical scoring systems (2015, neutral): “A proof of Theorem 2 can be found in Section 3.4 of Bousquet et al. 2004.”
The landscape of empirical risk for nonconvex losses (2016, background): “noisy half-spaces) is a very well-studied topic in machine learning, and many of its aspects have been investigated in depth, see for instance [3, 17] for readable introductions.”
Obtaining Fairness using Optimal Transport Theory (2018, methodology): “We refer to (Bousquet et al., 2004) for a complete description of classification problems in statistical learning.”
No Free Lunch Theorems: Limitations and Perspectives of Metaheuristics (2014, background): “[4].”
On regularization algorithms in learning theory (2007, background): “2.1 Learning from Examples: Notation and Assumptions We start giving a brief account of Learning Theory (see Vapnik (1998); Cucker and Smale (2002); Evgeniou et al. (2000); Bousquet et al. (2004a) and reference therein).”
Testing the Manifold Hypothesis (2013, background): “A consequence of (105) is that va ∈ [2, 2].”
Wireless Edge Computing With Latency and Reliability Guarantees (2019, background): “accuracy at the test phase, primarily because of unseen training data samples. This accuracy gap is known as the generalization error that measures the inference reliability under unseen data samples [66]. A straightforward way to reduce the generalization error is exchanging training data samples a”
Rademacher Observations, Private Data, and Boosting (2015, background): “(28) into the proof of the symmetrization Lemma (Lemma 2 in ([6])) yields the following symmetrization Lemma for the exponential rado-loss.”
On the Sample Complexity of Adversarial Multi-Source PAC Learning (2020, background): “In many common learning settings, the Rademacher complexity scales as O (1 / √ n ) with the sample size n (see e.g. (Bousquet et al., 2004)).”
Learning Non-Discriminatory Predictors (2017, methodology): “Using (42) and the standard VC dimension uniform bound [1], the following holds with high probability for absolute constants C1 and C2,”
Classification with a Reject Option using a Hinge Loss (2008, result): “The results are in line with recent theoretical developments (Boucheron et al., 2006, 2005; Massart, 2007) of standard binary classification (d = 1/2).”
How Much Does Your Data Exploration Overfit? Controlling Bias via Information Usage (2015, background): “Sauer’s lemma (see Lemma 1 of [7]) shows that”
Tikhonov, Ivanov and Morozov regularization for support vector machine learning (2016, methodology): “Alternatively, in order to avoid the overfitting issue that afflicts the ERM procedure, the Tikhonov regularization technique (Tikhonov et al. 1977) can be exploited, which was proposed to solve ill-posed problems (Bishop 1995): h : argmin w,b L̂(h) + λ 2 ‖w‖2 or argmin w,b 1 2 ‖w‖2 + C L̂(h), (4) w”
Learning to rank for information retrieval (2009, positive): “By fitting the theory of the Rademacher average [10, 11] to the query-level ranking framework, the query-level generalization bound for listwise ranking algorithms have been derived [75], as shown in the following theorem.”
Importance weighted active learning (2008, neutral): “dη/T [5].”
Kernel Analysis of Deep Networks (2011, background): “Indeed, the notion of simplicity is highly subjective (Bousquet et al., 2004) and typically depends on which prior knowledge on the learning problem is taken for granted.”