-convexity

By Walter Briec, C. Horvath. 2004

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Citations in the corpus

Variance-based Regularization with Convex Objectives (2016, background): “In many cases, such tradeoffs require either conditions such as the Mammen-Tsybakov noise condition [15, 6] or localization results [3, 2, 17] made possible by curvature conditions that relate the risk and variance.”
Local Rademacher complexities (2005, background): “Other examples are described in [26] and in [2].”
Houdini: Fooling Deep Structured Prediction Models (2017, methodology): “The first route is to use a consistent differentiable surrogate loss function in place of the task loss [5].”
History of Interactive Theorem Proving (2014, background): “For example, an invalid conjunction of linear arithmetic constraints can be checked by providing a linear combination that sums to give a trivial inequality like 1 < 0; the existence of such linear combinations is essentially the content of Farkas’s lemma [Webster, 1995].”
Towards good practice in large-scale learning for image classification (2012, background): “Put into the perspective of the statistical learning theory described in [3], this implies that the ψ(·) function associated to each surrogate loss – which defines how the performance in the surrogate loss transfers to the target loss – does not play a major role here (see Theorem 10 in [3]).”
Nonlinear Optimal Control Theory (2012, background): “Readers unfamiliar with the facts about convex sets that we use are referred to [32].”
Self-concordant analysis for logistic regression (2009, unknown): “Measuring the classification performance through the 0–1 loss [21] is out of the scope of this paper.”
Incremental Object Recognition in Robotics with Extension to New Classes in Constant Time (2016, unknown): “To this end, in practice, a so-called surrogate problem (see [5], [6]) is often adopted to simplify the optimization problem and asymptotically recover the optimal Bayes classifier.”
Estimating conditional quantiles with the help of the pinball loss (2011, background): “Consequently, our new self-calibration inequality is more general and, modulo the constant √ 2, also sharper It is well-known that self-calibration inequalities for Lipschitz continuous losses lead to variance bounds, which in turn are important for the statistical analysis of ERM approaches, see [1”
Image Classification with Deep Learning in the Presence of Noisy Labels: A Survey (2019, background): “Robust Losses Non-convex loss functions [111, 112, 113], 0-1 loss surrogate [114], MAE [115], IMEA [116] Generalized cross-entropy [117], symmetric loss [118], unbiased estimator [119], modified cross-entropy for omission [120], information theoric loss [121] linear-odd losses [122], classification ”
Learning from massive noisy labeled data for image classification (2015, background): “[3] prove that most of the loss functions are not completely robust to label noise.”
Volterra type integration operators from Bergman spaces to Hardy spaces (2019, background): “For reference, see for instance Lemma 5 of Luecking [23] or the paper of Kalton [19].”
Bounds for the Ratio of Two Gamma Functions (2009, methodology): “84) for t = 1 are rewritten in [83] as Γ(x + β) Γ(x) < exp(βψ(x + β)), 0 < β < 1, x > 0; (4.”
Convex Functions: Constructions, Characterizations and Counterexamples (2010, background): “We have not endeavored to provide an historical account of the study of convexity, for that we already recommendedAsplund [15], Fenchel [212], Berger [53] and make other such mention later in the book.”