Estimation of Dependences Based on Empirical Data

By Vladimir Naumovich Vapnik. 2006

2,422 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, General Social Sciences, Statistics and Probability

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Citations in the corpus

Optimization Methods for Large-Scale Machine Learning (2016, background): “n information contained in a set of labeled training data. Such a focus is reasonable as many unsupervised and other learning techniques reduce to optimization problems of comparable form; see, e.g., [155]. Fundamentals Our goal is to determine a prediction function h: X!Yfrom an input space X to an”
Counterfactual reasoning and learning systems: the example of computational advertising (2012, background): “Better models are sometimes obtained by deliberately avoiding to reproduce the true mechanisms (Vapnik, 1982, section 8.6).”
Continual Reinforcement Learning with Multi-Timescale Replay (2020, background): “…2019] is an approach that seeks to improve out-of-distribution generalisation in machine learning models by training them to learn invariant or stable predictors that avoid spurious correlations in the training data, a common problem with the framework of empirical risk minimisation [Vapnik, 2006].”
Lifelong Generative Modeling (2017, methodology): “For each different posterior reparameterization, we train a set of VAEs with varying latent dimensions, |z| ∈ [32, 64, 128, 256, 512, 1024].”
Kernel methods in machine learning (2007, neutral): “3] were the ﬁrst to use kernels to construct a nonlinear estimation algorithm, the hard margin predecessor of the Support Vector Machine, from its linear counterpart, the generalized portrait (Vapnik [139] and Vapnik and Lerner [145]). While all these uses were limited to kernels deﬁned on vectorial”
A Wholistic View of Continual Learning with Deep Neural Networks: Forgotten Lessons and the Bridge to Active and Open World Learning (2020, methodology): “This question has been elemental in later formalization of frameworks for empirical risk optimization (Tsypkin, 1971; Vapnik, 1982).”
Recent Advances in Open Set Recognition: A Survey (2018, background): “es minimize the empirical risk instead of the ideal risk R Iby using other knowledge, such as assuming that the label space is at least locally smooth and regularizing the empirical risk minimization [50]–[52]. Note that traditional recognition problem is usually performed under the closed set assum”
Rigorous Learning Curve Bounds from Statistical Mechanics (2005, methodology): “Hence some theorists have sought to preserve the functional form of the VC bounds, but to replace the VC dimension in this functional form by an appropriate distribution-specific quantity, such as the VC entropy (which is the expectation of the logarithm of the number of dichotomies realized by the ”
Support vector machines in remote sensing: A review (2011, neutral): “In its original formulation (Vapnik, 1979) the method is presented with a set of labeled datainstancesandtheSVMtrainingalgorithmaimstofindahyper-plane that separates the dataset into a discrete predefined number of classes in a fashion consistent with the training examples.”
Feature selection, L1 vs. L2 regularization, and rotational invariance (2004, methodology): “ther, the VC dimension for most models grows about linearly in the number of parameters (Vapnik, 1982), which typically grows at least linearly in the number of input features.”
Universum Prescription: Regularization Using Unlabeled Data (2015, background): “The effect of a regularization parameter – probability of sampling from unlabeled data – is also studied empirically.”
On the Learnability and Design of Output Codes for Multiclass Problems (2002, background): “As in more standard classification problems, the loss on a separate test set (generalization error) can also b e theoretically bounded given appropriate assumptions usin g uniform-convergence theory [3, 13, 23].”