The importance of convexity in learning with squared loss
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Summary
It is shown that if the closure of a function class under the metric induced by some probability distribution is not convex, then the sample complexity for agnostically learning with squared loss is lower than that for agnostic learning, so learning the convex hull provides better approximation capabilities with little sample complexity penalty.
- Type
- article
- Published
- 1998-09-01
- Cited by
- 120
- References
- 31
- OpenAlex
- https://openalex.org/W1988229590
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:1298646
Keywords
Citation, Library science, Ninth, Operations research, Management
References
- Nonlinear Approximation Theory
- Computational learning theory: an introduction
- Uniform ratio limit theorems for empirical processes
- Introduction to statistical pattern recognition (2nd ed.)
- A Generalization of Sauer's Lemma
- ON CONVERGENCE OF STOCHASTIC PROCESSES
- Learning Distributions by Their Density Levels: A Paradigm for Learning without a Teacher
- Weak Convergence and Empirical Processes: With Applications to Statistics
- Convergence rates for single hidden layer feedforward networks
- A Simple Lemma on Greedy Approximation in Hilbert Space and Convergence Rates for Projection Pursuit Regression and Neural Network Training
- Random Approximants and Neural Networks
- Bounding Sample Size with the Vapnik-Chervonenkis Dimension
- On efficient agnostic learning of linear combinations of basis functions
- Learnability with Respect to Fixed Distributions
- Decision Theoretic Generalizations of the PAC Model for Neural Net and Other Learning Applications
- Efficient distribution-free learning of probabilistic concepts
- Covering numbers for real-valued function classes
- Introduction to Statistical Pattern Recognition
- Universal approximation bounds for superpositions of a sigmoidal function
- Introductory Real Analysis
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- Smoothness, Low Noise and Fast Rates
- A Finite-Sample Generalization Bound for Semiparametric Regression: Partially Linear Models
- PAC-Bayesian aggregation and multi-armed bandits
- Exploiting Smoothness in Statistical Learning, Sequential Prediction, and Stochastic Optimization
- Ship efficiency forecast based on sensors data collection: Improving numerical models through data analytics
- Relative Expected Instantaneous Loss Bounds
- Oracle inequalities using truncation and cross-validation
- Passive Learning with Target Risk
- Applications of empirical processes in learning theory: algorithmic stability and generalization bounds
- Advances in kernel methods: support vector learning
- Hyper-Sparse Optimal Aggregation
- On the size of convex hulls of small sets
- Learning without concentration for general loss functions
- Fast rates in statistical and online learning
- Data-Dependent Analysis of Learning Algorithms
- Boosting the margin: A new explanation for the effectiveness of voting methods
- On universal estimators in learning theory
- Maximum mutual information regularized classification
- Regularization in kernel learning
- Obtaining fast error rates in nonconvex situations
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