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Multiple kernel learning, conic duality, and the SMO algorithm
Abstract
While classical kernel-based classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimization of the coefficients of such a combination reduces to a convex optimization problem known as a quadratically-constrained quadratic program (QCQP). Unfortunately, current convex optimization toolboxes can solve this problem only for a small number of kernels and a small number of data points; moreover, the sequential minimal optimization (SMO) techniques that are essential in large-scale implementations of the SVM cannot be applied because the cost function is non-differentiable. We propose a novel dual formulation of the QCQP as a second-order cone programming problem, and show how to exploit the technique of Moreau-Yosida regularization to yield a formulation to which SMO techniques can be applied. We present experimental results that show that our SMO-based algorithm is significantly more efficient than the general-purpose interior point methods available in current optimization toolboxes.
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“Let us first assume that each memory unit has a frozen value extraction function ψ.The training procedure can still make each memory unit statistically more efficient by tuning the parameters of the key extraction function φ, that is, by learning how to compare the current prediction context (x T , x T -1 , x T -2 . . . ) with past prediction contexts (x t , x t-1 , x t-2 . . . ) for t < T .”
From Memory Mosaics (2024) · cites this paper as Bach et al., 2004
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Metadata
- Authors
- Bach, F. R., Lanckriet, G. R. G., & Jordan, M. I.
- Affiliations
- University of California, Berkeley (US)
- Venue
- Twenty-first international conference on Machine learning - ICML '04
- Publisher
- ACM Press
- Published
- 2004
- Pages
- 6
- OpenAlex
- W2031823405
- Semantic Scholar
- 141e6c1dd532504611266d08458dbe2a0dbb4e98
- Cited by
- 1,453
- References
- 13
- Citations by year
- 2026: 7 · 2025: 4 · 2024: 19 · 2023: 20 · 2022: 22 · 2021: 36 · 2020: 52 · 2019: 84 · 2018: 89 · 2017: 86 · 2016: 84 · 2015: 116 · 2014: 136 · 2013: 123 · 2012: 132
- Type
- conference abstract
- Language
- en
- Open access
- closed
- Locations
- International Conference on Machine Learning (publishedVersion)
- Funders
- Intel Corporation
- Microsoft Research
- Topics
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Physical Sciences › Computer Science › Artificial Intelligence › Stochastic Gradient Optimization Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Algorithms
- Keywords
- multiple kernel learning, support vector machine, sequential minimal optimization, second-order cone programming, Moreau-Yosida regularization, quadratically constrained quadratic programming, non-differentiable cost functions
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