Learning the Kernel Matrix with Semidefinite Programming

By Gert R. G. Lanckriet, Nello Cristianini, Peter L. Bartlett, Laurent El Ghaoui, Michael I. Jordan. 2002

2,599 citations recorded by the source corpus.

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Citations in the corpus

Word Representations via Gaussian Embedding (2014, methodology): “This allows us to go beyond the Bayesian approach and use arbitrary (and even asymmetric) training criteria, and is more similar to methods that learn kernels (Lanckriet et al., 2004) or function-valued neural networks such as mixture density networks (Bishop, 1994).”
Clustered Multi-Task Learning: A Convex Formulation (2008, methodology): “Whereas a dual formulation could be easily derived following [8], a direct approach is to rewrite (16) as min W∈Rd×m ( lc(W ) + min Σc∈Sc trΠWΣ−1 c W Π ) (17)”
A Survey on Multi-view Learning (2013, methodology): “Lanckriet et al. (2004) showed that when a kernel is chosen from a convex combination of k base kernels, the estimation error of the learned classifier is bounded by O( √ k/γ2 n ), where γ is the margin of the learned classifier under the kernel.”
Optimization with Sparsity-Inducing Penalties (2011, background): “As shown in [77], the fact that G is a convex function of K suggests the possibility of optimizing the objective with respect to the choice of the kernel itself by solving a problem of the form minK∈KG(K) where K is a convex set of kernel matrices.”
Audio-Visual Instance Discrimination with Cross-Modal Agreement (2020, neutral): “…methods [49, 66] which seek to maximize the mutual agreement of two views of unlabeled data, multiple kernel learning procedures [5, 35, 39] which naturally model diﬀerent views by diﬀerent kernels, and subspace learning procedures [14, 64] which seek to learn the latent space that…”
Regularization Techniques for Learning with Matrices (2009, methodology): “For instance, Theorem 25 improves upon the bounds for multiple kernel learning given by Lanckriet et al. (2004) and Srebro and Ben-David (2006).”
Click-through-based cross-view learning for image search (2014, background): “The research in this direction has proceeded along three dimensions: co-training [16][22][33], subspace learning [2][9][25], and multi-kernel learning [5][14][17].”
Multi-Task Multiple Kernel Relationship Learning (2016, background): “Recent work in multiple kernel learning in a multitask framework focuses on sharing common representations and assumes that the tasks are all related [10].”
Heterogeneous Visual Features Fusion via Sparse Multimodal Machine (2013, methodology): “Considering different feature representations give rise to different kernel functions, the Multiple Kernel Learning (MKL) approaches [19, 9, 13] have been recently studied and employed to integrate heterogenous features or data and select multi-modal features.”
Semiparametric latent factor models (2005, methodology): “In fact, if we have [ and , then this model can be viewed as a Gaussian process version of the kernel learning proposed in [6].”
Consistency of the group Lasso and multiple kernel learning (2007, unknown): “This is also a condition uniquely on the input spaces and not on Y .”
Multi-task feature and kernel selection for SVMs (2004, methodology): “More specifically, we discuss optimizing the representation either as a feature selection configuration (Jebara & Jaakkola, 2000; Weston et al., 2000) or as a convex kernel combination (Lanckriet et al., 2002; Cristianini et al., 2001).”
Kernel Methods for Deep Learning (2009, methodology): “For MKMs, we are hoping to explore better schemes for feature selection [21, 22] and kernel selection [23].”
A nested heuristic for parameter tuning in Support Vector Machines (2014, methodology): “An alternative model studied, among others, in [1, 12, 22, 38, 37, 31, 39, 45], is the Multiple Kernel Learning (MKL) model.”