On the Equivalence between Quadrature Rules and Random Features

By Francis R. Bach. 2015

35 citations recorded by the source corpus.

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, methodology): “restricts attention to narrow classes of kernels and densities that combine to provide a closed-form for the mean element (e.g. O’Hagan, 1991; Huszar and Duvenaud, 2012; Lacoste-Julien et al., 2015; Bach, 2015). As a by-product, our novel gradient-based kernel broadens the scope of these methods. An”
Scalable Kernel Methods via Doubly Stochastic Gradients (2014, neutral): “. It is straightforward to replace the sampling strategy for random features with Fastfood [7] which enjoys the ecient computational cost, or Quasi-Monte Carlo sampling [43], data-dependent sampling [47] which enjoys faster convergence rate with fewer generated features. Meanwhile, by back-propogati”
Breaking the Curse of Dimensionality with Convex Neural Networks (2014, methodology): “Conditional gradient algorithms allow to incrementally build a set of elements of Fδ1 = {f ∈ F1, γ1(f) 6 δ}; see, e.g., Frank and Wolfe (1956); Dem’yanov and Rubinov (1967); Dudik et al. (2012); Harchaoui et al. (2013); Jaggi (2013); Bach (2014).”
Black-box Importance Sampling (2016, methodology): “Related results is also presented in Bach (2015).”
Kernel Exponential Family Estimation via Doubly Dual Embedding (2018, methodology): “Random feature approximation (Rahimi and Recht, 2008; Dai et al., 2014; Bach, 2015) can be utilized for scaling up kernel methods.”
Control Functionals for Quasi-Monte Carlo Integration (2015, methodology): “1 is also the ‘maximum mean discrepancy’ (MMD), as studied extensively in the kernel methods literature [4, 30].”