Gaussian processes:iterative sparse approximations

By Lehel Csató. 2002

135 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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In Probabilistic & Bayesian Methods

Citations in the corpus

Continual Learning via Sequential Function-Space Variational Inference (2023, positive): “…sparse GP regression (Cheng and Boots, 2016), streaming sparse GP s (Bui et al., 2017) and online sparse multi-output GP regression (Yang et al., 2019) built on the work of Csat´o and Opper (2002) and Csat´o (2002), and are effective approaches to continual learning for regression tasks.”
Variational Auto-Regressive Gaussian Processes for Continual Learning (2020, background): “Historically, Csató and Opper [7] and Csató [6] presented seminal works in the context of online regression.”
Functional Regularisation for Continual Learning using Gaussian Processes (2019, methodology): “…the online sparse Gaussian process approximation literature, the recent work of (Bui et al., 2017a) extends the two earlier seminal works of (Csato & Opper, 2002) and (Csato, 2002), unifying them within a power expectation framework and proposing methods for online learning of hyperparameters.”
Streaming Sparse Gaussian Process Approximations (2017, methodology): “For the case α = 1, which is called Expectation Propagation, we recover the seminal work by Csató and Opper [8].”
Learning to learn with the informative vector machine (2004, methodology): “Csató (2002). Thus we start with the GP prior q0 (f |X, θ) = p (f |X,θ) and we include the nth factor of the noise model p̂1 (f) ∝ q0 (f) p (yn|xn) to obtain a posterior distribution.”
Learning to soar: Resource-constrained exploration in reinforcement learning (2015, methodology): “As described in Csato´ (2002), points with b greater than the tolerance value b tol are included in the training set.”
On Sparse Variational Methods and the Kullback-Leibler Divergence between Stochastic Processes (2015, methodology): “The idea of using the KL -divergence between processes is also mentioned in the early work of Csato and Opper (2002; 2002) but the transition from ﬁnite dimensional multivariate Gaussians to inﬁnite dimensional Gaussian processes is not covered at the level of detail discussed here.”
Bayesian Gaussian process models : PAC-Bayesian generalisation error bounds and sparse approximations (2003, methodology): “The curve in [38] suggests that our choice of d = 500 was very conservative.”
A Unifying Framework for Sparse Gaussian Process Approximation using Power Expectation Propagation (2016, methodology): “…2 ) complexity, For regression, the calculus of variations can be used to ﬁnd the optimal approximate posterior distribution over pseudo-data, which is identical to that recovered using the DTC approximate generative model [8] (in fact DTC was originally derived using a related KL argument [9,11]).”
Bayesian Gaussian Process Latent Variable Model (2010, methodology): “Inducing variables were introduced originally for computational speed ups in GP regression models (Csató and Opper, 2002; Seeger et al., 2003; Csató, 2002; Snelson and Ghahramani, 2006; Quiñonero Candela and Rasmussen, 2005; Titsias, 2009).”
Fast Forward Selection to Speed Up Sparse Gaussian Process Regression (2003, methodology): “A strong motivation for this approximation is given by Csató (2002), showing that the minimisation of the relative entropy 2 D[· P (u|y)] over all distributions of the form ∝ P (u)R(u I ), R positive and dependent on u I only, is attained by R(u I ) = Q(y|u I ).”
Sparse Gaussian Process Classification With Multiple Classes (2004, methodology): “In fact, the ADATAP variational free energy would probably fit in better and has been used for model selection in single process models in [2].”
A Unifying Framework for Gaussian Process Pseudo-Point Approximations using Power Expectation Propagation (2016, methodology): “In fact, DTC was originally derived using a related KL argument (Csató, 2002; Seeger et al., 2003).”
Analysis of Some Methods for Reduced Rank Gaussian Process Regression (2003, methodology): “Besides the technical difficulties of the optimization process (observed for example by Csató (2002)), there is the fundamental issue of having an excessive amount of flexibility that may lead to overfitting (observed for example by Rasmussen (2002) and Seeger et al. (2003)).”
Gaussian predictive process models for large spatial data sets (2008, background): “KL-based justification for˜w .s Å / is discussed in Csató (2002) and Seeger et al. (2003).”
Cross-Validation Optimization for Large Scale Structured Classification Kernel Methods (2008, methodology): “Csató (2002) states 5.15% for his sparse online method with multiple sweeps over the data (Sect.”
Variable Noise and Dimensionality Reduction for Sparse Gaussian processes (2006, methodology): “There have been many methods proposed in recent years to address this problem, and bring the scaling down to O ( M 2 N ) where M N [Tresp, 2000, Smola and Bartlett, 2001, Williams and Seeger, 2001, Csat´o, 2002a,b, Lawrence et al., 2003, Seeger et al., 2003, Seeger, 2003, Qui˜nonero Candela, 2004].”