Multi-task Gaussian Process Prediction

By Edwin V. Bonilla, Kian Ming Adam Chai, Christopher K. I. Williams. 2007

1,357 citations recorded by the source corpus.

Subfields: Probabilistic & Bayesian Methods

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In Probabilistic & Bayesian Methods

Citations in the corpus

An Overview of Multi-task Learning (2018, background): “A multi-task Gaussian process is proposed in [42] to define a prior on f ij , the functional value corresponding to x ij , as f ∼ N ( 0 , (cid:5) ), where f = ( f 11 , . . . , f mn m ) T .”
Practical Bayesian Optimization of Machine Learning Algorithms (2012, neutral): “For our problems of interest, typically we would have D + 3 Gaussian process hyperparameters: D length scales θ 1: D , the covariance amplitude θ 0 , the observation noise ν , and a constant mean m .”
A Survey on Multi-Task Learning (2017, methodology): “Different from [79], [81] which are Bayesian models, Zhang and Yeung [4], [5] propose a regularized multi-task model called multi-task relationship learning (MTRL) by placing a matrixvariate normal prior on W as”
Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “An alternative view of the ICM model is that it deﬁnes a latent process that is rotated and scaled to produce each of the individual tasks.”
Non-Linear Regression for Bag-of-Words Data via Gaussian Process Latent Variable Set Model (2015, methodology): “Thus, the idea of the GP-LVSM can be applied to various machine learning problems, which have been solved based on GP regression such as multi-task learning (Bonilla, Chai, and Williams 2008) and active learning (Kapoor and Grauman 2007).”
Kernels for Vector-Valued Functions: a Review (2011, methodology): “The authors also refer to the autokrigeability effect as the cancellation of inter-task transfer [12], and discuss the similarities between the multi-task GP and the ICM, and its relationship to the SLFM and the LMC.”
Pre-Trained Models: Past, Present and Future (2021, methodology): “Therefore, these methods pre-encode knowledge into shared model parameters (Lawrence and Platt, 2004; Evgeniou and Pontil, 2004; Williams et al., 2007; Gao et al., 2008), and then transfer the knowledge by fine-tuning pre-trained parameters with the data of”
Functional Regularisation for Continual Learning using Gaussian Processes (2019, background): “By assuming for now that all possible tasks are simultaneously present similarly to multi-task GPs (Bonilla et al., 2008; Álvarez et al., 2012), the joint distribution over function values and output data for all tasks is written as ∏ i p(yi|fi)p(fi) = ∏ i p(yi|fi)N (fi|0,KXi),where the vector fi st”
Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling (2018, methodology): “Our implementation is a multi-task Gaussian process [23] with a linear and Matern 3/2 product kernel over the inputs and an exponentiated quadratic kernel over latent vectors for the different tasks.”
Input Warping for Bayesian Optimization of Non-Stationary Functions (2014, background): “However, a basic and surprisingly effective approach is to assume that each task is derived from a single latent function which is transformed to produce each output (Teh et al., 2005; Bonilla et al., 2008).”
A Convex Formulation for Learning Task Relationships in Multi-Task Learning (2010, methodology): “Our goal in this paper is to inherit the advantages of [7] while overcoming its disadvantages.”
Causal Transfer in Machine Learning (2015, methodology): “This idea originates in the hierarchical Bayesian literature [Bonilla et al., 2007, Gao et al., 2008].”
Surpassing Human-Level Face Verification Performance on LFW with GaussianFace (2014, methodology): “Since our model is based on GPs, it is natural to compare our model with four popular GP models: GPC [42], MTGP prediction [6], GPLVM [29], and DGPLVM [57].”
Gaussian Process Regression Networks (2011, background): “…an explosion of interest in extending the Gaussian process regression framework to account for ﬁxed correlations between output variables (Alvarez and Lawrence, 2011; Yu et al., 2009; Alvarez and Lawrence, 2008; Bonilla et al., 2008; Osborne et al., 2008; Teh et al., 2005; Boyle and Frean, 2004).”
Multi-Task Learning and Algorithmic Stability (2015, methodology): “Moreover, according to the analysis in (Zhang and Yeung 2010b), we can see that problem (8) is related to the weight-space view of a multi-task Gaussian process model proposed in (Bonilla, Chai, and Williams 2007).”
Continual Multi-task Gaussian Processes (2019, background): “It is demonstrated that by exploiting such correlations between channels, multiple-output data are better modelled (Bonilla et al., 2008).”
Revisiting Stein's paradox: multi-task averaging (2014, background): “In this paper we do just that: apply this regularizer to mean estimation, show that this special case enables new and useful analytic results, and demonstrate its performance with simulated and real data.”