Variational Heteroscedastic Gaussian Process Regression

By Miguel L'azaro-Gredilla, Michalis K. Titsias. 2011

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, neutral): “[103].”
Gaussian Process Regression Networks (2011, background): “…been great interest in extending Gaussian process (GP) regression to account for input dependent noise variances (Goldberg et al., 1998; Kersting et al., 2007; Adams and Stegle, 2008; Turner and Sahani, 2008; Turner, 2010; Wilson and Ghahramani, 2010a,b; L´azaro-Gredilla and Titsias, 2011).”
Continual Multi-task Gaussian Processes (2019, background): “(2) would require to evaluate expectations of the form E q ( f ) [log p ( y old , y new | f )] , where q ( f ) = p ( f | u ) q ( u | φ ) d u as in the uncollapsed version of the bound (L´azaro-Gredilla and Titsias, 2011; Hensman et al., 2012).”
Spike and Slab Variational Inference for Multi-Task and Multiple Kernel Learning (2011, methodology): “This problem is efficiently resolved by applying a Marginalized Variational step [20] which jointly updates the pair (q(φm),θm).”
Variational Bayesian Optimization for Runtime Risk-Sensitive Control (2012, methodology): “In the Bayesian setting, a second GP prior, g(θ) ∼ GP(μ0, kg(θ,θ)), is placed over the unknown log variance function, g(θ) ≡ log r(θ) [7, 10, 15].”
Wind Power Curve Modeling and Wind Power Forecasting With Inconsistent Data (2019, background): “First, the variances of the estimated errors will vary with the samples, which shows that the error is heteroscedastic [24].”
Recent Advances in Bayesian Optimization (2022, methodology): “Suggested alternative approximations include variational inference [102], Laplace approximation [182] and expectation propagation [1].”
A probabilistic data-driven model for planar pushing (2017, methodology): “The learned models rely on a variation of Gaussian processes with inputdependent noise called Variational Heteroscedastic Gaussian processes (VHGP) [1] that capture the mean and variance of a stochastic function.”
When Gaussian Process Meets Big Data: A Review of Scalable GPs (2018, methodology): “More elegantly, Almosallam et al. [177] derived a scalable heteroscedastic Bayesian model from the weight-space view by adopting an additional log GP, which is analogous to [178], [179], to account for noise variance as σ 2 ǫ ( x i ) = exp( φ ( x i ) w + b ) .”
A Review of Deep Learning Models for Time Series Prediction (2019, methodology): “To forecast such time series data, the GP-based volatility models were reported in recent years [140]–[142].”
Advances in Variational Inference (2017, background): “(CVI) relies on the idea of analytically integrating out certain model parameters [64], [83], [94], [97], [182], [188], [197].”