Latent Force Models

By Mauricio A Álvarez, David Luengo, Neil D. Lawrence. 2009

222 citations recorded by the source corpus.

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Citations in the corpus

Kernels for Vector-Valued Functions: a Review (2011, methodology): “In[3], the authors use a process convolution to model the dependencies between different body parts of an actor that performs modern dancing movements.”
Machine learning of linear differential equations using Gaussian processes (2017, background): “Perhaps the most significant related work in this direction is latent force models [3,2].”
Mechanistic Hierarchical Gaussian Processes (2014, methodology): “(4) Here G(t, ξ ) is Green’s function that is used to explicitly calculate the covariance kernel for latent force models (Lawrence, Sanguinetti, and Rattray 2007; Álvarez, Luengo-Garcia, and Lawrence 2009; Honkela et al. 2010; Álvarez, Luengo, and Lawrence 2013).”
Computationally Efficient Convolved Multiple Output Gaussian Processes (2011, methodology): “Other connections of the convolution process approach with methods in statistics and machine learning are further explored in Álvarez et al. (2011b). A general purpose convolution kernel for multiple outputs.”
Gaussian processes for time-series modelling (2013, background): “of exciting recent trends in GP modelling that allow for more explicit incorporation of differential equations governing the system dynamics (either observed or not), such as latent force models [26].”
Applied Stochastic Differential Equations (2019, unknown): “In the LFM framework of Álvarez et al. (2009) and Álvarez et al. (2013) (see also Hartikainen and Särkkä, 2011; Hartikainen et al.”
Efficient Multioutput Gaussian Processes through Variational Inducing Kernels (2010, methodology): “…p(f ,λ|y), we can compute the following Jensen’s lower bound on the true log marginal likelihood (a detailed derivation of the bound is available in Álvarez et al. (2009b)): FV = logN ( y|0,Kf ,λK−1λ,λKλ,f + Σ ) −1 2 tr ( Σ−1K̃ ) , where Σ is the covariance function associated with the…”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, methodology): “This is a key feature in Latent Force Models, which attempt to use equations in the physical model of the system to inform the learning from data [4, 160].”
Multi-output learning via spectral filtering (2012, methodology): “Starting from the work of Caruana (1997), related ideas have been developed in the context of regularization methods (Argyriou et al. 2008b; Jacob et al. 2008), Bayesian techniques—e.g. Gaussian processes (Boyle and Frean 2005; Chai et al. 2009; Alvarez et al. 2009), collaborative filtering (Abernet”
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, methodology): “1) [266] [10] [219] [158] [140] [182] [203] [76] [86] [130] [174] [204] [231] [313] [121] [125] [187] [92] [306] [180] [298] [184] [267] [39] [247] [133] [130] [231] [298] [173] [66] [24] [255] [12] [17] [203] [204] [213] [239] [125] [281] [214] [176] [249] [310] [309] [311] [245] [78] [266] [297] [”
Universal Differential Equations for Scientific Machine Learning (2020, background): “With initial condition X (0) = ζ has shown that the solution to ?? satisﬁes the following forward-backward SDE (FBSDE) [13]: f ( s, X s , u ( s, X s ) , σ T ( s, X s ) u ( s, X s )) ds with terminating condition g ( X T ) = u ( X T , W T ).”