A Bayesian Approach to Online Learning

By Manfred Opper. 2006

87 citations recorded by the source corpus.

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Citations in the corpus

Optimal Continual Learning has Perfect Memory and is NP-hard (2020, methodology): “For example, the work of Opper & Winther (1998) introduces an approximately Bayesian algorithm for neural networks that can be updated continuously in an on-line fashion.”
Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks (2015, methodology): “…method that approximates the exact posterior of a neural network (5) with a factored distribution given by The approximation parameters m ij,l , v ij,l , α γ , β γ , α λ and β λ are determined by applying an assumed density ﬁltering method (Opper & Winther, 1998; Minka, 2001) on the posterior (5).”
Streaming Sparse Gaussian Process Approximations (2017, methodology): “This section briefly highlights connections between the new framework and existing approaches including Power Expectation Propagation (Power-EP), Expectation Propagation (EP), Assumed Density Filtering (ADF), and streaming variational Bayes.”
Analytic moment-based Gaussian process filtering (2009, unknown): “We review results by Rasmussen and Ghahramani (2003), Quiñonero-Candela et al.”
Bayesian Online Multitask Learning of Gaussian Processes (2010, methodology): “Online methods developed in single-task contexts [31], [32] rely upon sparse representations of Gaussian models, obtained, for example, by replacing the posterior distribution with a simpler parametric description.”
A Bayesian Rule for Adaptive Control based on Causal Interventions (2009, background): “The distribution that minimizes the KL-divergence is a Bayesian mixture distribution over all possible environments [Haussler and Opper, 1997, Opper, 1998].”
Sparse Online Gaussian Processes (2008, methodology): “Our on-line Gaussian approximation (without sparseness) was found to be asymptotically efficient (in the sense of Fisher) in the finite dimensional (i.e. parametric) case (Opper 1996; Opper 1998).”
Bayesian indoor positioning systems (2005, methodology): “Again, alternatives to simulation such as online EM algorithms or quasi-Bayes ([16]) procedures may prove necessary.”
A Minimum Relative Entropy Principle for Learning and Acting (2008, background): “(3) The solution to Equation 3 is the system B deﬁned by the set of equations (5) P For reference, see Haussler and Opper (1997) and Opper (1998) where the P ( m ao t ) = w m ( ao t ) and P ( m ao t a t ) = w m ( ao t a t ) are just the posterior probabilities over the elements in M given the…”
Partitioned Variational Inference: A unified framework encompassing federated and continual learning (2018, background): “Continual learning has a rich literature [see e.g. Opper, 1998, Sato, 2001, Ghahramani and Attias, 2000, Csató and Opper, 2002, Minka, 2001, Smola et al., 2004] but is enjoying a resurgence of interest ranging from deepening understanding of transfer learning and catastrophic forgetting [Goodfellow…”