Fast Marginal Likelihood Maximisation for Sparse Bayesian Models

By Michael E. Tipping, Anita C. Faul. International Conference on Artificial Intelligence and Statistics, 2003

1,050 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/135f419219b63ce08dd002ef4dd7e03d9352ac23

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Citations in the corpus

Battery Health Prognosis for Electric Vehicles Using Sample Entropy and Sparse Bayesian Predictive Modeling (2016, unknown): “ing [49]: ⎪⎪⎪⎨ ⎪⎪⎪⎩ γi,k+1 = βi,k μ(2)i,k σ(2) k+1 = ‖t−Φμk‖(2) Ns− M ∑”
Sparse multinomial logistic regression: fast algorithms and generalization bounds (2005, methodology): “The weight update equation (15) provides an explicit criterion for whether or not to include each basis function in the classifier, in a similar vein to the criterion derived in [36].”
Bayesian Compressive Sensing (2008, methodology): “We omit the detailed discussion of this fast algorithm, and refer the reader to [26], [ 27 ] for more details.”
A Hybrid Prognostics Approach for Estimating Remaining Useful Life of Rolling Element Bearings (2020, methodology): “In order to reduce the computational burden, this paper uses a faster marginal likelihood maximization algorithm, namely the sequential sparse Bayesian learning algorithm [31].”
A Nonlinear Mapping Approach to Stain Normalization in Digital Histopathology Images Using Image-Specific Color Deconvolution (2014, methodology): “(RVM) method [24] is selected as it is a sparse kernel machine that results in a model with several orders of magnitude fewer support vectors (and thus runtime) than the related support vec-”
Estimating the age of healthy subjects from T1-weighted MRI scans using kernel methods: Exploring the influence of various parameters (2010, unknown): “This prior is a characteristic feature of the RVM, and its use results in a vector of independent hyperpara-meters that reduces the data set (Faul and Tipping, 2002; Tipping and Faul, 2003; Tipping, 2000).”
A New View of Automatic Relevance Determination (2007, methodology): “Finally, a third algorithm has recently been proposed that optimally updates a single hyperparameter γi at a time, which can be done very efficiently in closed form [16].”
The Bayesian backfitting relevance vector machine (2004, unknown): “We note that there are several \optimizations" that are suggested in (Tipping, 2001; Tipping & Faul, 2003).”
Multi-task compressive sensing with Dirichlet process priors (2008, methodology): “(30) may be derived based on the fast algorithm in [23], which is developed in a manner similar to the fast RVM algorithm [33].”
Bayesian Compressive Sampling for Pattern Synthesis With Maximally Sparse Non-Uniform Linear Arrays (2011, methodology): “∣ [ EREF , a, σ 2 ]) = p (EREF | [w, σ(2)]) p (w|a) p (EREF | [a, σ2]) (8) turns out to be equal to the following multivariate Gaussian distribution [34] p (”
Multitask Compressive Sensing (2009, methodology): “To apply the fast algorithm discussed above, an initial guess of is required, and this value is then fixed thereafter to allow the iterative update formulae [43].”
Sparse estimation automatically selects voxels relevant for the decoding of fMRI activity patterns (2008, unknown): “Two different algorithms based on this approach have been proposed for the logistic regression model with the ARD model (Tipping and Faul, 2003) and for the multinomial logistic regression with the Laplace prior (Krishnapuram et al., 2005).”
Examining the impact of driving style on the predictability and responsiveness of the driver: Real-world and simulator analysis (2010, methodology): “To summarize, sensor data from the vehicle, driver, and environment (such as steering angle, head movements, lateral lane position, etc.) are windowed over a period of two seconds; this raw data is used as a feature vector input to a classification scheme based on the Relevance Vector Machine [18].”