Sparse Bayesian Learning and the Relevance Vector Machine

By Michael E. Tipping. 2001

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, methodology): “Automatic relevance determination (ARD) assigns a separate prior for each regression coefﬁcient; the idea is to automatically shrink irrelevant coefﬁcients during inference (MacKay, 1992; Neal, 2012; Tipping, 2001; Wipf and Nagarajan, 2008). ARD works by pairing the prior precision of each regressio”
Methods and Models for Interpretable Linear Classification (2014, methodology): “In both cases, sparsity can be further induced using feature selection algorithms [36, 50, 62, 61, 91, 102].”
Bayesian group factor analysis with structured sparsity (2016, methodology): “The group factor analysis (GFA) model puts an ARD prior (Tipping, 2001) on the loading column for each observation to allow column-wise shrinkage (Virtanen et al., 2012; Klami et al., 2014b): λ (w) jh ∼ N 0, α (w) h −1 for j = 1, . . . , p w , α (w) h ∼ Ga(a 0 , b 0 ), for observation w = 1, . . .…”
The effect of machine learning regression algorithms and sample size on individualized behavioral prediction with functional connectivity features (2018, unknown): “This can be expected because these two algorithms are conceptually similar, and RVR was introduced by Tipping (2001) as a Bayesian alternative to LSVR. RVR has a few advantages over LSVR: RVR has far fewer ‘relevance vectors’ compared to the number of ‘support vectors’ in LSVR, which can reduce…”
Fault diagnosis of low speed bearing based on relevance vector machine and support vector machine (2009, methodology): “…applying the logistic sigmoid function r(y) = 1/(1 + e y) to y(x) and adopting the Bernoulli distribution for P(tjx), the likelihood is written as (Tipping, 2001) PðtjxÞ ¼ YN n¼1 rfyðxn; wÞgtn ½1 rfyðxn; wÞg 1 tn ð1Þ However, unlike the regression case, we cannot integrate the weights…”
Prediction of Blast-Induced Ground Vibration in a Mine Using Relevance Vector Regression Optimized by Metaheuristic Algorithms (2020, methodology): “Relevance Vector Regression The RVR proposed by Tipping (2001) is a probabilistic method that works based on the Bayesian approach.”
Photometric redshift analysis in the Dark Energy Survey Science Verification data (2014, methodology): “RVMz is an empirical photo-z code based on the relevance vector machine algorithm from Tipping (2001), a Bayesian sparse kernel method for regression.”
A unified Bayesian framework for MEG/EEG source imaging (2009, unknown): “For S-MAP algorithms, we will show that this selection of C leads to a generalized version of FOCUSS and MCE (Cotter et al., 2005), for γ-MAP and VB, a general form of sparse Bayesian learning (SBL) (Wipf, 2006), a variant of automatic relevance determination (ARD) (Neal, 1996).”
Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media (2017, methodology): “ˇ’ accounts for the Laplace approximation. After convergence of (t);~ (t) c ;~ (t) to ;~ c;MAP;~ MAP, the posterior on ~ cis approximated by (37) p(~ cjD) ˇN(~ cj~ c;MAP;~ MAP): It can be shown [21,74] that many of the prior variance parameters i converge to 0 such that the corresponding features ’ ”
Finding People in Images and Videos (2006, background): “Viola and Jones [2001], Viola et al. [2003] use AdaBoost to train cascades of weak classifiers for face and pedestrian detection, using spatial and temporal difference-of-rectangle based descriptors.”
Shrink Globally, Act Locally: Sparse Bayesian Regularization and Prediction (2012, unknown): “The relevance vector machine of Tipping [2001] involves computing posterior modes to find sparse solutions when ξ, the degrees-of-freedom parameter, goes to 0.”