Analysis of Sparse Bayesian Learning

By Anita C. Faul, Michael E. Tipping. Neural Information Processing Systems, 2001

342 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/f98497d63a286637262c98e07d5325aa22ad2a7a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Lawrence Carin
2. Yoshua Bengio
3. Bernhard Schölkopf
4. Jianfeng Gao
5. Michael I. Jordan
6. Ruslan Salakhutdinov
7. Sergey Levine
8. Francis R. Bach

In Computer Vision and Pattern Recognition

1. Lawrence Carin
2. Luc Van Gool
3. Xiaogang Wang
4. Dacheng Tao
5. Trevor Darrell
6. Cordelia Schmid
7. Andrew Zisserman
8. Bernt Schiele

In Signal Processing

1. Andrea Massa
2. Giacomo Oliveri
3. Zhilin Zhang
4. Bhaskar D. Rao
5. Lawrence Carin
6. Rabab Kreidieh Ward
7. Hamid Palangi
8. David B. Dunson

Citations in the corpus

• Bayesian Compressive Sensing (2008, methodology): “We omit the detailed discussion of this fast algorithm and refer the reader to [26] and [27] for more details.”
• Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) (2005, positive): “However, careful analysis of the RVM marginal likelihood by Faul and Tipping [2002] showed that one can carry out optimization w.”
• The generalized LASSO (2004, methodology): “It should be noticed, however, that recent work on the RVM addresses these shortcomings (see [9] and [10]).”
• Sparse Signal Recovery With Temporally Correlated Source Vectors Using Sparse Bayesian Learning (2011, background): “proposed by Tipping [28], [29], and then was greatly enriched”
• Sparse probabilistic projections (2008, methodology): “We apply Tipping’s sparse Bayesian theory [8], which is closely related to ARD [14].”
• Smart Regularization of Deep Architectures (2015, methodology): “For example we could employ a Horsehoe distribution [48], an Automatic Relevance Determination [49, 50] framework, or a Bayesian Lasso [51] framework.”
• Estimating the age of healthy subjects from T1-weighted MRI scans using kernel methods: Exploring the influence of various parameters (2010, positive): “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).”
• Sparse estimation automatically selects voxels relevant for the decoding of fMRI activity patterns (2008, neutral): “Faul and Tipping (2002) have analyzed the mechanism of sparsity from a mathematical perspective.”
• Multitask Compressive Sensing (2009, background): “A rigorous analysis for L = 1 is provided in [51].”
• Sparse Bayesian learning for basis selection (2004, background): “Similar effective weight pruning occurs in higher dimensional problems, as evidenced by simulation studies, Theorem 2, and the analysis in [35].”
• Fast Marginal Likelihood Maximisation for Sparse Bayesian Models (2003, methodology): “…effectively maps the classification problem to a regression one with ‘targets’ (cid:98) t and data-dependent (heteroscedastic) noise, with the inverse noise variance for n given by It will be convenient to utilise this linearised form in the classification variant of the newly-proposed algorithm.”
• Distributed Compressive Sensing: A Deep Learning Approach (2015, methodology): “It was shown that the global minimum of the proposed method is always the sparsest one.”
• Bayesian Compressive Sampling for Pattern Synthesis With Maximally Sparse Non-Uniform Linear Arrays (2011, background): “Hereinafter, the Gaussian hierarchical prior [32][33][34] is invoked p (w|a) = ∏N n=1 √ an exp ( −n2 n 2 )”
• Pattern Recognition and Machine Learning (2006, positive): “85) on a particular αi and then determine its stationary points explicitly (Faul and Tipping, 2002; Tipping and Faul, 2003).”
• Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media (2017, background): “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 ’ ”
• A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regime (2019, methodology): “…in order to induce sparsity in the feature functions of pc given in Equation (13), we make use of the Automatic Relevance Determination (ARD) model (Faul, 2003) corresponding to p(θ̃c|γ) = dim(λc)∏ m=1 Nfeatures,m∏ j=1 N (θ̃c,jm|0, γ−1jm), (16) where the precision hyperparameters γjm are equipped…”