Bayesian Interpolation

By David John Cameron MacKay. 1992

Subfields: Probabilistic & Bayesian Methods

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Citations in the corpus

PAC-Bayesian Theory Meets Bayesian Inference (2016, neutral): “ly mentioned by Grünwald [16]) obtained by considering the negative log-likelihood loss function (Section3). By doing so, we provide an alternative explanation for the Bayesian Occam’s razor criteria [23, 30] in the context of model selection, expressed as the complexity-accuracy trade-off appearing”
Variational Inference: A Review for Statisticians (2016, methodology): “e regression coefﬁcients. 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 p”
Weight Agnostic Neural Networks (2019, background): “The weight parameters of a BNN [3, 4, 26, 43, 68, 78] are not ﬁxed values, but sampled from a distribution.”
A Simple Baseline for Bayesian Uncertainty in Deep Learning (2019, methodology): “In the late 1990s, Bayesian methods were the state-of-the-art approach to learning with neural networks, through the seminal works of Neal [49] and MacKay [40].”
BayesNAS: A Bayesian Approach for Neural Architecture Search (2019, methodology): “In principle, the Bayesian approach to learn neural networks does not have problems of tuning a large amount of hyperparameters or overfitting the training data (MacKay, 1992b;a; Neal, 1995; HernándezLobato & Adams, 2015).”
Variational Dropout Sparsifies Deep Neural Networks (2017, methodology): “We follow (Kingma & Welling, 2013) and use the Repa-rameterization Trick to obtain an unbiased differentiable minibatch-based Monte Carlo estimator of the expected log-likelihood (3).”
Accurate Uncertainties for Deep Learning Using Calibrated Regression (2018, methodology): “The simplest model we study is Bayesian Ridge Regression (MacKay, 1992).”
Compression of Deep Convolutional Neural Networks for Fast and Low Power Mobile Applications (2015, methodology): “We employed recently developed global analytic solutions for variational Bayesian matrix factorization (VBMF) (Nakajima et al., 2013).”
Efficient Inference of Parsimonious Phenomenological Models of Cellular Dynamics Using S-Systems and Alternating Regression (2014, methodology): “This minimizes the generalization error [12, 19, 20].”
Gaussian Process Regression Networks (2011, background): “In machine learning, Gaussian process regression developed out of neural networks research.”
Exploiting compositionality to explore a large space of model structures (2012, background): “Minimum message length (Wal-lace, 2005), minimum description length (Barron et al., 1998), and Bayesian model comparison (MacKay, 1992) are frameworks which can, in principle, be used to compare very different generative models.”
A Bayesian framework for the analysis of microarray expression data: regularized t -test and statistical inferences of gene changes (2001, methodology): “The regularizing effect of the Cyber-T prior based on the background standard deviation is shown for this data in Figure 2 and in the simulation described below.”
Sparse Bayesian multi-task learning for predicting cognitive outcomes from neuroimaging measures in Alzheimer's disease (2012, methodology): “We estimate the hyperparameters in the evidence maximization framework [11, 15].”
Assessment and Propagation of Model Uncertainty (2011, unknown): “…and Spiegelhalter, 1981; Stewart and Davis, 1986; Brown and Lindley, 1986; Draper et al., 1987; Hodges, 1987; Lavine, 1988, 1992; Raftery, 1988; Madigan and Raftery, 1992); econometrics (e.g., Geisel, 1974; Leamer, 1978); and artiicial intelligence (e.g., Self and Cheeseman, 1987; Mackay, 1992).”
The Evidence Framework Applied to Classification Networks (1992, background): “This objective function was derived with active learning in mind. It could also be used for selection of a subset of a large quantity of data, as a filter to weed out fractions of the data that are unlikely to be informative. Unlike Plutowski and White's (1991) approach this filter depends only on t”
Neural networks for classification: a survey (2000, background): “…topics related to neural classification include network training [12], [15], [62], [124], [142], model design and selection [50], [72], [117], [121], [122], [180], [194], sample size issues [51], [135], [136], Bayesian analysis [102], [109], [110], [120], and wavelet networks [165], [166], [196].”