Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors

By Mark A. Girolami, Simon Rogers. 2006

223 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering

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Citations in the corpus

Adversarial Examples, Uncertainty, and Transfer Testing Robustness in Gaussian Process Hybrid Deep Networks (2017, methodology): “The robustmax is deﬁned as [24, 19]: Note that as we have distributions over the latent variables the gradient is able to ﬂow through these max selecting operations and the likelihood can be evaluated through one-dimensional Gaussian quadrature.”
Scalable Variational Gaussian Process Classification (2014, methodology): “Without modifying our original model, we can introduce a set of additional latent variables g which relate to the original latent variables f through a unit variance isotropic Gaussian, similar in spirit to Girolami and Rogers [2006]:”
Probabilistic multi-class multi-kernel learning: on protein fold recognition and remote homology detection (2008, methodology): “…where w cn is the weight with which data point n ‘votes’ for class c, and assuming a standardized normal noise model as in Albert and Chib (1993) and Girolami and Rogers (2006) is given by where N x ( m , v ) denotes the normal distribution of x with mean m and variance v , W and Y are C (cid:1)…”
General Latent Feature Models for Heterogeneous Datasets (2017, methodology): “Under this observation model, we can write y nr = znb d r + u d nr, where u d nr is a Gaussian noise variable with variance σ(2) y , therefore, we can obtain, as described in [10], the probability of each element x d n taking value r ∈ {1, .”
MCMC for Variationally Sparse Gaussian Processes (2015, methodology): “(12) As Girolami and Rogers [32] discuss, the ‘soft’ probit-like behaviour is recovered by adding a diagonal ‘nugget’ to the covariance function.”
Multi-Class Gaussian Process Classification Made Conjugate: Efficient Inference via Data Augmentation (2019, background): “Girolami and Rogers (2006) propose an augmentation strategy to multinomial probit regression but does not scale.”
Non-conjugate Variational Message Passing for Multinomial and Binary Regression (2011, methodology): “Here we have also included “Probit”, corresponding to a Bayesian multinomial probit regression model, estimated using VMP, and similar in setup to [6], except that we use EP to approximate the predictive distribution, rather than sampling.”
Variational learning for latent Gaussian model of discrete data (2012, background): “This is a very common assumption made in machine learning community, for example, see Girolami and Rogers [2006]; Seeger et al.”
Mean field variational bayes for elaborate distributions (2011, background): “In the multiparameter case, corresponding to Bayesian generalized additive models, the link function also impacts tractability of MFVB schemes (e.g., Girolami and Rogers 2006).”
Variational free energy and the Laplace approximation (2007, methodology): “See Girolami and Rogers (2005) for an example of comparing Laplace and variational approximations to exact Inference via Gibbs sampling in the context of multinomial probit regression with Gaussian process priors.”
Non-Parametric Calibration for Classification (2019, methodology): “We use variational inference to approximate the posterior (Girolami and Rogers, 2006, Paul et al., 2012).”
Explaining Variational Approximations (2010, methodology): “The same trick applies to product density variational approximation (Girolami & Rogers, 2006), as we now show.”
A Scalable Hierarchical Gaussian Process Classifier (2019, methodology): “As discussed in [36], this is equivalent to adding white noise to the latent function resulting in the probit-like behaviour.”
Graph-based approach for airborne light detection and ranging segmentation (2014, methodology): “vbmpRadial t, variational Bayesian multinomial probit regression with Gaussian process priors (Girolami and Rogers, 2006), uses the function vbmp from the vbmp package, which fits a multinomial probit regression model with radial basis function kernel and covariance parameters estimated from the tra”