John T. Ormerod

Bio: John T. Ormerod is an academic researcher from University of Sydney. The author has contributed to research in topics: Bayes' theorem & Bayesian inference. The author has an hindex of 17, co-authored 55 publications receiving 1561 citations. Previous affiliations of John T. Ormerod include University of Melbourne & University of Sydney School of Mathematics and Statistics.

Explaining Variational Approximations

Abstract: Variational approximations facilitate approximate inference for the parameters in complex statistical models and provide fast, deterministic alternatives to Monte Carlo methods. However, much of the contemporary literature on variational approximations is in Computer Science rather than Statistics, and uses terminology, notation, and examples from the former field. In this article we explain variational approximation in statistical terms. In particular, we illustrate the ideas of variational approximation using examples that are familiar to statisticians.

On semiparametric regression with O'Sullivan penalised splines

Abstract: This is an expos\'e on the use of O'Sullivan penalised splines in contemporary semiparametric regression, including mixed model and Bayesian formulations. O'Sullivan penalised splines are similar to P-splines, but have an advantage of being a direct generalisation of smoothing splines. Exact expressions for the O'Sullivan penalty matrix are obtained. Comparisons between the two reveals that O'Sullivan penalised splines more closely mimic the natural boundary behaviour of smoothing splines. Implementation in modern computing environments such as Matlab, R and BUGS is discussed.

On semiparametric regression with O'Sullivan penalized splines

Abstract: Summary An exposition on the use of O'Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented O'Sullivan penalized splines are similar to P-splines, but have the advantage of being a direct generalization of smoothing splines Exact expressions for the O'Sullivan penalty matrix are obtained Comparisons between the two types of splines reveal that O'Sullivan penalized splines more closely mimic the natural boundary behaviour of smoothing splines Implementation in modern computing environments such as Matlab, r and bugs is discussed

Mean Field Variational Bayes for Elaborate Distributions

Abstract: We develop strategies for mean eld variational Bayes approximate inference for Bayesian hierarchical models containing elaborate distributions. We loosely dene elaborate distributions to be those having more complicated forms compared with common distributions such as those in the Normal and Gamma families. Examples are Asymmetric Laplace, Skew Normal and Generalized Ex- treme Value distributions. Such models suer from the diculty that the param- eter updates do not admit closed form solutions. We circumvent this problem through a combination of (a) specially tailored auxiliary variables, (b) univariate quadrature schemes and (c) nite mixture approximations of troublesome den-

scMerge leverages factor analysis, stable expression, and pseudoreplication to merge multiple single-cell RNA-seq datasets

Abstract: Concerted examination of multiple collections of single-cell RNA sequencing (RNA-seq) data promises further biological insights that cannot be uncovered with individual datasets. Here we present scMerge, an algorithm that integrates multiple single-cell RNA-seq datasets using factor analysis of stably expressed genes and pseudoreplicates across datasets. Using a large collection of public datasets, we benchmark scMerge against published methods and demonstrate that it consistently provides improved cell type separation by removing unwanted factors; scMerge can also enhance biological discovery through robust data integration, which we show through the inference of development trajectory in a liver dataset collection.

Pattern Recognition and Machine Learning

Abstract: Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Machine Learning : A Probabilistic Perspective

Abstract: Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Abstract: Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

Variational Inference: A Review for Statisticians

Abstract: One of the core problems of modern statistics is to approximate difficult-to-compute probability densities. This problem is especially important in Bayesian statistics, which frames all inference about unknown quantities as a calculation involving the posterior density. In this article, we review variational inference (VI), a method from machine learning that approximates probability densities through optimization. VI has been used in many applications and tends to be faster than classical methods, such as Markov chain Monte Carlo sampling. The idea behind VI is to first posit a family of densities and then to find a member of that family which is close to the target density. Closeness is measured by Kullback–Leibler divergence. We review the ideas behind mean-field variational inference, discuss the special case of VI applied to exponential family models, present a full example with a Bayesian mixture of Gaussians, and derive a variant that uses stochastic optimization to scale up to massive data...