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Search Results: 1 - 10 of 196778 matches for " Neil D. Lawrence "
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A Unifying Probabilistic Perspective for Spectral Dimensionality Reduction: Insights and New Models
Neil D. Lawrence
Computer Science , 2010,
Abstract: We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian Markov random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting model, which we call maximum entropy unfolding (MEU) is a nonlinear generalization of principal component analysis. We relate the model to Laplacian eigenmaps and isomap. We show that parameter fitting in the locally linear embedding (LLE) is approximate maximum likelihood MEU. We introduce a variant of LLE that performs maximum likelihood exactly: Acyclic LLE (ALLE). We show that MEU and ALLE are competitive with the leading spectral approaches on a robot navigation visualization and a human motion capture data set. Finally the maximum likelihood perspective allows us to introduce a new approach to dimensionality reduction based on L1 regularization of the Gaussian random field via the graphical lasso.
Semi-described and semi-supervised learning with Gaussian processes
Andreas Damianou,Neil D. Lawrence
Computer Science , 2015,
Abstract: Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described learning". We then introduce a GP framework that solves both, the semi-described and the semi-supervised learning problems (where missing values occur in the outputs). Auto-regressive state space simulation is also recognised as a special case of semi-described learning. To achieve our goal we develop variational methods for handling semi-described inputs in GPs, and couple them with algorithms that allow for imputing the missing values while treating the uncertainty in a principled, Bayesian manner. Extensive experiments on simulated and real-world data study the problems of iterative forecasting and regression/classification with missing values. The results suggest that the principled propagation of uncertainty stemming from our framework can significantly improve performance in these tasks.
Nested Variational Compression in Deep Gaussian Processes
James Hensman,Neil D. Lawrence
Statistics , 2014,
Abstract: Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The original approach to approximate inference in these models used variational compression to allow for approximate variational marginalization of the hidden variables leading to a lower bound on the marginal likelihood of the model [Damianou and Lawrence, 2013]. In this paper we extend this idea with a nested variational compression. The resulting lower bound on the likelihood can be easily parallelized or adapted for stochastic variational inference.
Joint Modelling of Confounding Factors and Prominent Genetic Regulators Provides Increased Accuracy in Genetical Genomics Studies
Nicoló Fusi ,Oliver Stegle ,Neil D. Lawrence
PLOS Computational Biology , 2012, DOI: 10.1371/journal.pcbi.1002330
Abstract: Expression quantitative trait loci (eQTL) studies are an integral tool to investigate the genetic component of gene expression variation. A major challenge in the analysis of such studies are hidden confounding factors, such as unobserved covariates or unknown subtle environmental perturbations. These factors can induce a pronounced artifactual correlation structure in the expression profiles, which may create spurious false associations or mask real genetic association signals. Here, we report PANAMA (Probabilistic ANAlysis of genoMic dAta), a novel probabilistic model to account for confounding factors within an eQTL analysis. In contrast to previous methods, PANAMA learns hidden factors jointly with the effect of prominent genetic regulators. As a result, this new model can more accurately distinguish true genetic association signals from confounding variation. We applied our model and compared it to existing methods on different datasets and biological systems. PANAMA consistently performs better than alternative methods, and finds in particular substantially more trans regulators. Importantly, our approach not only identifies a greater number of associations, but also yields hits that are biologically more plausible and can be better reproduced between independent studies. A software implementation of PANAMA is freely available online at http://ml.sheffield.ac.uk/qtl/.
A Simple Approach to Ranking Differentially Expressed Gene Expression Time Courses through Gaussian Process Regression
Alfredo A Kalaitzis, Neil D Lawrence
BMC Bioinformatics , 2011, DOI: 10.1186/1471-2105-12-180
Abstract: We review Gaussian process (GP) regression for estimating the continuous trajectories underlying in gene expression time-series. We present a simple approach which can be used to filter quiet genes, or for the case of time series in the form of expression ratios, quantify differential expression. We assess via ROC curves the rankings produced by our regression framework and compare them to a recently proposed hierarchical Bayesian model for the analysis of gene expression time-series (BATS). We compare on both simulated and experimental data showing that the proposed approach considerably outperforms the current state of the art.Gaussian processes offer an attractive trade-off between efficiency and usability for the analysis of microarray time series. The Gaussian process framework offers a natural way of handling biological replicates and missing values and provides confidence intervals along the estimated curves of gene expression. Therefore, we believe Gaussian processes should be a standard tool in the analysis of gene expression time series.Gene expression profiles give a snapshot of mRNA concentration levels as encoded by the genes of an organism under given experimental conditions. Early studies of this data often focused on a single point in time which biologists assumed to be critical along the gene regulation process after the perturbation. However, the static nature of such experiments severely restricts the inferences that can be made about the underlying dynamical system.With the decreasing cost of gene expression microarrays time series experiments have become commonplace giving a far broader picture of the gene regulation process. Such time series are often irregularly sampled and may involve differing numbers of replicates at each time point [1]. The experimental conditions under which gene expression measurements are taken cannot be perfectly controlled leading the signals of interest to be corrupted by noise, either of biological origin or arising
Residual Component Analysis
Alfredo A. Kalaitzis,Neil D. Lawrence
Computer Science , 2011,
Abstract: Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situation where the data variance is already partially explained by other factors, e.g. covariates of interest, or temporal correlations leaving some residual variance. We decompose the residual variance into its components through a generalized eigenvalue problem, which we call residual component analysis (RCA). We show that canonical covariates analysis (CCA) is a special case of our algorithm and explore a range of new algorithms that arise from the framework. We illustrate the ideas on a gene expression time series data set and the recovery of human pose from silhouette.
Fast Variational Inference in the Conjugate Exponential Family
James Hensman,Magnus Rattray,Neil D. Lawrence
Computer Science , 2012,
Abstract: We present a general method for deriving collapsed variational inference algo- rithms for probabilistic models in the conjugate exponential family. Our method unifies many existing approaches to collapsed variational inference. Our collapsed variational inference leads to a new lower bound on the marginal likelihood. We exploit the information geometry of the bound to derive much faster optimization methods based on conjugate gradients for these models. Our approach is very general and is easily applied to any model where the mean field update equations have been derived. Empirically we show significant speed-ups for probabilistic models optimized using our bound.
Deep Gaussian Processes
Andreas C. Damianou,Neil D. Lawrence
Computer Science , 2012,
Abstract: In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.
Gaussian Processes for Big Data
James Hensman,Nicolo Fusi,Neil D. Lawrence
Computer Science , 2013,
Abstract: We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to depend on a set of globally relevant inducing variables which factorize the model in the necessary manner to perform variational inference. Our ap- proach is readily extended to models with non-Gaussian likelihoods and latent variable models based around Gaussian processes. We demonstrate the approach on a simple toy problem and two real world data sets.
Fast nonparametric clustering of structured time-series
James Hensman,Magnus Rattray,Neil D. Lawrence
Computer Science , 2014,
Abstract: In this publication, we combine two Bayesian non-parametric models: the Gaussian Process (GP) and the Dirichlet Process (DP). Our innovation in the GP model is to introduce a variation on the GP prior which enables us to model structured time-series data, i.e. data containing groups where we wish to model inter- and intra-group variability. Our innovation in the DP model is an implementation of a new fast collapsed variational inference procedure which enables us to optimize our variationala pproximation significantly faster than standard VB approaches. In a biological time series application we show how our model better captures salient features of the data, leading to better consistency with existing biological classifications, while the associated inference algorithm provides a twofold speed-up over EM-based variational inference.
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