What if end-users could own the software development lifecycle from conception to deployment using only requirements expressed in language, images, video or audio? We explore this idea, building on the capabilities that Generative AI brings to software generation and maintenance techniques. How could designing software in this way better serve end-users? What are the implications of this process for the future of end-user software engineering and the software development lifecycle? We discuss the research needed to bridge the gap between where we are today and these imagined systems of the future.

Software designed using dataflow architecture naturally produces a graphical model of the data transformation process through the system. Interpreting this as a causal graph, we can leverage techniques from causal inference to estimate downstream effects of changes in code components, which can be interpreted as interventions within the causal graph. This allows for less costly software experimentation and can add another layer of protection against undesirable production updates.

Component-based development is one of the core principles behind modern software engineering practices. Understanding of causal relationships between components of a software system can yield significant benefits to developers. Yet modern software design approaches make it difficult to track and discover such relationships at system scale, which leads to growing intellectual debt. In this paper we consider an alternative approach to software design, flow-based programming (FBP), and draw the attention of the community to the connection between dataflow graphs produced by FBP and structural causal models. With expository examples we show how this connection can be leveraged to improve day-to-day tasks in software projects, including fault localisation, business analysis and experimentation.

Gaussian process latent variable models (GPLVM) are a flexible and non-linear approach to dimensionality reduction, extending classical Gaussian processes to an unsupervised learning context. The Bayesian incarnation of the GPLVM uses a variational framework, where the posterior over latent variables is approximated by a well-behaved variational family, a factorised Gaussian yielding a tractable lower bound. However, the non-factorisability of the lower bound prevents truly scalable inference. In this work, we study the doubly stochastic formulation of the Bayesian GPLVM model amenable with minibatch training. We show how this framework is compatible with different latent variable formulations and perform experiments to compare a suite of models. Further, we demonstrate how we can train in the presence of massively missing data and obtain high-fidelity reconstructions. We demonstrate the model’s performance by benchmarking against the canonical sparse GPLVM for high dimensional data examples.

Classically, statistical datasets have a larger number of data points than features ($n > p$). The standard model of classical statistics caters for the case where data points are considered conditionally independent given the parameters. However, for $n \approx p$ or $p > n$ such models are poorly determined. Kalaitzis et al. (2013) introduced the Bigraphical Lasso, an estimator for sparse precision matrices based on the Cartesian product of graphs. Unfortunately, the original Bigraphical Lasso algorithm is not applicable in case of large $p$ and $n$ due to memory requirements. We exploit eigenvalue decomposition of the Cartesian product graph to present a more efficient version of the algorithm which reduces memory requirements from $O(n^2p^2)$ to $O(n^2 +p^2)$. Many datasets in different application fields, such as biology, medicine and social science, come with count data, for which Gaussian based models are not applicable. Our multiway network inference approach can be used for discrete data. Our methodology accounts for the dependencies across both instances and features, reduces the computational complexity for high dimensional data and enables to deal with both discrete and continuous data. Numerical studies on both synthetic and real datasets are presented to showcase the performance of our method.

As use of data driven technologies spreads, software engineers are more often faced with the task of solving a business problem using data-driven methods such as machine learning (ML) algorithms. Deployment of ML within large software systems brings new challenges that are not addressed by standard engineering practices and as a result businesses observe high rate of ML deployment project failures. Data Oriented Architecture (DOA) is an emerging approach that can support data scientists and software developers when addressing such challenges. However, there is a lack of clarity about how DOA systems should be implemented in practice. This paper proposes to consider Flow-Based Programming (FBP) as a paradigm for creating DOA applications. We empirically evaluate FBP in the context of ML deployment on four applications that represent typical data science projects. We use Service Oriented Architecture (SOA) as a baseline for comparison. Evaluation is done with respect to different application domains, ML deployment stages, and code quality metrics. Results reveal that FBP is a suitable paradigm for data collection and data science tasks, and is able to simplify data collection and discovery when compared with SOA. We discuss the advantages of FBP as well as the gaps that need to be addressed to increase FBP adoption as a standard design paradigm for DOA.

Amid mounting concern about the reliability and credibility of machine learning research, we present a principled framework for making robust and generalizable claims: the multiverse analysis. Our framework builds upon the multiverse analysis introduced in response to psychology's own reproducibility crisis. To efficiently explore high-dimensional and often continuous ML search spaces, we model the multiverse with a Gaussian Process surrogate and apply Bayesian experimental design. Our framework is designed to facilitate drawing robust scientific conclusions about model performance, and thus our approach focuses on exploration rather than conventional optimization. In the first of two case studies, we investigate disputed claims about the relative merit of adaptive optimizers. Second, we synthesize conflicting research on the effect of learning rate on the large batch training generalization gap. For the machine learning community, the multiverse analysis is a simple and effective technique for identifying robust claims, for increasing transparency, and a step toward improved reproducibility.

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.

A continuing challenge for machine learning is providing methods to perform computation on data while ensuring the data remains private. In this paper we build on the provable privacy guarantees of differential privacy which has been combined with Gaussian processes through the previously published cloaking method, an approach that tackles the problem of providing privacy for the outputs of a training set. In this paper we solve several shortcomings of this method, starting with the problem of predictions in regions with low data density. We experiment with the use of inducing points to provide a sparse approximation and show that these can provide robust differential privacy in outlier areas and at higher dimensions. We then look at classification, and modify the Laplace approximation approach to provide differentially private predictions. We then combine this with the sparse approximation and demonstrate the capability to perform classification in high dimensions. We finally explore the issue of hyperparameter selection and develop a method for their private selection. This paper and associated libraries provide a robust toolkit for combining differential privacy and Gaussian processes in a practical manner.

In modern plants, industrial processes typically operate under different states to meet the different requirements of high-quality products. Many monitoring models for industrial processes were constructed based on the prior knowledge (the mechanism's model or the process data characteristics) to monitor such processes (called multimode processes). However, obtaining this prior knowledge is difficult in practice. Efficiently monitoring nonlinear multimode processes without any prior knowledge is an open problem that demands further exploration. Since data from different modes follow different distributions while data from the same mode are considered to be sampled from the same distribution, the modes of multimode processes can be uncovered based on the characteristics of the process data. This article proposes using a Dirichlet process Gaussian mixed model to classify the modes of multimode processes based on historical data, and then, determine the mode types of the monitored data. A nonlinear monitoring strategy based on the t-distributed stochastic neighbor embedding is then proposed to achieve nonlinear dimensionality reduction and visualize the data. Finally, a monitoring index that is integrated with support vector data description is constructed for comprehensive monitoring. The proposed nonlinear multimode framework completely realizes data-driven mode identification and unsupervised fault detection without knowing any prior knowledge. The effectiveness and feasibility of the proposed model are demonstrated using data from a simulated wastewater treatment plant.

Transferring knowledge from a teacher neural network pretrained on the same or a similar task to a student neural network can significantly improve the performance of the student neural network. Existing knowledge transfer approaches match the activations or the corresponding hand-crafted features of the teacher and the student networks. We propose an information-theoretic framework for knowledge transfer which formulates knowledge transfer as maximizing the mutual information between the teacher and the student networks. We compare our method with existing knowledge transfer methods on both knowledge distillation and transfer learning tasks and show that our method consistently outperforms existing methods. We further demonstrate the strength of our method on knowledge transfer across heterogeneous network architectures by transferring knowledge from a convolutional neural network (CNN) to a multi-layer perceptron (MLP) on CIFAR-10. The resulting MLP significantly outperforms the-state-of-the-art methods and it achieves similar performance to the CNN with a single convolutional layer.

Despite the recent progress in hyperparameter optimization (HPO), available benchmarks that resemble real-world scenarios consist of a few and very large problem instances that are expensive to solve. This blocks researchers and practitioners no only from systematically running large-scale comparisons that are needed to draw statistically significant results but also from reproducing experiments that were conducted before. This work proposes a method to alleviate these issues by means of a meta-surrogate model for HPO tasks trained on off-line generated data. The model combines a probabilistic encoder with a multi-task model such that it can generate inexpensive and realistic tasks of the class of problems of interest. We demonstrate that benchmarking HPO methods on samples of the generative model allows us to draw more coherent and statistically significant conclusions that can be reached orders of magnitude faster than using the original tasks. We provide evidence of our findings for various HPO methods on a wide class of problems.

A major challenge for machine learning is increasing the availability of data while respecting the privacy of individuals. Here we combine the provable privacy guarantees of the differential privacy framework with the flexibility of Gaussian processes (GPs). We propose a method using GPs to provide differentially private (DP) regression. We then improve this method by crafting the DP noise covariance structure to efficiently protect the training data, while minimising the scale of the added noise. We find that this cloaking method achieves the greatest accuracy, while still providing privacy guarantees, and offers practical DP for regression over multi-dimensional inputs. Together these methods provide a starter toolkit for combining differential privacy and GPs.

We tackle the problem of optimizing a black-box objective function defined over a highly-structured input space. This problem is ubiquitous in science and engineering. In machine learning, inferring the structure of a neural network or the Automatic Statistician (AS), where the optimal kernel combination for a Gaussian process is selected, are two important examples. We use the \as as a case study to describe our approach, that can be easily generalized to other domains. We propose an Structure Generating Variational Auto-encoder (SG-VAE) to embed the original space of kernel combinations into some low-dimensional continuous manifold where Bayesian optimization (BO) ideas are used. This is possible when structural knowledge of the problem is available, which can be given via a simulator or any other form of generating potentially good solutions. The right exploration-exploitation balance is imposed by propagating into the search the uncertainty of the latent space of the SG-VAE, that is computed using variational inference. The key aspect of our approach is that the SG-VAE can be used to bias the search towards relevant regions, making it suitable for transfer learning tasks. Several experiments in various application domains are used to illustrate the utility and generality of the approach described in this work.

Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimize black-box functions where direct queries of the objective are expensive. We consider the case where direct access to the function is not possible, but information about user preferences is. Such scenarios arise in problems where human preferences are modeled, such as A/B tests or recommender systems. We present a new framework for this scenario that we call Preferential Bayesian Optimization (PBO) and that allows to find the optimum of a latent function that can only be queried through pairwise comparisons, so-called duels. PBO extend the applicability of standard BO ideas and generalizes previous discrete dueling approaches by modeling the probability of the the winner of each duel by means of Gaussian process model with a Bernoulli likelihood. The latent preference function is used to define a family of acquisition functions that extend usual policies used in BO. We illustrate the benefits of PBO in a variety of experiments in which we show how the way correlations are modeled is the key ingredient to drastically reduce the number of comparisons to find the optimum of the latent function of interest.

Often in machine learning, data are collected as a combination of multiple conditions, e.g., the voice recordings of multiple persons, each labeled with an ID. How could we build a model that captures the latent information related to these conditions and generalize to a new one with few data? We present a new model called Latent Variable Multiple Output Gaussian Processes (LVMOGP) that allows to jointly model multiple conditions for regression and generalize to a new condition with a few data points at test time. LVMOGP infers the posteriors of Gaussian processes together with a latent space representing the information about different conditions. We derive an efficient variational inference method for LVMOGP for which the computational complexity is as low as sparse Gaussian processes. We show that LVMOGP significantly outperforms related Gaussian process methods on various tasks with both synthetic and real data.

MOTIVATION: Regulation of gene expression in prokaryotes involves complex co-regulatory mechanisms involving large numbers of transcriptional regulatory proteins and their target genes. Uncovering these genome-scale interactions constitutes a major bottleneck in systems biology. Sparse latent factor models, assuming activity of transcription factors (TFs) as unobserved, provide a biologically interpretable modelling framework, integrating gene expression and genome-wide binding data, but at the same time pose a hard computational inference problem. Existing probabilistic inference methods for such models rely on subjective filtering and suffer from scalability issues, thus are not well-suited for realistic genome-scale applications. RESULTS: We present a fast Bayesian sparse factor model, which takes input gene expression and binding sites data, either from ChIP-seq experiments or motif predictions, and outputs active TF-gene links as well as latent TF activities. Our method employs an efficient variational Bayes scheme for model inference enabling its application to large datasets which was not feasible with existing MCMC-based inference methods for such models. We validate our method on synthetic data against a similar model in the literature, employing MCMC for inference, and obtain comparable results with a small fraction of the computational time. We also apply our method to large-scale data from Mycobacterium tuberculosis involving ChIP-seq data on 113 TFs and matched gene expression data for 3863 putative target genes. We evaluate our predictions using an independent transcriptomics experiment involving over-expression of TFs. AVAILABILITY AND IMPLEMENTATION: An easy-to-use Jupyter notebook demo of our method with data is available at https://github.com/zhenwendai/SITAR. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The popularity of Bayesian optimization methods for efficient exploration of parameter spaces has lead to a series of papers applying Gaussian processes as surrogates in the optimization of functions. However, most proposed approaches only allow the exploration of the parameter space to occur sequentially. Often, it is desirable to simultaneously propose batches of parameter values to explore. This is particularly the case when large parallel processing facilities are available. These could either be computational or physical facets of the process being optimized. Batch methods, however, require the modeling of the interaction between the different evaluations in the batch, which can be expensive in complex scenarios. We investigate this issue and propose a highly effective heuristic based on an estimate of the function’s Lipschitz constant that captures the most important aspect of this interaction–local repulsion–at negligible computational overhead. A penalized acquisition function is used to collect batches of points minimizing the non-parallelizable computational effort. The resulting algorithm compares very well, in run-time, with much more elaborate alternatives.

We present GLASSES: Global optimisation with Look-Ahead through Stochastic Simulation and Expected-loss Search. The majority of global optimisation approaches in use are myopic, in only considering the impact of the next function value; the non-myopic approaches that do exist are able to consider only a handful of future evaluations. Our novel algorithm, GLASSES, permits the consideration of dozens of evaluations into the future. This is done by approximating the ideal look-ahead loss function, which is expensive to evaluate, by a cheaper alternative in which the future steps of the algorithm are simulated beforehand. An Expectation Propagation algorithm is used to compute the expected value of the loss. We show that the far-horizon planning thus enabled leads to substantive performance gains in empirical tests.

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to an linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models "Chained Gaussian Processes": the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.

The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximised over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximising an analytic lower bound on the exact marginal likelihood. We apply this method for learning a GP-LVM from i.i.d. observations and for learning non-linear dynamical systems where the observations are temporally correlated. We show that a benefit of the variational Bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the non-linear latent space. The resulting framework is generic, flexible and easy to extend for other purposes, such as Gaussian process regression with uncertain or partially missing inputs. We demonstrate our method on synthetic data and standard machine learning benchmarks, as well as challenging real world datasets, including high resolution video data.

BACKGROUND: Transcription factors (TFs) act downstream of the major signalling pathways functioning as master regulators of cell fate. Their activity is tightly regulated at the transcriptional, post-transcriptional and post-translational level. Proteins modifying TF activity are not easily identified by experimental high-throughput methods. RESULTS: We developed a computational strategy, called Differential Multi-Information (DMI), to infer post-translational modulators of a transcription factor from a compendium of gene expression profiles (GEPs). DMI is built on the hypothesis that the modulator of a TF (i.e. kinase/phosphatases), when expressed in the cell, will cause the TF target genes to be co-expressed. On the contrary, when the modulator is not expressed, the TF will be inactive resulting in a loss of co-regulation across its target genes. DMI detects the occurrence of changes in target gene co-regulation for each candidate modulator, using a measure called Multi-Information. We validated the DMI approach on a compendium of 5,372 GEPs showing its predictive ability in correctly identifying kinases regulating the activity of 14 different transcription factors. CONCLUSIONS: DMI can be used in combination with experimental approaches as high-throughput screening to efficiently improve both pathway and target discovery. An on-line web-tool enabling the user to use DMI to identify post-transcriptional modulators of a transcription factor of interest che be found at http://dmi.tigem.it.

In this publication, we combine two Bayesian nonparametric 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 variational approximation 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 significant speed-up over EM-based variational inference.

We present a novel method for approximate inference. Using some of the constructs from expectation propagation (EP), we derive a lower bound of the marginal likelihood in a similar fashion to variational Bayes (VB). The method combines some of the benefits of VB and EP: it can be used with light-tailed likelihoods (where traditional VB fails), and it provides a lower bound on the marginal likelihood. We apply the method to Gaussian process classification, a situation where the Kullback-Leibler divergence minimized in traditional VB can be infinite, and to robust Gaussian process regression, where the inference process is dramatically simplified in comparison to EP. Code to reproduce all the experiments can be found at github.com/SheffieldML/TVB.

Machine learning practitioners are often faced with a choice between a discriminative and a generative approach to modelling. Here, we present a model based on a hybrid approach that breaks down some of the barriers between the discriminative and generative points of view, allowing continuous dimensionality reduction of hybrid discrete-continuous data, discriminative classification with missing inputs and manifold learning informed by class labels.

Gene transcription mediated by RNA polymerase II (pol-II) is a key step in gene expression. The dynamics of pol-II moving along the transcribed region influence the rate and timing of gene expression. In this work, we present a probabilistic model of transcription dynamics which is fitted to pol-II occupancy time course data measured using ChIP-Seq. The model can be used to estimate transcription speed and to infer the temporal pol-II activity profile at the gene promoter. Model parameters are estimated using either maximum likelihood estimation or via Bayesian inference using Markov chain Monte Carlo sampling. The Bayesian approach provides confidence intervals for parameter estimates and allows the use of priors that capture domain knowledge, e.g. the expected range of transcription speeds, based on previous experiments. The model describes the movement of pol-II down the gene body and can be used to identify the time of induction for transcriptionally engaged genes. By clustering the inferred promoter activity time profiles, we are able to determine which genes respond quickly to stimuli and group genes that share activity profiles and may therefore be co-regulated. We apply our methodology to biological data obtained using ChIP-seq to measure pol-II occupancy genome-wide when MCF-7 human breast cancer cells are treated with estradiol (E2). The transcription speeds we obtain agree with those obtained previously for smaller numbers of genes with the advantage that our approach can be applied genome-wide. We validate the biological significance of the pol-II promoter activity clusters by investigating cluster-specific transcription factor binding patterns and determining canonical pathway enrichment. We find that rapidly induced genes are enriched for both estrogen receptor alpha (ERα) and FOXA1 binding in their proximal promoter regions.

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.

The i.i.d. assumption in machine learning is endemic, but often flawed. Complex data sets exhibit partial correlations between both instances and features. A model specifying both types of correlation can have a number of parameters that scales quadratically with the number of features and data points. We introduce the bigraphical lasso, an estimator for precision matrices of matrix-normals based on the Cartesian product of graphs. A prominent product in spectral graph theory, this structure has appealing properties for regression, enhanced sparsity and interpretability. To deal with the parameter explosion we introduce L1 penalties and fit the model through a flip-flop algorithm that results in a linear number of lasso regressions.

MOTIVATION: Genomic studies have revealed a substantial heritable component of the transcriptional state of the cell. To fully understand the genetic regulation of gene expression variability, it is important to study the effect of genotype in the context of external factors such as alternative environmental conditions. In model systems, explicit environmental perturbations have been considered for this purpose, allowing to directly test for environment-specific genetic effects. However, such experiments are limited to species that can be profiled in controlled environments, hampering their use in important systems such as human. Moreover, even in seemingly tightly regulated experimental conditions, subtle environmental perturbations cannot be ruled out, and hence unknown environmental influences are frequent. Here, we propose a model-based approach to simultaneously infer unmeasured environmental factors from gene expression profiles and use them in genetic analyses, identifying environment-specific associations between polymorphic loci and individual gene expression traits. RESULTS: In extensive simulation studies, we show that our method is able to accurately reconstruct environmental factors and their interactions with genotype in a variety of settings. We further illustrate the use of our model in a real-world dataset in which one environmental factor has been explicitly experimentally controlled. Our method is able to accurately reconstruct the true underlying environmental factor even if it is not given as an input, allowing to detect genuine genotype-environment interactions. In addition to the known environmental factor, we find unmeasured factors involved in novel genotype-environment interactions. Our results suggest that interactions with both known and unknown environmental factors significantly contribute to gene expression variability. AVAILABILITY: and implementation: Software available at http://pmbio.github.io/envGPLVM/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Time course data from microarrays and high-throughput sequencing experiments require simple, computationally efficient and powerful statistical models to extract meaningful biological signal, and for tasks such as data fusion and clustering. Existing methodologies fail to capture either the temporal or replicated nature of the experiments, and often impose constraints on the data collection process, such as regularly spaced samples, or similar sampling schema across replications. RESULTS: We propose hierarchical Gaussian processes as a general model of gene expression time-series, with application to a variety of problems. In particular, we illustrate the method's capacity for missing data imputation, data fusion and clustering.The method can impute data which is missing both systematically and at random: in a hold-out test on real data, performance is significantly better than commonly used imputation methods. The method's ability to model inter- and intra-cluster variance leads to more biologically meaningful clusters. The approach removes the necessity for evenly spaced samples, an advantage illustrated on a developmental Drosophila dataset with irregular replications. CONCLUSION: The hierarchical Gaussian process model provides an excellent statistical basis for several gene-expression time-series tasks. It has only a few additional parameters over a regular GP, has negligible additional complexity, is easily implemented and can be integrated into several existing algorithms. Our experiments were implemented in python, and are available from the authors' website: http://staffwww.dcs.shef.ac.uk/people/J.Hensman/.

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.

We present a general method for deriving collapsed variational inference algorithms 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.

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/.

Meiosis is the cell division that halves the genetic component of diploid cells to form gametes or spores. To achieve this, meiotic cells undergo a radical spatial reorganisation of chromosomes. This reorganisation is a prerequisite for the pairing of parental homologous chromosomes and the reductional division, which halves the number of chromosomes in daughter cells. Of particular note is the change from a centromere clustered layout (Rabl configuration) to a telomere clustered conformation (bouquet stage). The contribution of the bouquet structure to homologous chromosome pairing is uncertain. We have developed a new in silico model to represent the chromosomes of Saccharomyces cerevisiae in space, based on a worm-like chain model constrained by attachment to the nuclear envelope and clustering forces. We have asked how these constraints could influence chromosome layout, with particular regard to the juxtaposition of homologous chromosomes and potential nonallelic, ectopic, interactions. The data support the view that the bouquet may be sufficient to bring short chromosomes together, but the contribution to long chromosomes is less. We also find that persistence length is critical to how much influence the bouquet structure could have, both on pairing of homologues and avoiding contacts with heterologues. This work represents an important development in computer modeling of chromosomes, and suggests new explanations for why elucidating the functional significance of the bouquet by genetics has been so difficult.

High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the variational Gaussian process dynamical system. Our work builds on recent variational approximations for Gaussian process latent variable models to allow for nonlinear dimensionality reduction simultaneously with learning a dynamical prior in the latent space. The approach also allows for the appropriate dimensionality of the latent space to be automatically determined. We demonstrate the model on a human motion capture data set and a series of high resolution video sequences.

Inference in matrix-variate Gaussian models has major applications for multi- output prediction and joint learning of row and column covariances from matrix- variate data. Here, we discuss an approach for efficient inference in such models that explicitly account for iid observation noise. Computational tractability can be retained by exploiting the Kronecker product between row and column covariance matrices. Using this framework, we show how to generalize the Graphical Lasso in order to learn a sparse inverse covariance between features while accounting for a low-rank confounding covariance between samples. We show practical utility on applications to biology, where we model covariances with more than 100,000 di- mensions. We find greater accuracy in recovering biological network structures and are able to better reconstruct the confounders.

UNLABELLED: tigre is an R/Bioconductor package for inference of transcription factor activity and ranking candidate target genes from gene expression time series. The underlying methodology is based on Gaussian process inference on a differential equation model that allows the use of short, unevenly sampled, time series. The method has been designed with efficient parallel implementation in mind, and the package supports parallel operation even without additional software. AVAILABILITY: The tigre package is included in Bioconductor since release 2.6 for R 2.11. The package and a user's guide are available at http://www.bioconductor.org.

BACKGROUND: The analysis of gene expression from time series underpins many biological studies. Two basic forms of analysis recur for data of this type: removing inactive (quiet) genes from the study and determining which genes are differentially expressed. Often these analysis stages are applied disregarding the fact that the data is drawn from a time series. In this paper we propose a simple model for accounting for the underlying temporal nature of the data based on a Gaussian process. RESULTS: 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. CONCLUSIONS: 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.

Latent force models encode the interaction between multiple related dynamical systems in the form of a kernel or covariance function. Each variable to be modeled is represented as the output of a differential equation and each differential equation is driven by a weighted sum of latent functions with uncertainty given by a Gaussian process prior. In this paper we consider employing the latent force model framework for the problem of determining robot motor primitives. To deal with discontinuities in the dynamical systems or the latent driving force we introduce an extension of the basic latent force model, that switches between different latent functions and potentially different dynamical systems. This creates a versatile representation for robot movements that can capture discrete changes and non-linearities in the dynamics. We give illustrative examples on both synthetic data and for striking movements recorded using a Barrett WAM robot as haptic input device. Our inspiration is robot motor primitives, but we expect our model to have wide application for dynamical systems including models for human motion capture data and systems biology.

SUMMARY: TFInfer is a novel open access, standalone tool for genome-wide inference of transcription factor activities from gene expression data. Based on an earlier MATLAB version, the software has now been extended in a number of ways. It has been significantly optimised in terms of performance, and it was given novel functionality, by allowing the user to model both time series and data from multiple independent conditions. With a full documentation and intuitive graphical user interface, together with an in-built data base of yeast and Escherichia coli transcription factors, the software does not require any mathematical or computational expertise to be used effectively. AVAILABILITY: http://homepages.inf.ed.ac.uk/gsanguin/TFInfer.html CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

For model-based 3D human pose estimation, even simple models of the human body lead to high-dimensional state spaces. Where the class of activity is known a priori, low-dimensional activity models learned from training data make possible a thorough and efficient search for the best pose. Conversely, searching for solutions in the full state space places no restriction on the class of motion to be recovered, but is both difficult and expensive. This paper explores a potential middle ground between these approaches, using the hierarchical Gaussian process latent variable model to learn activity at different hierarchical scales within the human skeleton. We show that by training on full-body activity data then descending through the hierarchy in stages and exploring subtrees independently of one another, novel poses may be recovered. Experimental results on motion capture data and monocular video sequences demonstrate the utility of the approach, and comparisons are drawn with existing low-dimensional activity models. © 2009. The copyright of this document resides with its authors.

A popular approach to collaborative filtering is matrix factorization. In this paper we develop a non-linear probabilistic matrix factorization using Gaussian process latent variable models. We use stochastic gradient descent (SGD) to optimize the model. SGD allows us to apply Gaussian processes to data sets with millions of observations without approximate methods. We apply our approach to benchmark movie recommender data sets. The results show better than previous state-of-the-art performance.

BACKGROUND: Most analyses of microarray data are based on point estimates of expression levels and ignore the uncertainty of such estimates. By determining uncertainties from Affymetrix GeneChip data and propagating these uncertainties to downstream analyses it has been shown that we can improve results of differential expression detection, principal component analysis and clustering. Previously, implementations of these uncertainty propagation methods have only been available as separate packages, written in different languages. Previous implementations have also suffered from being very costly to compute, and in the case of differential expression detection, have been limited in the experimental designs to which they can be applied. RESULTS: puma is a Bioconductor package incorporating a suite of analysis methods for use on Affymetrix GeneChip data. puma extends the differential expression detection methods of previous work from the 2-class case to the multi-factorial case. puma can be used to automatically create design and contrast matrices for typical experimental designs, which can be used both within the package itself but also in other Bioconductor packages. The implementation of differential expression detection methods has been parallelised leading to significant decreases in processing time on a range of computer architectures. puma incorporates the first R implementation of an uncertainty propagation version of principal component analysis, and an implementation of a clustering method based on uncertainty propagation. All of these techniques are brought together in a single, easy-to-use package with clear, task-based documentation. CONCLUSION: For the first time, the puma package makes a suite of uncertainty propagation methods available to a general audience. These methods can be used to improve results from more traditional analyses of microarray data. puma also offers improvements in terms of scope and speed of execution over previously available methods. puma is recommended for anyone working with the Affymetrix GeneChip platform for gene expression analysis and can also be applied more generally.

In dimensionality reduction approaches, the data are typically embedded in a Euclidean latent space. However for some data sets this is inappropriate. For example, in human motion data we expect latent spaces that are cylindrical or a toroidal, that are poorly captured with a Euclidean space. In this paper, we present a range of approaches for embedding data in a non-Euclidean latent space. Our focus is the Gaussian Process latent variable model. In the context of human motion modeling this allows us to (a) learn models with interpretable latent directions enabling, for example, style/content separation, and (b) generalise beyond the data set enabling us to learn transitions between motion styles even though such transitions are not present in the data.

We present a sparse approximation approach for dependent output Gaussian processes (GP). Employing a latent function framework, we apply the convolution process formalism to establish dependencies between output variables, where each latent function is represented as a GP. Based on these latent functions, we establish an approximation scheme using a conditional independence assumption between the output processes, leading to an approximation of the full covariance which is determined by the locations at which the latent functions are evaluated. We show results of the proposed methodology for synthetic data and real world applications on pollution prediction and a sensor network.

Identification and comparison of nonlinear dynamical systems using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our method involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible without solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and delay differential equations, and provide a comprehensive comparison with current state of the art methods.

Sampling functions in Gaussian process (GP) models is challenging because of the highly correlated posterior distribution. We describe an efficient Markov chain Monte Carlo algorithm for sampling from the posterior process of the GP model. This algorithm uses control variables which are auxiliary function values that provide a low dimensional representation of the function. At each iteration, the algorithm proposes new values for the control variables and generates the function from the conditional GP prior. The control variable input locations are found by continuously minimizing an objective function. We demonstrate the algorithm on regression and classification problems and we use it to estimate the parameters of a differential equation model of gene regulation.

The Gaussian process latent variable model (GPLVM) is a novel unsupervised approach to nonlinear low dimensional embedding proposed by Lawrence (2005). This paper presents the development of a framework for the implementation of the GPLVM for fault detection. A series of experiments have been carried out comparing and combining the GPLVM to the conventional and widely used linear dimension reduction technique of principal component analysis (PCA). The inclusion of the GPLVM for the visualisation and data analysis, led to a considerable improvement in the classification results

The Gaussian process latent variable model (GP-LVM) is a powerful approach for probabilistic modelling of high dimensional data through dimensional reduction. In this paper we extend the GP-LVM through hierarchies. A hierarchical model (such as a tree) allows us to express conditional independencies in the data as well as the manifold structure. We first introduce Gaussian process hierarchies through a simple dynamical model, we then extend the approach to a more complex hierarchy which is applied to the visualisation of human motion data sets.

Listeners may be able to recognise speech in adverse conditions by “glimpsing” time-frequency regions where the target speech is dominant. Previous computational attempts to identify such regions have been source-driven, using primitive cues. This paper describes a model-driven approach in which the likelihood of spectro-temporal patches of a noisy mixture representing speech is given by a generative model. The focus is on patch size and patch modelling. Small patches lead to a lack of discrimination, while large patches are more likely to contain contributions from other sources. A “cleanness” measure reveals that a good patch size is one which extends over a quarter of the speech frequency range and lasts for 40 ms. Gaussian mixture models are used to represent patches. A compact representation based on a 2D discrete cosine transform leads to reasonable speech/background discrimination.

The Gaussian process latent variable model (GP-LVM) is a generative approach to nonlinear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a non-linear generalization of probabilistic PCA (PPCA) (Tipping & Bishop, 1999). While most approaches to non-linear dimensionality methods focus on preserving local distances in data space, the GP-LVM focusses on exactly the opposite. Being a smooth mapping from latent to data space, it focusses on keeping things apart in latent space that are far apart in data space. In this paper we first provide an overview of dimensionality reduction techniques, placing the emphasis on the kind of distance relation preserved. We then show how the GP-LVM can be generalized, through back constraints, to additionally preserve local distances. We give illustrative experiments on common data sets.

Modelling the dynamics of transcriptional processes in the cell requires the knowledge of a number of key biological quantities. While some of them are relatively easy to measure, such as mRNA decay rates and mRNA abundance levels, it is still very hard to measure the active concentration levels of the transcription factor proteins that drive the process and the sensitivity of target genes to these concentrations. In this paper we show how these quantities for a given transcription factor can be inferred from gene expression levels of a set of known target genes. We treat the protein concentration as a latent function with a Gaussian process prior, and include the sensitivities, mRNA decay rates and baseline expression levels as hyperparameters. We apply this procedure to a human leukemia dataset, focusing on the tumour repressor p53 and obtaining results in good accordance with recent biological studies.

Microarray technology is associated with many sources of experimental uncertainty. In this review we discuss a number of approaches for dealing with this uncertainty in the processing of data from microarray experiments. We focus here on the analysis of high-density oligonucleotide arrays, such as the popular Affymetrix GeneChip array, which contain multiple probes for each target. This set of probes can be used to determine an estimate for the target concentration and can also be used to determine the experimental uncertainty associated with this measurement. This measurement uncertainty can then be propagated through the downstream analysis using probabilistic methods. We give examples showing how these credibility intervals can be used to help identify differential expression, to combine information from replicated experiments and to improve the performance of principal component analysis.

MOTIVATION: Finding differentially expressed genes is a fundamental objective of a microarray experiment. Numerous methods have been proposed to perform this task. Existing methods are based on point estimates of gene expression level obtained from each microarray experiment. This approach discards potentially useful information about measurement error that can be obtained from an appropriate probe-level analysis. Probabilistic probe-level models can be used to measure gene expression and also provide a level of uncertainty in this measurement. This probe-level measurement error provides useful information which can help in the identification of differentially expressed genes. RESULTS: We propose a Bayesian method to include probe-level measurement error into the detection of differentially expressed genes from replicated experiments. A variational approximation is used for efficient parameter estimation. We compare this approximation with MAP and MCMC parameter estimation in terms of computational efficiency and accuracy. The method is used to calculate the probability of positive log-ratio (PPLR) of expression levels between conditions. Using the measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we test PPLR on a spike-in dataset and a mouse time-course dataset. Results show that the inclusion of probe-level measurement error improves accuracy in detecting differential gene expression. AVAILABILITY: The MAP approximation and variational inference described in this paper have been implemented in an R package pplr. The MCMC method is implemented in Matlab. Both software are available from http://umber.sbs.man.ac.uk/resources/puma.

MOTIVATION: Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. Recent experimental high-throughput techniques, such as Chromatin Immunoprecipitation (ChIP) provide important information about the architecture of the regulatory networks in the cell. However, it is very difficult to measure the concentration levels of transcription factor proteins and determine their regulatory effect on gene transcription. It is therefore an important computational challenge to infer these quantities using gene expression data and network architecture data. RESULTS: We develop a probabilistic state space model that allows genome-wide inference of both transcription factor protein concentrations and their effect on the transcription rates of each target gene from microarray data. We use variational inference techniques to learn the model parameters and perform posterior inference of protein concentrations and regulatory strengths. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates, as well as providing a tool to detect which binding events lead to significant regulation. We demonstrate our model on artificial data and on two yeast datasets in which the network structure has previously been obtained using ChIP data. Predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell. AVAILABILITY: MATLAB code is available from http://umber.sbs.man.ac.uk/resources/puma

MOTIVATION: Quantitative estimation of the regulatory relationship between transcription factors and genes is a fundamental stepping stone when trying to develop models of cellular processes. This task, however, is difficult for a number of reasons: transcription factors' expression levels are often low and noisy, and many transcription factors are post-transcriptionally regulated. It is therefore useful to infer the activity of the transcription factors from the expression levels of their target genes. RESULTS: We introduce a novel probabilistic model to infer transcription factor activities from microarray data when the structure of the regulatory network is known. The model is based on regression, retaining the computational efficiency to allow genome-wide investigation, but is rendered more flexible by sampling regression coefficients independently for each gene. This allows us to determine the strength with which a transcription factor regulates each of its target genes, therefore providing a quantitative description of the transcriptional regulatory network. The probabilistic nature of the model also means that we can associate credibility intervals to our estimates of the activities. We demonstrate our model on two yeast datasets. In both cases the network structure was obtained using chromatin immunoprecipitation data. We show how predictions from our model are consistent with the underlying biology and offer novel quantitative insights into the regulatory structure of the yeast cell. AVAILABILITY: MATLAB code is available from http://umber.sbs.man.ac.uk/resources/puma.

In this paper we consider a novel Bayesian interpretation of Fisher's discriminant analysis. We relate Rayleigh's coefficient to a noise model that minimises a cost based on the most probable class centres and that abandons the 'regression to the labels' assumption used by other algorithms. Optimisation of the noise model yields a direction of discrimination equivalent to Fisher's discriminant, and with the incorporation of a prior we can apply Bayes' rule to infer the posterior distribution of the direction of discrimination. Nonetheless, we argue that an additional constraining distribution has to be included if sensible results are to be obtained. Going further, with the use of a Gaussian process prior we show the equivalence of our model to a regularised kernel Fisher's discriminant. A key advantage of our approach is the facility to determine kernel parameters and the regularisation coefficient through the optimisation of the marginal log-likelihood of the data. An added bonus of the new formulation is that it enables us to link the regularisation coefficient with the generalisation error.

The aim of this work is to develop a practical framework, which extends the classical Hidden Markov Models (HMM) for continuous speech recognition based on the Maximum Entropy (MaxEnt) principle. The MaxEnt models can estimate the posterior probabilities directly as with Hybrid NN/HMM connectionist speech recognition systems. In particular, a new acoustic modelling based on discriminative MaxEnt models is formulated and is being developed to replace the generative Gaussian Mixture Models (GMM) commonly used to model acoustic variability. Initial experimental results using the TIMIT phone task are reported.

MOTIVATION: Affymetrix GeneChip arrays are currently the most widely used microarray technology. Many summarization methods have been developed to provide gene expression levels from Affymetrix probe-level data. Most of the currently popular methods do not provide a measure of uncertainty for the expression level of each gene. The use of probabilistic models can overcome this limitation. A full hierarchical Bayesian approach requires the use of computationally intensive MCMC methods that are impractical for large datasets. An alternative computationally efficient probabilistic model, mgMOS, uses Gamma distributions to model specific and non-specific binding with a latent variable to capture variations in probe affinity. Although promising, the main limitations of this model are that it does not use information from multiple chips and does not account for specific binding to the mismatch (MM) probes. RESULTS: We extend mgMOS to model the binding affinity of probe-pairs across multiple chips and to capture the effect of specific binding to MM probes. The new model, multi-mgMOS, provides improved accuracy, as demonstrated on some bench-mark datasets and a real time-course dataset, and is much more computationally efficient than a competing hierarchical Bayesian approach that requires MCMC sampling. We demonstrate how the probabilistic model can be used to estimate credibility intervals for expression levels and their log-ratios between conditions. AVAILABILITY: Both mgMOS and the new model multi-mgMOS have been implemented in an R package, which is available at http://www.bioinf.man.ac.uk/resources/puma.

MOTIVATION: Principal Component Analysis (PCA) is one of the most popular dimensionality reduction techniques for the analysis of high-dimensional datasets. However, in its standard form, it does not take into account any error measures associated with the data points beyond a standard spherical noise. This indiscriminate nature provides one of its main weaknesses when applied to biological data with inherently large variability, such as expression levels measured with microarrays. Methods now exist for extracting credibility intervals from the probe-level analysis of cDNA and oligonucleotide microarray experiments. These credibility intervals are gene and experiment specific, and can be propagated through an appropriate probabilistic downstream analysis. RESULTS: We propose a new model-based approach to PCA that takes into account the variances associated with each gene in each experiment. We develop an efficient EM-algorithm to estimate the parameters of our new model. The model provides significantly better results than standard PCA, while remaining computationally reasonable. We show how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles. The probabilistic nature of the model means that the correct number of principal components is automatically obtained.

Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component analysis (PCA) that we term dual probabilistic PCA (DPPCA). The DPPCA model has the additional advantage that the linear mappings from the embedded space can easily be non-linearised through Gaussian processes. We refer to this model as a Gaussian process latent variable model (GP-LVM). Through analysis of the GP-LVM objective function, we relate the model to popular spectral techniques such as kernel PCA and multidimensional scaling. We then review a practical algorithm for GP-LVMs in the context of large data sets and develop it to also handle discrete valued data and missing attributes. We demonstrate the model on a range of real-world and artificially generated data sets.

We propose a discriminative approach to acoustic space dimensionality selection based on maximum entropy modelling. We form a set of constraints by composing the acoustic space with the space of phone classes, and use a continuous feature formulation of maximum entropy modelling to select an optimal feature set. The suggested approach has two steps: (1) the selection of the best acoustic space that efficiently and economically represents the acoustic data and its variability; (2) the combination of selected acoustic features in the maximum entropy framework to estimate the posterior probabilities over the phonetic labels given the acoustic input. Specific contributions of the paper include a parameter estimation algorithm (generalized improved iterative scaling) that enables the use of negative features, the parameterization of constraint functions using Gaussian mixture models, and experimental results using the TIMIT database.

This paper describes an efficient method for learning the parameters of a Gaussian process (GP). The parameters are learned from multiple tasks which are assumed to have been drawn independently from the same GP prior. An efficient algorithm is obtained by extending the informative vector machine (IVM) algorithm to handle the multi-task learning case. The multi-task IVM (MTIVM) saves computation by greedily selecting the most informative examples from the separate tasks. The MT-IVM is also shown to be more efficient than random sub-sampling on an artificial data-set and more effective than the traditional IVM in a speaker dependent phoneme recognition task.

We present a probabilistic approach to learning a Gaussian Process classifier in the presence of unlabeled data. Our approach involves a "null category noise model" (NCNM) inspired by ordered cate- gorical noise models. The noise model reflects an assumption that the data density is lower between the class-conditional densities. We illustrate our approach on a toy problem and present compar- ative results for the semi-supervised classification of handwritten digits.

Abstract Motivation: Gene expression levels are obtained from microarray experiments through the extraction of pixel intensities from a scanned image of the slide. It is widely acknowledged that variabilities can occur in expression levels extracted from the same images by different users with the same software packages. These inconsistencies arise due to differences in the refinement of the placement of the microarray ‘grids’. We introduce a novel automated approach to the refinement of grid placements that is based upon the use of Bayesian inference for determining the size, shape and positioning of the microarray ‘spots’, capturing uncertainty that can be passed to downstream analysis. Results: Our experiments demonstrate that variability between users can be significantly reduced using the approach. The automated nature of the approach also saves hours of researchers’ time normally spent in refining the grid placement. Availability: A MATLAB implementation of the algorithm and tiff images of the slides used in our experiments, as well as the code necessary to recreate them are available for non-commercial use from http://www.dcs.shef.ac.uk/~neil/VIS

The likelihood models used in probabilistic visual tracking applications are often complex non-linear and/or non-Gaussian functions, leading to analytically intractable inference. Solutions then require numerical approximation techniques, of which the particle filter is a popular choice. Particle filters, however, degrade in performance as the dimensionality of the state space increases and the support of the likelihood decreases. As an alternative to particle filters this paper introduces a variational approximation to the tracking recursion. The variational inference is intractable in itself, and is combined with an efficient importance sampling procedure to obtain the required estimates. The algorithm is shown to compare favorably with particle filtering techniques on a synthetic example and two real tracking problems. The first involves the tracking of a designated object in a video sequence based on its color properties, whereas the second involves contour extraction in a single image.

In this paper we introduce a new underlying probabilistic model for prin- cipal component analysis (PCA). Our formulation interprets PCA as a particular Gaussian process prior on a mapping from a latent space to the observed data-space. We show that if the prior’s covariance func- tion constrains the mappings to be linear the model is equivalent to PCA, we then extend the model by considering less restrictive covariance func- tions which allow non-linear mappings. This more general Gaussian pro- cess latent variable model (GPLVM) is then evaluated as an approach to the visualisation of high dimensional data for three different data-sets. Additionally our non-linear algorithm can be further kernelised leading to ‘twin kernel PCA’ in which a mapping between feature spaces occurs.

We present a framework for sparse Gaussian process (GP) methods which uses forward selection with criteria based on information- theoretic principles, previously suggested for active learning. Our goal is not only to learn d{sparse predictors (which can be evalu- ated in O(d) rather than O(n), d (cid:28) n, n the number of training points), but also to perform training under strong restrictions on time and memory requirements. The scaling of our method is at most O(n (cid:1) d2), and in large real-world classi(cid:12)cation experiments we show that it can match prediction performance of the popular support vector machine (SVM), yet can be signi(cid:12)cantly faster in training. In contrast to the SVM, our approximation produces esti- mates of predictive probabilities (‘error bars’), allows for Bayesian model selection and is less complex in implementation.

It is common in distributed systems to replicate data. In many cases this data evolves in a consistent fashion, and this evolution can be modelled. A probabilistic model of the evolution allows us to estimate the divergence of the replicas and can be used by the application to alter its behaviour, for example to control synchronisation times, to determine the propagation of writes, and to convey to the user information about how much the data may have evolved. In this paper, we describe how the evolution of the data may be modelled and outline how the probabilistic model may be utilised in various applications, concentrating on a news database example.

With the increasing number of users of mobile computing devices (e.g. personal digital assistants) and the advent of third generation mobile phones, wireless communications are becoming increasingly important. Many applications rely on the device maintaining a replica of a data-structure which is stored on a server, for exam(cid:173) ple news databases, calendars and e-mail. ill this paper we explore the question of the optimal strategy for synchronising such replicas. We utilise probabilistic models to represent how the data-structures evolve and to model user behaviour. We then formulate objective functions which can be minimised with respect to the synchronisa(cid:173) tion timings. We demonstrate, using two real world data-sets, that a user can obtain more up-to-date information using our approach.