6643803
Exploiting the full power of temporal gene expression profiling through a new statistical test: Application to the analysis of muscular dystrophy data
BackgroundThe identification of biologically interesting genes in a temporal expression profiling dataset is challenging and complicated by high levels of experimental noise. Most statistical methods used in the literature do not fully exploit the temporal ordering in the dataset and are not suited to the case where temporal profiles are measured for a number of different biological conditions. We present a statistical test that makes explicit use of the temporal order in the data by fitting polynomial functions to the temporal profile of each gene and for each biological condition. A Hotelling T2-statistic is derived to detect the genes for which the parameters of these polynomials are significantly different from each other.ResultsWe validate the temporal Hotelling T2-test on muscular gene expression data from four mouse strains which were profiled at different ages: dystrophin-, beta-sarcoglycan and gamma-sarcoglycan deficient mice, and wild-type mice. The first three are animal models for different muscular dystrophies. Extensive biological validation shows that the method is capable of finding genes with temporal profiles significantly different across the four strains, as well as identifying potential biomarkers for each form of the disease. The added value of the temporal test compared to an identical test which does not make use of temporal ordering is demonstrated via a simulation study, and through confirmation of the expression profiles from selected genes by quantitative PCR experiments. The proposed method maximises the detection of the biologically interesting genes, whilst minimising false detections.ConclusionThe temporal Hotelling T2-test is capable of finding relatively small and robust sets of genes that display different temporal profiles between the conditions of interest. The test is simple, it can be used on gene expression data generated from any experimental design and for any number of conditions, and it allows fast interpretation of the temporal behaviour of genes. The R code is available from V.V. The microarray data have been submitted to GEO under series GSE1574 and GSE3523.
14510898
Evolutionary learning of dynamic probabilistic models with large time lags
In this paper, we explore the automatic explanation of multivariate time series (MTS) through learning dynamic Bayesian networks (DBNs). We have developed an evolutionary algorithm which exploits certain characteristics of MTS in order to generate good networks as quickly as possible. We compare this algorithm to other standard learning algorithms that have traditionally been used for static Bayesian networks but are adapted for DBNs in this paper. These are extensively tested on both synthetic and real-world MTS for various aspects of efficiency and accuracy. By proposing a simple representation scheme, an efficient learning methodology, and several useful heuristics, we have found that the proposed method is more efficient for learning DBNs from MTS with large time lags, especially in time-demanding situations. © 2001 John Wiley & Sons, Inc.
16058917
Learning Dynamic Bayesian Networks from Multivariate Time Series with Changing Dependencies
Many examples exist of multivariate time series where dependencies between variables change over time. If these changing dependencies are not taken into account, any model that is learnt from the data will average over the different dependency structures. Paradigms that try to explain underlying processes and observed events in multivariate time series must explicitly model these changes in order to allow non-experts to analyse and understand such data. In this paper we have developed a method for generating explanations in multivariate time series that takes into account changing dependency structure. We make use of a dynamic Bayesian network model with hidden nodes. We introduce a representation and search technique for learning such models from data and test it on synthetic time series and real-world data from an oil refinery, both of which contain changing underlying structure. We compare our method to an existing EM-based method for learning structure. Results are very promising for our method and we include sample explanations, generated from models learnt from the refinery dataset.
39184835
Improved Robustness in Time Series Analysis of Gene Expression Data by Polynomial Model Based Clustering
Microarray experiments produce large data sets that often contain noise and considerable missing data. Typical clustering methods such as hierarchical clustering or partitional algorithms can often be adversely affected by such data. This paper introduces a method to overcome such problems associated with noise and missing data by modelling the time series data with polynomials and using these models to cluster the data. Similarity measures for polynomials are given that comply with commonly used standard measures. The polynomial model based clustering is compared with standard clustering methods under different conditions and applied to a real gene expression data set. It shows significantly better results as noise and missing data are increased.
40113853
A Framework for Modelling Short, High-Dimensional Multivariate Time Series: Preliminary Results in Virus Gene Expression Data Analysis
Short, high-dimensional Multivariate Time Series (MTS) data are common in many fields such as medicine, finance and science, and any advance in modelling this kind of data would be beneficial. Nowhere is this more true than functional genomics where effective ways of analysing gene expression data are urgently needed. Progress in this area could help obtain a "global" view of biological processes, and ultimately lead to a great improvement in the quality of human life. We present a computational framework for modelling this type of data, and report preliminary experimental results of applying this framework to the analysis of gene expression data in the virology domain. The framework contains a threestep modelling strategy: correlation search, variable grouping, and short MTS modelling. Novel research is involved in each step which has been individually tested on different real-world datasets in engineering and medicine. This is the first attempt to integrate all these components into a coherent computational framework, and test the framework on a very challenging application area, which has produced promising results.
6104018
A framework for modelling virus gene expression data
Short, high-dimensional, Multivariate Time Series (MTS) data are common in many fields such as medicine, finance and science, and any advance in modelling this kind of data would be beneficial. Nowhere is this truer than functional genomics where effective ways of analysing gene expression data are urgently needed. Progress in this area could help obtain a “global” view of biological processes, and ultimately lead to a great improvement in the quality of human life. We present a computational framework for modelling this type of data, and report experimental results of applying this framework to the analysis of gene expression data in the virology domain. The framework contains a three-step modelling strategy: correlation search, variable grouping, and short MTS modelling. Novel research is involved in each step which has been individually tested on different real-world datasets in engineering and medicine. This is the first attempt to integrate all these components into a coherent computational framework, and test the framework on a very challenging application area, producing promising results.
2422545
Probe-level measurement error improves accuracy in detecting differential gene expression
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.
27917358
Continuous dependence on initial values for impulsive delay differential equations
This paper studies the property of continuous dependence of solutions with respect to initial values for impulsive delay differential equations. Criteria on continuous dependence of solutions with respect to initial functions are established. It is shown, however, that due to the discontinuities of the function space and the time delays in the system, continuous dependence with respect to the initial time, or more generally with respect to the entire initial data, is unfortunately not generally satisfied.
15506913
A class of perfect graphs containing P6
Let P6 denote the induced path on six nodes. We prove that if a perfect graph G contains P6 as an induced subgraph but not two families introduced by Conforti and Cornuejols then G is bipartite or disconnected, or G has a star cutset.
8835059
Computing the maximum similarity bi-clusters of gene expression data
MOTIVATIONS
Bi-clustering is an important approach in microarray data analysis. The underlying bases for using bi-clustering in the analysis of gene expression data are (1) similar genes may exhibit similar behaviors only under a subset of conditions, not all conditions, (2) genes may participate in more than one function, resulting in one regulation pattern in one context and a different pattern in another. Using bi-clustering algorithms, one can obtain sets of genes that are co-regulated under subsets of conditions.


RESULTS
We develop a polynomial time algorithm to find an optimal bi-cluster with the maximum similarity score. To our knowledge, this is the first formulation for bi-cluster problems that admits a polynomial time algorithm for optimal solutions. The algorithm works for a special case, where the bi-clusters are approximately squares. We then extend the algorithm to handle various kinds of other cases. Experiments on simulation data and real data show that the new algorithms outperform most of the existing methods in many cases. Our new algorithms have the following advantages: (1) no discretization procedure is required, (2) performs well for overlapping bi-clusters and (3) works well for additive bi-clusters.


AVAILABILITY
The software is available at http://www.cs.cityu.edu.hk/~liuxw/msbe/help.html.
34468051
Approximation Algorithms for Bi-clustering Problems
One of the main goals in the analysis of microarray data is to identify groups of genes and groups of experimental conditions (including environments, individuals and tissues), that exhibit similar expression patterns. This is the so-called bi-clustering problem. In this paper, we consider two variations of the bi-clustering problem: the Consensus Submatrix Problem and the Bottleneck Submatrix Problem. The input of the problems contains a m×n matrix A and integers l and k. The Consensus Submatrix Problem is to find a l×k submatrix with l<m and k<n and a consensus vector such that the sum of distance between all rows in the submatrix and the vector is minimized. The Bottleneck Submatrix Problem is to find a l×k submatrix with l<m and k<n, an integer d and a center vector such that the distance between every row in the submatrix and the vector is at most d and d is minimized. We show that both problems are NP-hard and give randomized approximation algorithms for special cases of the two problems. Using standard techniques, we can derandomize the algorithms to get polynomial time approximation schemes for the two problems. To our knowledge, this is the first time that approximation algorithms with guaranteed ratio are presented for microarray analysis.