Performance evaluation of DNA copy number segmentation methods

A number of bioinformatic or biostatistical methods are available for analyzing DNA copy number profiles measured from microarray or sequencing technologies. In the absence of rich enough gold standard data sets, the performance of these methods is generally assessed using unrealistic simulation studies, or based on small real data analyses. We have designed and implemented a framework to generate realistic DNA copy number profiles of cancer samples with known truth. These profiles are generated by resampling real SNP microarray data from genomic regions with known copy-number state. The original real data have been extracted from dilutions series of tumor cell lines with matched blood samples at several concentrations. Therefore, the signal-to-noise ratio of the generated profiles can be controlled through the (known) percentage of tumor cells in the sample. In this paper, we describe this framework and illustrate some of the benefits of the proposed data generation approach on a practical use case: a comparison study between methods for segmenting DNA copy number profiles from SNP microarrays. This study indicates that no single method is uniformly better than all others. It also helps identifying pros and cons for the compared methods as a function of biologically informative parameters, such as the fraction of tumor cells in the sample and the proportion of heterozygous markers. Availability: R package jointSeg: http://r-forge.r-project.org/R/?group\_id=156

SegAnnot: an R package for fast segmentation of annotated piecewise constant signals

We describe and propose an implementation of a dynamic programming algorithm for the segmentation of annotated piecewise constant signals. The algorithm is exact in the sense that it recovers the best possible segmentation w.r.t. the quadratic loss that agrees with the annotations

New efficient algorithms for multiple change-point detection with kernels

Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good statistical properties (oracle inequality, \ldots). Nonetheless, they have a high computational cost both in terms of time and memory. This makes their application difficult even for small and medium sample sizes ($n< 10^4$). This computational issue is addressed by first describing a new efficient and exact algorithm for kernel multiple change-point detection with an improved worst-case complexity that is quadratic in time and linear in space. It allows dealing with medium size signals (up to $n \approx 10^5$). Second, a faster but approximation algorithm is described. It is based on a low-rank approximation to the Gram matrix. It is linear in time and space. This approximation algorithm can be applied to large-scale signals ($n \geq 10^6$). These exact and approximation algorithms have been implemented in \texttt{R} and \texttt{C} for various kernels. The computational and statistical performances of these new algorithms have been assessed through empirical experiments. The runtime of the new algorithms is observed to be faster than that of other considered procedures. Finally, simulations confirmed the higher statistical accuracy of kernel-based approaches to detect changes that are not only in the mean. These simulations also illustrate the flexibility of kernel-based approaches to analyze complex biological profiles made of DNA copy number and allele B frequencies. An R package implementing the approach will be made available on github

Changepoint Detection in the Presence of Outliers

Many traditional methods for identifying changepoints can struggle in the presence of outliers, or when the noise is heavy-tailed. Often they will infer additional changepoints in order to fit the outliers. To overcome this problem, data often needs to be pre-processed to remove outliers, though this is difficult for applications where the data needs to be analysed online. We present an approach to changepoint detection that is robust to the presence of outliers. The idea is to adapt existing penalised cost approaches for detecting changes so that they use loss functions that are less sensitive to outliers. We argue that loss functions that are bounded, such as the classical biweight loss, are particularly suitable -- as we show that only bounded loss functions are robust to arbitrarily extreme outliers. We present an efficient dynamic programming algorithm that can find the optimal segmentation under our penalised cost criteria. Importantly, this algorithm can be used in settings where the data needs to be analysed online. We show that we can consistently estimate the number of changepoints, and accurately estimate their locations, using the biweight loss function. We demonstrate the usefulness of our approach for applications such as analysing well-log data, detecting copy number variation, and detecting tampering of wireless devices

Constrained Dynamic Programming and Supervised Penalty Learning Algorithms for Peak Detection in Genomic Data

Peak detection in genomic data involves segmenting counts of DNA sequence reads aligned to different locations of a chromosome. The goal is to detect peaks with higher counts, and filter out background noise with lower counts. Most existing algorithms for this problem are unsupervised heuristics tailored to patterns in specific data types. We propose a supervised framework for this problem, using optimal changepoint detection models with learned penalty functions. We propose the first dynamic programming algorithm that is guaranteed to compute the optimal solution to changepoint detection problems with constraints between adjacent segment mean parameters. Implementing this algorithm requires the choice of penalty parameter that determines the number of segments that are estimated. We show how the supervised learning ideas of Rigaill et al. (2013) can be used to choose this penalty. We compare the resulting implementation of our algorithm to several baselines in a benchmark of labeled ChIP-seq data sets with two dierent patterns (broad H3K36me3 data and sharp H3K4me3 data). Whereas baseline unsupervised methods only provide accurate peak detection for a single pattern, our supervised method achieves state-of-the-art accuracy in all data sets. The log-linear timings of our proposed dynamic programming algorithm make it scalable to the large genomic data sets that are now common. Our implementation is available in the PeakSegOptimal R package on CRAN

Online Multivariate Changepoint Detection: Leveraging Links With Computational Geometry

The increasing volume of data streams poses significant computational challenges for detecting changepoints online. Likelihood-based methods are effective, but their straightforward implementation becomes impractical online. We develop two online algorithms that exactly calculate the likelihood ratio test for a single changepoint in p-dimensional data streams by leveraging fascinating connections with computational geometry. Our first algorithm is straightforward and empirically quasi-linear. The second is more complex but provably quasi-linear: $\mathcal{O}(n\log(n)^{p+1})$ for $n$ data points. Through simulations, we illustrate, that they are fast and allow us to process millions of points within a matter of minutes up to $p=5$.Comment: 31 pages,15 figure

Fast Online Changepoint Detection via Functional Pruning CUSUM statistics

Many modern applications of online changepoint detection require the ability to process high-frequency observations, sometimes with limited available computational resources. Online algorithms for detecting a change in mean often involve using a moving window, or specifying the expected size of change. Such choices affect which changes the algorithms have most power to detect. We introduce an algorithm, Functional Online CuSUM (FOCuS), which is equivalent to running these earlier methods simultaneously for all sizes of window, or all possible values for the size of change. Our theoretical results give tight bounds on the expected computational cost per iteration of FOCuS, with this being logarithmic in the number of observations. We show how FOCuS can be applied to a number of different change in mean scenarios, and demonstrate its practical utility through its state-of-the art performance at detecting anomalous behaviour in computer server data

gfpop: an R Package for Univariate Graph-Constrained Change-point Detection

In a world with data that change rapidly and abruptly, it is important to detect those changes accurately. In this paper we describe an R package implementing an algorithm recently proposed by Hocking et al. [2017] for penalised maximum likelihood inference of constrained multiple change-point models. This algorithm can be used to pinpoint the precise locations of abrupt changes in large data sequences. There are many application domains for such models, such as medicine, neuroscience or genomics. Often, practitioners have prior knowledge about the changes they are looking for. For example in genomic data, biologists sometimes expect peaks: up changes followed by down changes. Taking advantage of such prior information can substantially improve the accuracy with which we can detect and estimate changes. Hocking et al. [2017] described a graph framework to encode many examples of such prior information and a generic algorithm to infer the optimal model parameters, but implemented the algorithm for just a single scenario. We present the gfpop package that implements the algorithm in a generic manner in R/C++. gfpop works for a user-defined graph that can encode the prior nformation of the types of change and implements several loss functions (Gauss, Poisson, Binomial, Biweight and Huber). We then illustrate the use of gfpop on isotonic simulations and several applications in biology. For a number of graphs the algorithm runs in a matter of seconds or minutes for 10^5 datapoints