Change-point Algorithm Research Articles

An exact approach to Bayesian sequential change point detection

Change point models seek to fit a piecewise regression model with unknown breakpoints to a data set whose parameters are suspected to change through time. However, the exponential number of possible solutions to a multiple change point problem requires an efficient algorithm if long time series are to be analyzed. A sequential Bayesian change point algorithm is introduced that provides uncertainty bounds on both the number and location of change points. The algorithm is able to quickly update itself in linear time as each new data point is recorded and uses the exact posterior distribution to infer whether or not a change point has been observed. Simulation studies illustrate how the algorithm performs under various parameter settings, including detection speeds and error rates, and allow for comparison with several existing multiple change point algorithms. The algorithm is then used to analyze two real data sets, including global surface temperature anomalies over the last 130 years.

Fuzzy Change-Point Algorithms for Regression Models

Change-point (CP) regression models have been widely applied in various fields, where detecting CPs is an important problem. Detecting the location of CPs in regression models could be equivalent to partitioning data points into clusters of similar individuals. In the literature, fuzzy clustering has been widely applied in various fields, but it is less used in locating CPs in CP regression models. In this paper, a new method, called fuzzy CP (FCP) algorithm, is proposed to detect the CPs and simultaneously estimate the parameters of regression models. The fuzzy c -partitions concept is first embedded into the CP regression models. Any possible collection of all CPs is considered as a partitioning of data with a fuzzy membership. We then transfer these memberships into the pseudomemberships of data points belonging to each individual cluster, and therefore, we can obtain the estimates for model parameters by the fuzzy c -regressions method. Subsequently, we use the fuzzy c -means clustering to obtain the new iterates of the CP collection memberships by minimizing an objective function concerning the deviations between the predicted response values and data values. We illustrate the new approach with several numerical examples and real datasets. Experimental results actually show that the proposed FCP is an effective and useful CP detection algorithm for CP regression models and can be applied to various fields, such as econometrics, medicine, quality control, and signal processing.

An Information-Based Approach to Change-Point Analysis with Applications to Biophysics and Cell Biology

This article describes the application of a change-point algorithm to the analysis of stochastic signals in biological systems whose underlying state dynamics consist of transitions between discrete states. Applications of this analysis include molecular-motor stepping, fluorophore bleaching, electrophysiology, particle and cell tracking, detection of copy number variation by sequencing, tethered-particle motion, etc. We present a unified approach to the analysis of processes whose noise can be modeled by Gaussian, Wiener, or Ornstein-Uhlenbeck processes. To fit the model, we exploit explicit, closed-form algebraic expressions for maximum-likelihood estimators of model parameters and estimated information loss of the generalized noise model, which can be computed extremely efficiently. We implement change-point detection using the frequentist information criterion (which, to our knowledge, is a new information criterion). The frequentist information criterion specifies a single, information-based statistical test that is free from ad hoc parameters and requires no prior probability distribution. We demonstrate this information-based approach in the analysis of simulated and experimental tethered-particle-motion data.

Detecting translational regulation by change point analysis of ribosome profiling data sets.

Ribo-Seq maps the location of translating ribosomes on mature mRNA transcripts. While during normal translation, ribosome density is constant along the length of the mRNA coding region, this can be altered in response to translational regulatory events. In the present study, we developed a method to detect translational regulation of individual mRNAs from their ribosome profiles, utilizing changes in ribosome density. We used mathematical modeling to show that changes in ribosome density should occur along the mRNA at the point of regulation. We analyzed a Ribo-Seq data set obtained for mouse embryonic stem cells and showed that normalization by corresponding RNA-Seq can be used to improve the Ribo-Seq quality by removing bias introduced by deep-sequencing and alignment artifacts. After normalization, we applied a change point algorithm to detect changes in ribosome density present in individual mRNA ribosome profiles. Additional sequence and gene isoform information obtained from the UCSC Genome Browser allowed us to further categorize the detected changes into different mechanisms of regulation. In particular, we detected several mRNAs with known post-transcriptional regulation, e.g., premature termination for selenoprotein mRNAs and translational control of Atf4, but also several more mRNAs with hitherto unknown translational regulation. Additionally, our approach proved useful for identification of new transcript isoforms.

Deciphering behavioral changes in animal movement with a “multiple change point algorithm- classification tree” framework

The recent development of tracking tools has improved our nascent knowledge on animal movement. Because of model complexity, unrealistic a priori hypotheses and heavy computational resources, behavioral changes along an animal path are still often assessed visually. A new avenue has recently been opened with change point algorithms because tracking data can be organized as time series with potential periodic change points segregating the movement in segments of different statistical properties. So far this approach was restricted to single change point detection and we propose a straightforward analytical framework based on a recent multiple change point algorithm: the PELT algorithm, a dynamic programming pruning search method to find, within time series, the optimal combination of number and locations of change points. Data segments found by the algorithm are then sorted out with a supervised classification tree procedure to organize segments by movement classes. We apply this framework to investigate changes in variance in daily distances of a migratory bird, the Macqueen’s Bustard, Chlamydotis macqueenii, and describe its movements in three classes: staging, non-migratory and migratory movements. Using simulation experiments, we show that the algorithm is robust to identify exact behavioral shift (on average more than 80% of the time) but that positive autocorrelation when present is likely to lead to the detection of false change points (in 36% of the iterations with an average of 1.97 (se = 0.06) additional change points). A case study is provided to illustrate the biases associated with visual analysis of movement patterns compared to the reliability of our analytical framework. Technological improvement will provide new opportunities for the study of animal behavior, bringing along huge and various data sets, a growing challenge for biologists, and this straightforward and standardized framework could be an asset in the attempt to decipher animal behavior.

The Bayesian Change Point and Variable Selection Algorithm: Application to the δ18O Proxy Record of the Plio-Pleistocene

In this article, we introduce the Bayesian change point and variable selection algorithm that uses dynamic programming recursions to draw direct samples from a very high-dimensional space in a computationally efficient manner, and apply this algorithm to a geoscience problem that concerns the Earth's history of glaciation. Strong evidence exists for at least two changes in the behavior of the Earth's glaciers over the last five million years. Around 2.7 Ma, the extent of glacial cover on the Earth increased, but the frequency of glacial melting events remained constant at 41 kyr. A more dramatic change occurred around 1 Ma. For over three decades, the “Mid-Pleistocene Transition” has been described in the geoscience literature not only by a further increase in the magnitude of glacial cover, but also as the dividing point between the 41 kyr and the 100 kyr glacial worlds. Given such striking changes in the glacial record, it is clear that a model whose parameters can change through time is essential for the analysis of these data. The Bayesian change point algorithm provides a probabilistic solution to a data segmentation problem, while the exact Bayesian inference in regression procedure performs variable selection within each regime delineated by the change points. Together, they can model a time series in which the predictor variables as well as the parameters of the model are allowed to change with time. Our algorithm allows one to simultaneously perform variable selection and change point analysis in a computationally efficient manner. Supplementary materials including MATLAB code for the Bayesian change point and variable selection algorithm and the datasets described in this article are available online or by contacting the first author.

Ecp: AnRPackage for Nonparametric Multiple Change Point Analysis of Multivariate Data

There are many different ways in which change point analysis can be performed, from purely parametric methods to those that are distribution free. The ecp package is designed to perform multiple change point analysis while making as few assumptions as possible. While many other change point methods are applicable only for univariate data, this R package is suitable for both univariate and multivariate observations. Hierarchical estimation can be based upon either a divisive or agglomerative algorithm. Divisive estimation sequentially identifies change points via a bisection algorithm. The agglomerative algorithm estimates change point locations by determining an optimal segmentation. Both approaches are able to detect any type of distributional change within the data. This provides an advantage over many existing change point algorithms which are only able to detect changes within the marginal distributions.

Simultaneous Imaging of Leading- and Lagging-Strand Synthesis Reveals Distinct Operational Modes of Single Replication Machines

The proliferation of all organisms depends on the precise coordination of a large number of enzymatic events within multiprotein replisomes to ensure that chromosome duplication occurs in a timely and faithful manner. While the core architectural characteristics of replisomes are known, the inner workings of these sophisticated molecular machines remain poorly understood. In particular, it remains unclear how discontinuous synthesis on the lagging strand, which requires several slow enzymatic steps, can occur without causing loss of coordination with continuous synthesis of the leading strand. To study the coordination of enzymatic events during replication, we have developed an assay to simultaneously monitor the synthesis of each daughter strand by single replisomes. Using ultra-low-magnification single-molecule microscopy, we image up to 30,000 individual surface-immobilized DNA molecules simultaneously. Beads attached at either end of these molecules reveal the rates of synthesis on the leading- and lagging-strand independently. To derive detailed kinetic information from these complex multistate observations, we have developed a novel change-point algorithm for identifying and fitting distinct kinetic regimes in an unbiased manner. We have applied our single-molecule assay and analysis method to study the coordination of daughter stand synthesis by the bacteriophage T7 replisome. Using inhibitors and a variety of different enzymatic conditions, we have selectively altered the rates of helicase unwinding, priming and polymerase loading. These studies have allowed us to deconstruct the relative timing of events on the leading- and lagging-strands, resulting in a revised understanding of how enzymatic events are coordinated at the replication fork.

What is learned during simultaneous temporal acquisition? An individual-trials analysis

The processes involved in the acquisition of simultaneous temporal processing are currently less understood. For example, it is unclear whether scalar property emerges early during simultaneous temporal acquisition. Using an information-processing model which accounts for the amount of information that each temporal process provides in regard to reward time, we predicted that scalar property would emerge early during the acquisition process, but that subjects should take about 27% longer (more trials) to acquire the long duration than the short duration. To evaluate these predictions, we performed individual-trials analyses to identify changes in timing behavior when rats simultaneously acquire two criterion durations, either 10s and 20s (group 10/20) or 20s and 40s (group 20/40). To analyze the individual trials we used a change-point algorithm to identify changes in rats’ wait time. For each individual rat, and for each criterion duration, analyses indicated that simultaneous temporal acquisition is characterized by a sudden change in waiting to a wait-time proportional to the associated criterion. The results failed to indicate group differences in regard to the number of trials it takes for the change in wait-time to occur, but that in both groups, it took longer (more trials) to acquire the long duration than the shorter one, not significantly different from the theoretical prediction. These results are discussed in the framework of an information-processing model informing both associative and temporal learning, thus providing a bridge between the two fields.This article is part of a Special Issue entitled: Associative and Temporal Learning.

Novelty detection in long-term attentional habituation processes using a Bayesian change point algorithm

Habituation is defined as a response decrement resulting from repeated stimulation [1]. This process is very important in filtering a large amount of information in the surrounding environment and focusing our attention on only the features of the environment that are important to us. Here we address the problem of objectively assessing long-term habituation using electroencephalographic auditory late responses (ALRs). We propose using a Bayesian change point algorithm to measure the novelty process and apply it to two experimental data sets of 50dB and 100dB stimuli responses. These correspond to cases of habituation and non-habituation respectively.

Statistical trend and change-point analysis of land-cover-change patterns in East Africa

This work presents a new four-tier hierarchical change-point algorithm designed to detect land-cover change from satellite data. We tested the algorithm using Global Inventory Modelling and Mapping Studies (GIMMS) data for eastern Africa. Using a unique sequence of four statistical change-point detection methods, we identified significant increases or decreases in normalized difference vegetation index (NDVI), estimated the approximate time of change, and characterized the likely forms of change (i.e. linear trend, abrupt mean and/or variability change, and hockey-stick shaped change). Our method allows not just the identification of the change point but also the manner of change, and it can provide considerable insights into land-cover trajectories. In that sense, our approach has a significant advantage over other types of change-detection methods commonly reported in the remote-sensing literature. Although we demonstrated our algorithm using annual averages for coarse resolution data, our method can be easily adapted to finer spatial or temporal scale data, assuming assumptions of normality and independence are met. Overall, the changes detected by the algorithm are consistent with changes observed by other authors for the East Africa study area. We have demonstrated a powerful new tool for the detection of land-cover change using multi-temporal satellite data.

Breaking the Millisecond Barrier: Single Molecule Motors Wobble to Find their Next Binding Sites

Breaking the Millisecond Barrier: Single Molecule Motors Wobble to Find their Next Binding Sites

Tilting and Wobble of Myosin V by High-Speed Single-Molecule Polarized Fluorescence Microscopy

Myosin V is biomolecular motor with two actin-binding domains (heads) that take multiple steps along actin by a hand-over-hand mechanism. We used high-speed polarized total internal reflection fluorescence (polTIRF) microscopy to study the structural dynamics of single myosin V molecules that had been labeled with bifunctional rhodamine linked to one of the calmodulins along the lever arm. With the use of time-correlated single-photon counting technology, the temporal resolution of the polTIRF microscope was improved ∼50-fold relative to earlier studies, and a maximum-likelihood, multitrace change-point algorithm was used to objectively determine the times when structural changes occurred. Short-lived substeps that displayed an abrupt increase in rotational mobility were detected during stepping, likely corresponding to random thermal fluctuations of the stepping head while it searched for its next actin-binding site. Thus, myosin V harnesses its fluctuating environment to extend its reach. Additional, less frequent angle changes, probably not directly associated with steps, were detected in both leading and trailing heads. The high-speed polTIRF method and change-point analysis may be applicable to single-molecule studies of other biological systems.

Evaluation of calling algorithms for array-CGH

Copy number variation (CNV) detection has become an integral part many of genetic studies and new technologies promise to revolutionize our ability to detect and link them to disease. However, recent studies highlight discrepancies in the genome wide CNV profile when measured by different technologies and even by the same technology. Furthermore, the change point algorithms used to call CNVs can have substantial disagreement on the same data set. We focus this article on comparative genomic hybridization (CGH) arrays because this platform lends itself well to accurate statistical modeling. We describe some newer methodological developments in local statistics that are well suited for CNV detection and calling on CGH arrays. Then we use both simulation studies and public data to compare these new local methods with the global methods that currently dominate literature. These results offer suggestions for choosing a particular method and provide insight to the lack of reproducibility that has been seen in the field so far.

A Late 20th Century European Climate Shift: Fingerprint of Regional Brightening?

We investigate the spatial extent of a statistically highly significant shift in atmospheric temperatures over Europe around 1987-1988 using a boot-strap change point algorithm. According to this algorithm, this change point (average warming of about one degree Celsius) is statistically highly significant (p > 99.9999%). The change point is consistently present in satellite and surface temperature measurements as well as temperature re-analyses and ocean heat content over most of Western Europe. We also find a connection with parts of the North Atlantic Ocean and eastern Asia. Although the time of change coincides with the North Atlantic Oscillation (NAO) going from negative to positive, the consistent warmer temperatures throughout the decades after 1987-1988 does not coincide with a persistent shift of the NAO, as it returns to a neutral/negative in the 1990’s. Furthermore, the shift does not coincide with any other known mode of multidecadal internal climate variability. We argue that the notion of a shift is “spurious”, i.e. the result of a fast change in Europe from dimming to brightening combined with an accidental sequence of cold (negative NAO) and warm (positive) NAO years during this period. The “shift” could therefore be considered as a fingerprint of European brightening during the last few decades.

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

ChIPseq is a widely used technique for investigating protein-DNA interactions. Read density profiles are generated by using next-sequencing of protein-bound DNA and aligning the short reads to a reference genome. Enriched regions are revealed as peaks, which often differ dramatically in shape, depending on the target protein(1). For example, transcription factors often bind in a site- and sequence-specific manner and tend to produce punctate peaks, while histone modifications are more pervasive and are characterized by broad, diffuse islands of enrichment(2). Reliably identifying these regions was the focus of our work. Algorithms for analyzing ChIPseq data have employed various methodologies, from heuristics(3-5) to more rigorous statistical models, e.g. Hidden Markov Models (HMMs)(6-8). We sought a solution that minimized the necessity for difficult-to-define, ad hoc parameters that often compromise resolution and lessen the intuitive usability of the tool. With respect to HMM-based methods, we aimed to curtail parameter estimation procedures and simple, finite state classifications that are often utilized. Additionally, conventional ChIPseq data analysis involves categorization of the expected read density profiles as either punctate or diffuse followed by subsequent application of the appropriate tool. We further aimed to replace the need for these two distinct models with a single, more versatile model, which can capably address the entire spectrum of data types. To meet these objectives, we first constructed a statistical framework that naturally modeled ChIPseq data structures using a cutting edge advance in HMMs(9), which utilizes only explicit formulas-an innovation crucial to its performance advantages. More sophisticated then heuristic models, our HMM accommodates infinite hidden states through a Bayesian model. We applied it to identifying reasonable change points in read density, which further define segments of enrichment. Our analysis revealed how our Bayesian Change Point (BCP) algorithm had a reduced computational complexity-evidenced by an abridged run time and memory footprint. The BCP algorithm was successfully applied to both punctate peak and diffuse island identification with robust accuracy and limited user-defined parameters. This illustrated both its versatility and ease of use. Consequently, we believe it can be implemented readily across broad ranges of data types and end users in a manner that is easily compared and contrasted, making it a great tool for ChIPseq data analysis that can aid in collaboration and corroboration between research groups. Here, we demonstrate the application of BCP to existing transcription factor(10,11) and epigenetic data(12) to illustrate its usefulness.

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types

A Bayesian approach to detecting change points in climatic records

AbstractGiven distinct climatic periods in the various facets of the Earth's climate system, many attempts have been made to determine the exact timing of ‘change points’ or regime boundaries. However, identification of change points is not always a simple task. A time series containing N data points has approximately Nk distinct placements of k change points, rendering brute force enumeration futile as the length of the time series increases. Moreover, how certain are we that any one placement of change points is superior to the rest? This paper introduces a Bayesian Change Point algorithm which provides uncertainty estimates both in the number and location of change points through an efficient probabilistic solution to the multiple change point problem. To illustrate its versatility, the Bayesian Change Point algorithm is used to analyse both the NOAA/NCDC annual global surface temperature anomalies time series and the much longer δ18O record of the Plio‐Pleistocene. Copyright © 2012 Royal Meteorological Society

Single Molecule Myosin V Dynamics Using High Time Resolution Polarized TIRF

Translocation of the molecular motor myosin along its actin filament track was studied using polarized total internal reflection (polTIRF) microscopy, a technique that determines the 3D orientation and dynamic wobble of single fluorophores. The maximum time resolution of the experimental setup was increased 50-fold by cycling through 8 different input laser paths and linear polarizations in approximately 1 ms. The arrival time and polarization state of each photon was recorded using a modified time-correlated single photon counting module. A new analysis, the Multiple Channel Change Point algorithm, was developed to detect changes in molecular orientation and wobble using the raw time-stamped data with no user-defined bins or thresholds. The analysis objectively identified changes in orientation and wobble of each fluorophore with a time resolution limited only by the photon counting rate. The polarized fluorescence from single rhodamine probes bifunctionally attached to one of the calmodulins on the myosin V lever arm was recorded as the motor translocated along a fixed actin filament in the presence of ATP. At the low (10 uM) ATP concentrations used here, the time intervals between sudden polarization changes averaged 120 ms and corresponded to stable orientations of the lever arm after each step. Occasionally, 10–80 ms substeps with increased probe wobble were detected between the longer duration dwells, possibly corresponding to the putative diffusive search of the detached head for its next actin binding site. Periods of large wobble were also detected at the end of many runs and when molecules were attached to actin in the absence of ATP. In both situations motors are probably bound to actin by only one head. This work was supported by NSF grants DMR-0832802, EF-0928048, IGERT DGE02-21664 and NIH grant GM-086352.

Detection of slightly expressed changes in random environment

Consider a regular parametric family of distributions F(·, θ). The classical change point problem deals with observations corresponding to θ = 0 before a point of change, and θ = µ after that. We substitute the latter constant µ by a set of random variables θ i,n called a random environment assuming that E[θ i,n ] = µ n → 0. The random environment can be independent or obtained by random permutations of a given set. We define the rates of convergence and give the conditions under which the classical parametric change point algorithms apply.