On optimal multiple changepoint algorithms for large data

Disentangling sex-dependent effects of APOE on diverse trajectories of cognitive decline in Alzheimer's disease

Current diagnostic systems for Alzheimer's disease (AD) rely upon clinical signs and symptoms, despite the fact that the multiplicity of clinical symptoms renders various neuropsychological assessments inadequate to reflect the underlying pathophysiological mechanisms. Since putative neuroimaging biomarkers play a crucial role in understanding the etiology of AD, we sought to stratify the diverse relationships between AD biomarkers and cognitive decline in the aging population and uncover risk factors contributing to the diversities in AD. To do so, we capitalized on a large amount of neuroimaging data from the ADNI study to examine the inflection points along the dynamic relationship between cognitive decline trajectories and whole-brain neuroimaging biomarkers, using a state-of-the-art statistical model of change point detection. Our findings indicated that the temporal relationship between AD biomarkers and cognitive decline may differ depending on the synergistic effect of genetic risk and biological sex. Specifically, tauopathy-PET biomarkers exhibit a more dynamic and age-dependent association with Mini-Mental State Examination scores (p<0.05), with inflection points at 72, 78, and 83 years old, compared with amyloid-PET and neurodegeneration (cortical thickness from MRI) biomarkers. In the landscape of health disparities in AD, our analysis indicated that biological sex moderates the rate of cognitive decline associated with APOE4 genotype. Meanwhile, we found that higher education levels may moderate the effect of APOE4, acting as a marker of cognitive reserve.

Assessment of small strain modulus in soil using advanced computational models

Small-strain shear modulus ([Formula: see text]) of soils is a crucial dynamic parameter that significantly impacts seismic site response analysis and foundation design. [Formula: see text] is susceptible to multiple factors, including soil uniformity coefficient ([Formula: see text]), void ratio (e), mean particle size ([Formula: see text]), and confining stress ([Formula: see text]). This study aims to establish a [Formula: see text] database and suggests three advanced computational models for [Formula: see text] prediction. Nine performance indicators, including four new indices, are employed to calculate and analyze the model's performance. The XGBoost model outperforms the other two models, with all three models achieving [Formula: see text] values exceeding 0.9, RMSE values below 30, MAE values below 25, VAF values surpassing 80%, and ARE values below 50%. Compared to the empirical formula-based traditional prediction models, the model proposed in this study exhibits better performance in IOS, IOA, a20-index, and PI metrics values. The model has higher prediction accuracy and better generalization ability.

DiffSegR: an RNA-seq data driven method for differential expression analysis using changepoint detection

To fully understand gene regulation, it is necessary to have a thorough understanding of both the transcriptome and the enzymatic and RNA-binding activities that shape it. While many RNA-Seq-based tools have been developed to analyze the transcriptome, most only consider the abundance of sequencing reads along annotated patterns (such as genes). These annotations are typically incomplete, leading to errors in the differential expression analysis. To address this issue, we present DiffSegR - an R package that enables the discovery of transcriptome-wide expression differences between two biological conditions using RNA-Seq data. DiffSegR does not require prior annotation and uses a multiple changepoints detection algorithm to identify the boundaries of differentially expressed regions in the per-base log2 fold change. In a few minutes of computation, DiffSegR could rightfully predict the role of chloroplast ribonuclease Mini-III in rRNA maturation and chloroplast ribonuclease PNPase in (3'/5')-degradation of rRNA, mRNA and tRNA precursors as well as intron accumulation. We believe DiffSegR will benefit biologists working on transcriptomics as it allows access to information from a layer of the transcriptome overlooked by the classical differential expression analysis pipelines widely used today. DiffSegR is available at https://aliehrmann.github.io/DiffSegR/index.html.

Quantifying uncertainty in spikes estimated from calcium imaging data

In recent years, a number of methods have been proposed to estimate the times at which a neuron spikes on the basis of calcium imaging data. However, quantifying the uncertainty associated with these estimated spikes remains an open problem. We consider a simple and well-studied model for calcium imaging data, which states that calcium decays exponentially in the absence of a spike, and instantaneously increases when a spike occurs. We wish to test the null hypothesis that the neuron did not spike-i.e., that there was no increase in calcium-at a particular timepoint at which a spike was estimated. In this setting, classical hypothesis tests lead to inflated Type I error, because the spike was estimated on the same data used for testing. To overcome this problem, we propose a selective inference approach. We describe an efficient algorithm to compute finite-sample $p$-values that control selective Type I error, and confidence intervals with correct selective coverage, for spikes estimated using a recent proposal from the literature. We apply our proposal in simulation and on calcium imaging data from the $\texttt{spikefinder}$ challenge.

Epidemic changepoint detection in the presence of nuisance changes

Many time series problems feature epidemic changes-segments where a parameter deviates from a background baseline. Detection of such changepoints can be improved by accounting for the epidemic structure, but this is currently difficult if the background level is unknown. Furthermore, in practical data the background often undergoes nuisance changes, which interfere with standard estimation techniques and appear as false alarms. To solve these issues, we develop a new, efficient approach to simultaneously detect epidemic changes and estimate unknown, but fixed, background level, based on a penalised cost. Using it, we build a two-level detector that models and separates nuisance and signal changes. The analytic and computational properties of the proposed methods are established, including consistency and convergence. We demonstrate via simulations that our two-level detector provides accurate estimation of changepoints under a nuisance process, while other state-of-the-art detectors fail. In real-world genomic and demographic datasets, the proposed method identified and localised target events while separating out seasonal variations and experimental artefacts.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00362-022-01307-x.

Multi-threshold proportional hazards model and subgroup identification

We propose a novel two-stage procedure for change point detection and parameter estimation in a multi-threshold proportional hazards model. In the first stage, we estimate the number of thresholds by formulating the threshold detection problem as a variable selection problem and applying the penalized partial likelihood approach. In the second stage, the change point locations are refined by a grid search and the standard inference for segment regression can then follow. The proposed model and estimation procedure could lend support to subgroup identification and personalized treatment recommendation in medical research. We establish the consistency of the threshold estimators and regression coefficient estimators under technical conditions. The finite sample performance of the method is demonstrated via simulation studies and two cancer data examples.

Impact of comparative effectiveness research on Medicare coverage of direct oral anticoagulants

Aim: To evaluate the association of comparative effectiveness research with Medicare coverage of direct oral anticoagulants. Materials & methods: A literature review for direct oral anticoagulants was conducted from 2011 to 2017. Monthly prescription drug plan and formulary files (n = 28) were used to conduct change-point analysis and assess each outcome variable. Results: Up to 2013, studies showed that dabigatran was more effective than rivaroxaban. In 2015, apixaban was shown to be the safest and most effective drug in comparison with all direct oral anticoagulants. In 2016-2017, dabigatran and apixaban were shown to have similar efficacy. Approximately 75% of plans covered dabigatran under tier 3 until 2015. From 2011 to 2017, less than 30% of plans required prior authorizations, 50% imposed quantity limits and mean copayment was lowest for rivaroxaban. Conclusion: Consistent with comparative effectiveness research, Medicare plans covered apixaban more favorably and edoxaban less favorably. However, discrepancies in comparative effectiveness research translation were found for rivaroxaban and dabigatran.

Testing for a Change in Mean After Changepoint Detection

While many methods are available to detect structural changes in a time series, few procedures are available to quantify the uncertainty of these estimates post-detection. In this work, we fill this gap by proposing a new framework to test the null hypothesis that there is no change in mean around an estimated changepoint. We further show that it is possible to efficiently carry out this framework in the case of changepoints estimated by binary segmentation and its variants, ℓ 0 segmentation, or the fused lasso. Our setup allows us to condition on much less information than existing approaches, which yields higher powered tests. We apply our proposals in a simulation study and on a dataset of chromosomal guanine-cytosine content. These approaches are freely available in the R package ChangepointInference at https://jewellsean.github.io/changepoint-inference/.

GNSSseg, a Statistical Method for the Segmentation of Daily GNSS IWV Time Series

Homogenization is an important and crucial step to improve the usage of observational data for climate analysis. This work is motivated by the analysis of long series of GNSS Integrated Water Vapour (IWV) data, which have not yet been used in this context. This paper proposes a novel segmentation method called segfunc that integrates a periodic bias and a heterogeneous, monthly varying, variance. The method consists in estimating first the variance using a robust estimator and then estimating the segmentation and periodic bias iteratively. This strategy allows for the use of the dynamic programming algorithm, which is the most efficient exact algorithm to estimate the change point positions. The performance of the method is assessed through numerical simulation experiments. It is implemented in the R package GNSSseg, which is available on the CRAN. This paper presents the application of the method to a real data set from a global network of 120 GNSS stations. A hit rate of 32% is achieved with respect to available metadata. The final segmentation is made in a semi-automatic way, where the change points detected by three different penalty criteria are manually selected. In this case, the hit rate reaches 60% with respect to the metadata.

Change-Point Detection in Homogeneous Segments of COVID-19 Daily Infection

Modeling the number of individuals in different states is a principal tool in the event of an epidemic. The natural transition of individuals between possible states often includes deliberate interference such as isolation or vaccination. Thus, the mathematical model may need to be re-calibrated due to various factors. The model considered in this paper is the SIRD epidemic model. An additional parameter is the moment of changing the description of the phenomenon when the parameters of the model change and the change is not pre-specified. Detecting and estimating the moment of change in real time is the subject of statistical research. A sequential (online) approach was applied using the Bayesian shift point detection algorithm and trimmed exact linear time. We show how methods of analysis behave in different instances. These methods are verified on simulated data and applied to pandemic data of a selected European country. The simulation is performed with a social network graph to obtain a practical representation ability. The epidemiological data used come from the territory of Poland and concern the COVID-19 epidemic in Poland. The results show satisfactory detection of the moments where the applied model needs to be verified and re-calibrated. These show the effectiveness of the proposed combination of methods.

Detecting multiple generalized change-points by isolating single ones

We introduce a new approach, called Isolate-Detect (ID), for the consistent estimation of the number and location of multiple generalized change-points in noisy data sequences. Examples of signal changes that ID can deal with are changes in the mean of a piecewise-constant signal and changes, continuous or not, in the linear trend. The number of change-points can increase with the sample size. Our method is based on an isolation technique, which prevents the consideration of intervals that contain more than one change-point. This isolation enhances ID's accuracy as it allows for detection in the presence of frequent changes of possibly small magnitudes. In ID, model selection is carried out via thresholding, or an information criterion, or SDLL, or a hybrid involving the former two. The hybrid model selection leads to a general method with very good practical performance and minimal parameter choice. In the scenarios tested, ID is at least as accurate as the state-of-the-art methods; most of the times it outperforms them. ID is implemented in the R packages IDetect and breakfast, available from CRAN.

SUPPLEMENTARY INFORMATION

The online version supplementary material available at 10.1007/s00184-021-00821-6.

Multithreshold change plane model: Estimation theory and applications in subgroup identification

We propose a multithreshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of observed covariates and thus multiple thresholds produce change planes in the covariate space. We contribute a novel two-stage estimation approach to determine the number of subgroups, the location of thresholds, and all other regression parameters. In the first stage we adopt a group selection principle to consistently identify the number of subgroups, while in the second stage change point locations and model parameter estimates are refined by a penalized induced smoothing technique. Our procedure allows sparse solutions for relatively moderate- or high-dimensional covariates. We further establish the asymptotic properties of our proposed estimators under appropriate technical conditions. We evaluate the performance of the proposed methods by simulation studies and provide illustrations using two medical data examples. Our proposal for subgroup identification may lead to an immediate application in personalized medicine.

Heterogeneous Idealization of Ion Channel Recordings - Open Channel Noise

We propose a new model-free segmentation method for idealizing ion channel recordings. This method is designed to deal with heterogeneity of measurement errors. This in particular applies to open channel noise which, in general, is particularly difficult to cope with for model-free approaches. Our methodology is able to deal with lowpass filtered data which provides a further computational challenge. To this end we propose a multiresolution testing approach, combined with local deconvolution to resolve the lowpass filter. Simulations and statistical theory confirm that the proposed idealization recovers the underlying signal very accurately at presence of heterogeneous noise, even when events are shorter than the filter length. The method is compared to existing approaches in computer experiments and on real data. We find that it is the only one which allows to identify openings of the PorB porine at two different temporal scales. An implementation is available as an R package.

Five centuries of reconstructed streamflow in Athabasca River Basin, Canada: Non-stationarity and teleconnection to climate patterns

Given the challenge to estimate representative long-term natural variability of streamflow from limited observed data, a hierarchical, multilevel Bayesian regression (HBR) was developed to reconstruct the 1489-2006 annual streamflow data at six Athabasca River Basin (ARB) gauging stations based on 14 tree ring chronologies. Seven nested models were developed to maximize the applications of available tree ring predictors. Based on results of goodness-of-fit tests, the HBR developed was skillful and reliable in reconstructing the streamflow of ARB. From five centuries of reconstructed streamflow for ARB, five or six abrupt change points are detected. The streamflow time series obtained from a backward moving, 46-year window for six gauging sites in ARB vary significantly over five centuries (1489-2006) and at times could exceed the 90% and/or 95% confidence intervals, denoting significant non-stationarities. Apparently changes in the mean state and the lag-1 autocorrelation of reconstructed streamflow across the gauging sites can be similar or radically different from each other. These nonstationary features imply that the default stationary assumption is not applicable in ARB. Further, the reconstructed streamflow shows statistically significant oscillations at interannual, interdecadal and multidecadal time scales and are teleconnected to climate patterns such as El Niño Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO) and Atlantic Multi-decadal Oscillation (AMO). A composite analysis shows that La Niña (El Niño), cold (warm) PDO, and cold (warm) AMO events are typically associated with increased (decreased) streamflow anomalies of ARB. The reconstructed streamflow data provides us the full range of streamflow variability and recurrence characteristics of extremes spanned over five centuries from which it is useful for us to evaluate and manage the current water systems of ARB more effectively and a better risk analysis of future droughts of ARB.

Optimized variable selection via repeated data splitting

Model selection in high-dimensional settings has received substantial attention in recent years, however, similar advancements in the low-dimensional setting have been lacking. In this article, we introduce a new variable selection procedure for low to moderate scale regressions (n>p). This method repeatedly splits the data into two sets, one for estimation and one for validation, to obtain an empirically optimized threshold which is then used to screen for variables to include in the final model. In an extensive simulation study, we show that the proposed variable selection technique enjoys superior performance compared with candidate methods (backward elimination via repeated data splitting, univariate screening at 0.05 level, adaptive LASSO, SCAD), being amongst those with the lowest inclusion of noisy predictors while having the highest power to detect the correct model and being unaffected by correlations among the predictors. We illustrate the methods by applying them to a cohort of patients undergoing hepatectomy at our institution.

The essential histogram

The histogram is widely used as a simple, exploratory way of displaying data, but it is usually not clear how to choose the number and size of the bins. We construct a confidence set of distribution functions that optimally deal with the two main tasks of the histogram: estimating probabilities and detecting features such as increases and modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the essential histogram is the simplest visualization of the data that optimally achieves the main tasks of the histogram. The only assumption we make is that the data are independent and identically distributed. We provide a fast algorithm for computing the essential histogram and illustrate our method with examples.

Fast nonconvex deconvolution of calcium imaging data

Calcium imaging data promises to transform the field of neuroscience by making it possible to record from large populations of neurons simultaneously. However, determining the exact moment in time at which a neuron spikes, from a calcium imaging data set, amounts to a non-trivial deconvolution problem which is of critical importance for downstream analyses. While a number of formulations have been proposed for this task in the recent literature, in this article, we focus on a formulation recently proposed in Jewell and Witten (2018. Exact spike train inference via $\ell_{0} $ optimization. The Annals of Applied Statistics12(4), 2457-2482) that can accurately estimate not just the spike rate, but also the specific times at which the neuron spikes. We develop a much faster algorithm that can be used to deconvolve a fluorescence trace of 100 000 timesteps in less than a second. Furthermore, we present a modification to this algorithm that precludes the possibility of a "negative spike". We demonstrate the performance of this algorithm for spike deconvolution on calcium imaging datasets that were recently released as part of the $\texttt{spikefinder}$ challenge (http://spikefinder.codeneuro.org/). The algorithm presented in this article was used in the Allen Institute for Brain Science's "platform paper" to decode neural activity from the Allen Brain Observatory; this is the main scientific paper in which their data resource is presented. Our $\texttt{C++}$ implementation, along with $\texttt{R}$ and $\texttt{python}$ wrappers, is publicly available. $\texttt{R}$ code is available on $\texttt{CRAN}$ and $\texttt{Github}$, and $\texttt{python}$ wrappers are available on $\texttt{Github}$; see https://github.com/jewellsean/FastLZeroSpikeInference.

EXACT SPIKE TRAIN INFERENCE VIA ℓ0 OPTIMIZATION

In recent years new technologies in neuroscience have made it possible to measure the activities of large numbers of neurons simultaneously in behaving animals. For each neuron a fluorescence trace is measured; this can be seen as a first-order approximation of the neuron's activity over time. Determining the exact time at which a neuron spikes on the basis of its fluorescence trace is an important open problem in the field of computational neuroscience. Recently, a convex optimization problem involving an ℓ1 penalty was proposed for this task. In this paper we slightly modify that recent proposal by replacing the ℓ1 penalty with an ℓ0 penalty. In stark contrast to the conventional wisdom that ℓ0 optimization problems are computationally intractable, we show that the resulting optimization problem can be efficiently solved for the global optimum using an extremely simple and efficient dynamic programming algorithm. Our R-language implementation of the proposed algorithm runs in a few minutes on fluorescence traces of 100,000 timesteps. Furthermore, our proposal leads to substantial improvements over the previous ℓ1 proposal, in simulations as well as on two calcium imaging datasets. R-language software for our proposal is available on CRAN in the package LZeroSpikeInference. Instructions for running this software in python can be found at https://github.com/jewellsean/LZeroSpikeInference.

Fully Automatic Multiresolution Idealization for Filtered Ion Channel Recordings: Flickering Event Detection

We propose a new model-free segmentation method, JULES, which combines recent statistical multiresolution techniques with local deconvolution for idealization of ion channel recordings. The multiresolution criterion takes into account scales down to the sampling rate enabling the detection of flickering events, i.e., events on small temporal scales, even below the filter frequency. For such small scales the deconvolution step allows for a precise determination of dwell times and, in particular, of amplitude levels, a task which is not possible with common thresholding methods. This is confirmed theoretically and in a comprehensive simulation study. In addition, JULES can be applied as a preprocessing method for a refined hidden Markov analysis. Our new methodology allows us to show that gramicidin A flickering events have the same amplitude as the slow gating events. JULES is available as an R function jules in the package clampSeg.