Detection of multiple undocumented change-points using adaptive Lasso

Change point detection for high-dimensional data is an important yet challenging problem for many applications. In this paper, we consider multiple change point detection in the context of high-dimensional generalized linear models, allowing the covariate dimension p to grow exponentially with the sample size n. The model considered is general and flexible in the sense that it covers various specific models as special cases. It can automatically account for the underlying data generation mechanism without specifying any prior knowledge about the number of change points. Based on dynamic programming and binary segmentation techniques, two algorithms are proposed to detect multiple change points, allowing the number of change points to grow with n. To further improve the computational efficiency, a more efficient algorithm designed for the case of a single change point is proposed. We present theoretical properties of our proposed algorithms, including estimation consistency for the number and locations of change points as well as consistency and asymptotic distributions for the underlying regression coefficients. Finally, extensive simulation studies and application to the Alzheimer's Disease Neuroimaging Initiative data further demonstrate the competitive performance of our proposed methods.

This paper is concerned with the detection of multiple change-points in linear regression models. The proposed procedure relies on the local estimation for global change-point estimation. We propose a multiple change-point estimator based on the local least squares estimators for the regression coefficients and the split measure when the number of change-points is unknown. Its statistical properties are shown and its performance is assessed by simulations and real data applications.

Analyzing COVID-19 data presents a challenge in Bayesian computations of the Poisson process because the experimental conditions are not under control. This lack of homogeneity can lead to inconsistent model parameters, which violates the assumptions of Bayesian inference. In this paper, we study the multiple change-point detection problem from this viewpoint for a non-homogeneous sample path of the Poisson process as the response variable. The rate parameters are linked to some explanatory using a generalized linear model. The number of change-points is considered to be unknown as well as their locations. We introduce a Bayesian paradigm to estimate the number and location of change-points. We also present an adaptive RJMCMC algorithm to generate pseudo-random samples from the posterior distributions. We apply the proposed model to analyze the COVID-19 infection curves from different countries and identify patterns of cases. We also assess the efficacy of interventions, such as vaccination and public health emergency responses, implemented by different countries. The results of the analysis provide valuable insights into the spread of COVID-19 and the effectiveness of interventions. The proposed model can be used to inform public health decision-making and help to improve the management of the pandemic.

This paper provides a solution for the multiple changepoint detection problems in financial time series prediction without knowing the number and location of changepoints. The proposed approach is a Sequential Monte Carlo (SMC) method for estimating GARCH based volatility models which are subject to an unknown number of changepoints. Recent Auxiliary Particle Filtering (APF) techniques are used to calculate the posterior densities and forecasts in real-time. This approach also automatically deals with the common path dependence problem of these type volatility models. We studied on simulated volatility data using GARCH model and have shown that the proposed approach works well with the generated data. For the non-linearity multiple changepoint detection problem, APF is investigated over the simulated volatility to model the switching regimes. In this study, a full structural changepoint specification is defined in which all parameters of the conditional variance of GARCH are subject to change respectively.

Economic system mathematical model often contains multiple variance change points about structure model. In the same mean, we combine the Bayesian method with the maximum likelihood method on the detection of the variance multiple change points. With Bayesian method, we can eliminate extra parameters first, and then use maximum likelihood method to find the change position. So we both can eliminate extra parameters and can avoid the change point on the prior distribution unknown problem. In addition, the benefit of the maximum likelihood method is just needed to find out likelihood density function of the maximal solution in the solution space, thus the variance of multiple change point detection problem is resolved. By making substantial analysis with an example from commodity house prices in Wuhan, three changes of variance are found in all. They correspond to the major structure changes of contemporary property market in Wuhan city. The method is practical and effective as the final results shown. It also has a certain practical significance.

ABSTRACTIn this paper, we show the validity of the adaptive least absolute shrinkage and selection operator (LASSO) procedure in estimating stationary autoregressive distributed lag(p,q) models with innovations in a broad class of conditionally heteroskedastic models. We show that the adaptive LASSO selects the relevant variables with probability converging to one and that the estimator is oracle efficient, meaning that its distribution converges to the same distribution of the oracle-assisted least squares, i.e., the least square estimator calculated as if we knew the set of relevant variables beforehand. Finally, we show that the LASSO estimator can be used to construct the initial weights. The performance of the method in finite samples is illustrated using Monte Carlo simulation.

Agencies that regulate electricity providers often apply nonparametric data envelopment analysis (DEA) to assess the relative efficiency of each firm. The reliability and validity of DEA are contingent upon selecting relevant input variables. In the era of big (wide) data, the assumptions of traditional variable selection techniques are often violated due to challenges related to high-dimensional data and their standard empirical properties. Currently, regulators have access to a large number of potential input variables. Therefore, our aim is to introduce new machine learning methods for regulators of the energy market. We also propose a new two-step analytical approach where, in the first step, the machine learning-based adaptive least absolute shrinkage and selection operator (ALASSO) is used to select variables and, in the second step, selected variables are used in a DEA model. In contrast to previous research, we find, by using a more realistic data-generating process common for production functions (i.e., Cobb–Douglas and Translog), that the performance of different machine learning techniques differs substantially in different empirically relevant situations. Simulations also reveal that the ALASSO is superior to other machine learning and regression-based methods when the collinearity is low or moderate. However, in situations of multicollinearity, the LASSO approach exhibits the best performance. We also use real data from the Swedish electricity distribution market to illustrate the empirical relevance of selecting the most appropriate variable selection method.

We propose a methodology for detecting multiple change points in the mean of an otherwise stationary, autocorrelated, linear time series. It combines solution path generation based on the wild contrast maximisation principle, and an information criterion‐based model selection strategy termed gappy Schwarz algorithm. The former is well‐suited to separating shifts in the mean from fluctuations due to serial correlations, while the latter simultaneously estimates the dependence structure and the number of change points without performing the difficult task of estimating the level of the noise as quantified e.g. by the long‐run variance. We provide modular investigation into their theoretical properties and show that the combined methodology, named WCM.gSa, achieves consistency in estimating both the total number and the locations of the change points. The good performance of WCM.gSa is demonstrated via extensive simulation studies, and we further illustrate its usefulness by applying the methodology to London air quality data.

The accelerated failure time (AFT) model is a linear model under the log-transformation of survival time that has been introduced as a useful alternative to the proportional hazards (PH) model. In this paper we propose variable-selection procedures of fixed effects in a parametric AFT model using penalized likelihood approaches. We use three popular penalty functions, least absolute shrinkage and selection operator (LASSO), adaptive LASSO and smoothly clipped absolute deviation (SCAD). With these procedures we can select important variables and estimate the fixed effects at the same time. The performance of the proposed method is evaluated using simulation studies, including the investigation of impact of misspecifying the assumed distribution. The proposed method is illustrated with a primary biliary cirrhosis (PBC) data set.

Gene regulatory networks (GRNs) reveal the regulatory interactions among genes and provide a visual tool to explain biological processes. However, how to identify direct relations among genes from gene expression data in the case of high-dimensional and small samples is a critical challenge. In this paper, we proposed a new GRN inference method based on a modified adaptive least absolute shrinkage and selection operator (MALasso). MALasso expands the number of samples based on the distance correlation and defines a new weighting manner for adaptive lasso to remove false positive edges of the networks in the iterative process. Simulated data and gene expression data from DREAM challenge were used to validate the performance of the proposed method MALasso. The comparison results among MALasso, adaptive lasso and other six state-of-the-art methods show that MALasso outperformed the competition methods in AUROCC and AUPRC in most cases and had a better ability to distinguish direct edges from indirect ones. Hence, by modifying the adaptive weighting manner of adaptive lasso, MALasso can detect linear and nonlinear relations, remove the false positive edges and identify direct relations among genes more accurately.

BackgroundA considerable portion of the HIV pandemic is composed of people under antiretroviral therapy, many of whom get a late diagnosis. Patients starting antiretroviral therapy (ART) at a very advanced stage of HIV disease attain a low recovery of CD4 T cells. Factors associated with poor recovery are incompletely described. This study aimed at finding variables associated with CD4 T cell recovery in late-presenting HIV patients.MethodsWe studied a cohort of HIV+ patients initiating ART with very low basal CD4 T cell counts. We defined immune recovery as the net increase in circulating CD4 T cell counts after one year on ART. We analyzed diverse routine laboratory determinations at different times using Least Absolute Shrinkage and Selection Operator (LASSO), adaptive LASSO and Conditional Inference Random Forest.ResultsCD4/CD8 ratio, % CD4 T cells and CD8 T cell counts at different times were the main recovery correlates, validated by all approaches. Unexpectedly, basal hematocrit was a consistent predictor. Additionally, week 24 creatinine had a high lasso coefficient, and alkaline phosphatase had a high conditional inference random forest coefficients, although neither was verified by other tests.ConclusionsCD4 T cell proportions are associated with CD4 T cell recovery, independently of cell counts. Inflammation-related variables could also affect reconstitution. These accessible variables may reflect underlying mechanisms and could improve the follow up of patients starting ART with an advanced HIV infection.

In the field of quantitative remote sensing of forest biomass, a prominent phenomenon is the increasing number of explanatory variables. Then how to effectively select explanatory variables has become an important issue. Linear regression model is one of the commonly used remote sensing models. In the process of establishing the linear regression model, a vital step is to select explanatory variables. Focusing on variable selection and model stability, this paper conducts a comparative study on the performance of eight linear regression parameter estimation methods (Stepwise Regression Method (SR), Criterions Based on The Bayes Method (BIC), Criterions Based on The Bayes Method (AIC), Criterions Based on Prediction Error (Cp), Least Absolute Shrinkage and Selection Operator (Lasso), Adaptive Lasso, Smoothly Clipped Absolute Deviation (SCAD), Non-negative garrote (NNG)) in the subtropical forest biomass remote sensing model development. For the purpose of comparison, OLS and RR, are commonly used as methods with no variable selection ability, and are also compared and discussed. The performance of five aspects are evaluated in this paper: (i) Determination coefficient, prediction error, model error, etc., (ii) significance test about the difference between determination coefficients, (iii) parameter stability, (iv) variable selection stability and (v) variable selection ability of the methods. All the results are obtained through a five ten-fold CV. Some evaluation indexes are calculated with or without degrees of freedom. The results show that BIC performs best in comprehensive evaluation, while NNG, Cp and AIC perform poorly as a whole. Other methods show a great difference in the performance on each index. SR has a strong capability in variable selection, although it is poor in commonly used indexes. The short-wave infrared band and the texture features derived from it are selected most frequently by various methods, indicating that these variables play an important role in forest biomass estimation. Some of the conclusions in this paper are likely to change as the study object changes. The ultimate goal of this paper is to introduce various model establishment methods with variable selection capability, so that we can have more choices when establishing similar models, and we can know how to select the most appropriate and effective method for specific problems.

To quickly and efficiently recognize abnormal patterns from large-scale time series and pathological signals in epilepsy, this paper presents here a preliminary RSW&TST framework for Multiple Change-Points (MCPs) detection based on the Random Slide Window (RSW) and Trigeminal Search Tree (TST) methods. To avoid the remaining local optima, the proposed framework applies a random strategy for selecting the size of each slide window from a predefined collection, in terms of data feature and experimental knowledge. For each data segment to be diagnosed in a current slide window, an optimal path towards a potential change point is detected by TST methods from the top root to leaf nodes with O(log3(N)). Then, the resulting MCPs vector is assembled by means of TST-based single CP detection on data segments within each of the slide windows. In our experiments, the RSW&TST framework was tested by using large-scale synthetic time series, and then its performance was evaluated by comparing it with existing binary search tree (BST), Kolmogorov-Smirnov (KS)-statistics, and T-test under the fixed slide window (FSW) approach, as well as the integrated method of wild binary segmentation and CUSUM test (WBS&CUSUM). The simulation results indicate that our RSW&TST is both more efficient and effective, with a higher hit rate, shorter computing time, and lower missed, error and redundancy rates. When the proposed RSW&TST framework is executed for MCPs detection on pathological ECG (electrocardiogram)/EEG (electroencephalogram) recordings of people in epileptic states, the abnormal patterns are roughly recognized in terms of the number and position of the resultant MCPs. Furthermore, the severity of epilepsy is roughly analyzed based on the strength and period of signal fluctuations among multiple change points in the stage of a sudden epileptic attack. The purpose of our RSW&TST framework is to provide an encouraging platform for abnormal pattern recognition through MCPs detection on large-scale time series quickly and efficiently.

With improvements to cancer diagnoses and treatments, incidences and mortality rates have changed. However, the most commonly used analysis methods do not account for such distributional changes. In survival analysis, change point problems can concern a shift in a distribution for a set of time‐ordered observations, potentially under censoring or truncation. We propose a sequential testing approach for detecting multiple change points in the Weibull accelerated failure time model, since this is sufficiently flexible to accommodate increasing, decreasing, or constant hazard rates and is also the only continuous distribution for which the accelerated failure time model can be reparameterized as a proportional hazards model. Our sequential testing procedure does not require the number of change points to be known; this information is instead inferred from the data. We conduct a simulation study to show that the method accurately detects change points and estimates the model. The numerical results along with real data applications demonstrate that our proposed method can detect change points in the hazard rate.

ABSTRACTIn the multiple changepoint setting, various search methods have been proposed, which involve optimizing either a constrained or penalized cost function over possible numbers and locations of changepoints using dynamic programming. Recent work in the penalized optimization setting has focused on developing an exact pruning-based approach that, under certain conditions, is linear in the number of data points. Such an approach naturally requires the specification of a penalty to avoid under/over-fitting. Work has been undertaken to identify the appropriate penalty choice for data-generating processes with known distributional form, but in many applications the model assumed for the data is not correct and these penalty choices are not always appropriate. To this end, we present a method that enables us to find the solution path for all choices of penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitable penalty choice. The computational complexity of this approach can be linear in the number of data points and linear in the difference between the number of changepoints in the optimal segmentations for the smallest and largest penalty values. Supplementary materials for this article are available online.