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On the adaptive partition approach to the detection of multiple change-points.

Lai Y - PLoS ONE (2011)

Bottom Line: However, the widely used recursive combination or partition procedures do not guarantee a global optimization.Our method can provide consistent estimation results.In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics and Biostatistics Center, The George Washington University, Washington, DC, United States of America. ylai@gwu.edu

ABSTRACT
With an adaptive partition procedure, we can partition a "time course" into consecutive non-overlapped intervals such that the population means/proportions of the observations in two adjacent intervals are significantly different at a given level . However, the widely used recursive combination or partition procedures do not guarantee a global optimization. We propose a modified dynamic programming algorithm to achieve a global optimization. Our method can provide consistent estimation results. In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures. In practice, can be determined based on a cross-validation procedure. As an application, we consider the well-known Pima Indian Diabetes data. We explore the relationship among the diabetes risk and several important variables including the plasma glucose concentration, body mass index and age.

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Simulation based comparison of the overall mean squared                            errors.All y-axes represent the overall mean squared error. DP represents our                            dynamic programming algorithm; RC and RP represent the recursive                            combination and recursive partition algorithms, respectively. The                            boxplots in each row (1–4) are generated from the analysis results                            based on the corresponding simulation scenario (1–4). The boxplots                            in each column (1–3) are generated from the analysis results based                            on different  (1, 10 and                            100).
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pone-0019754-g002: Simulation based comparison of the overall mean squared errors.All y-axes represent the overall mean squared error. DP represents our dynamic programming algorithm; RC and RP represent the recursive combination and recursive partition algorithms, respectively. The boxplots in each row (1–4) are generated from the analysis results based on the corresponding simulation scenario (1–4). The boxplots in each column (1–3) are generated from the analysis results based on different (1, 10 and 100).

Mentions: For all the above four scenarios, Figures 2 and 4 shows similar patterns. When is as small as one for each time point, the approximation algorithms give a better performance in term of overall MSE, but the global optimization algorithm still gives a quite comparable performance (Figure 2); on the choice of , the global optimization algorithm gives a better performance and the approximation algorithms can give a comparable performance (Figure 4). When becomes larger to 10 and then to 100, we observe a clear performance improvement from the global optimization algorithm: we can achieve a clearly smaller overall MSE and also much more significant (Figures 2 and 4).


On the adaptive partition approach to the detection of multiple change-points.

Lai Y - PLoS ONE (2011)

Simulation based comparison of the overall mean squared                            errors.All y-axes represent the overall mean squared error. DP represents our                            dynamic programming algorithm; RC and RP represent the recursive                            combination and recursive partition algorithms, respectively. The                            boxplots in each row (1–4) are generated from the analysis results                            based on the corresponding simulation scenario (1–4). The boxplots                            in each column (1–3) are generated from the analysis results based                            on different  (1, 10 and                            100).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3101215&req=5

pone-0019754-g002: Simulation based comparison of the overall mean squared errors.All y-axes represent the overall mean squared error. DP represents our dynamic programming algorithm; RC and RP represent the recursive combination and recursive partition algorithms, respectively. The boxplots in each row (1–4) are generated from the analysis results based on the corresponding simulation scenario (1–4). The boxplots in each column (1–3) are generated from the analysis results based on different (1, 10 and 100).
Mentions: For all the above four scenarios, Figures 2 and 4 shows similar patterns. When is as small as one for each time point, the approximation algorithms give a better performance in term of overall MSE, but the global optimization algorithm still gives a quite comparable performance (Figure 2); on the choice of , the global optimization algorithm gives a better performance and the approximation algorithms can give a comparable performance (Figure 4). When becomes larger to 10 and then to 100, we observe a clear performance improvement from the global optimization algorithm: we can achieve a clearly smaller overall MSE and also much more significant (Figures 2 and 4).

Bottom Line: However, the widely used recursive combination or partition procedures do not guarantee a global optimization.Our method can provide consistent estimation results.In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics and Biostatistics Center, The George Washington University, Washington, DC, United States of America. ylai@gwu.edu

ABSTRACT
With an adaptive partition procedure, we can partition a "time course" into consecutive non-overlapped intervals such that the population means/proportions of the observations in two adjacent intervals are significantly different at a given level . However, the widely used recursive combination or partition procedures do not guarantee a global optimization. We propose a modified dynamic programming algorithm to achieve a global optimization. Our method can provide consistent estimation results. In a comprehensive simulation study, our method shows an improved performance when it is compared to the recursive combination/partition procedures. In practice, can be determined based on a cross-validation procedure. As an application, we consider the well-known Pima Indian Diabetes data. We explore the relationship among the diabetes risk and several important variables including the plasma glucose concentration, body mass index and age.

Show MeSH
Related in: MedlinePlus