| 1. |
- Burdakov, Oleg, 1953-, et al.
(författare)
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A Dual Active-Set Algorithm for Regularized Monotonic Regression
- 2017
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Ingår i: Journal of Optimization Theory and Applications. - : Springer. - 0022-3239 .- 1573-2878. ; 172:3, s. 929-949
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Tidskriftsartikel (refereegranskat)abstract
- Monotonic (isotonic) regression is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the monotonic regression, formulated as a least distance problem with monotonicity constraints. The resulting smoothed monotonic regression is a convex quadratic optimization problem. We focus on the case, where the set of observations is completely (linearly) ordered. Our smoothed pool-adjacent-violators algorithm is designed for solving the regularized problem. It belongs to the class of dual active-set algorithms. We prove that it converges to the optimal solution in a finite number of iterations that does not exceed the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of our algorithm grows quadratically with the problem size, we found its running time to grow almost linearly in our computational experiments.
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| 2. |
- Burdakov, Oleg, 1953-, et al.
(författare)
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A Dual Active-Set Algorithm for Regularized Slope-Constrained Monotonic Regression
- 2017
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Ingår i: Iranian Journal of Operations Research. - Tehran : CMV Verlag. - 2008-1189. ; 8:2, s. 40-47
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Tidskriftsartikel (refereegranskat)abstract
- In many problems, it is necessary to take into account monotonic relations. Monotonic (isotonic) Regression (MR) is often involved in solving such problems. The MR solutions are of a step-shaped form with a typical sharp change of values between adjacent steps. This, in some applications, is regarded as a disadvantage. We recently introduced a Smoothed MR (SMR) problem which is obtained from the MR by adding a regularization penalty term. The SMR is aimed at smoothing the aforementioned sharp change. Moreover, its solution has a far less pronounced step-structure, if at all available. The purpose of this paper is to further improve the SMR solution by getting rid of such a structure. This is achieved by introducing a lowed bound on the slope in the SMR. We call it Smoothed Slope-Constrained MR (SSCMR) problem. It is shown here how to reduce it to the SMR which is a convex quadratic optimization problem. The Smoothed Pool Adjacent Violators (SPAV) algorithm developed in our recent publications for solving the SMR problem is adapted here to solving the SSCMR problem. This algorithm belongs to the class of dual active-set algorithms. Although the complexity of the SPAV algorithm is o(n2) its running time is growing in our computational experiments almost linearly with n. We present numerical results which illustrate the predictive performance quality of our approach. They also show that the SSCMR solution is free of the undesirable features of the MR and SMR solutions.
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| 3. |
- Burdakov, Oleg, et al.
(författare)
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Regularized monotonic regression
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Monotonic (isotonic) Regression (MR) is a powerful tool used for solving a wide range of important applied problems. One of its features, which poses a limitation on its use in some areas, is that it produces a piecewise constant fitted response. For smoothing the fitted response, we introduce a regularization term in the MR formulated as a least distance problem with monotonicity constraints. The resulting Smoothed Monotonic Regrassion (SMR) is a convex quadratic optimization problem. We focus on the SMR, where the set of observations is completely (linearly) ordered. Our Smoothed Pool-Adjacent-Violators (SPAV) algorithm is designed for solving the SMR. It belongs to the class of dual activeset algorithms. We proved its finite convergence to the optimal solution in, at most, n iterations, where n is the problem size. One of its advantages is that the active set is progressively enlarging by including one or, typically, more constraints per iteration. This resulted in solving large-scale SMR test problems in a few iterations, whereas the size of that problems was prohibitively too large for the conventional quadratic optimization solvers. Although the complexity of the SPAV algorithm is O(n2), its running time was growing in our computational experiments in proportion to n1:16.
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| 4. |
- Kalish, Michael L., et al.
(författare)
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A statistical test of the equality of latent orders
- 2016
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Ingår i: Journal of mathematical psychology (Print). - : Academic Press. - 0022-2496 .- 1096-0880. ; 70, s. 1-11
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Tidskriftsartikel (refereegranskat)abstract
- It is sometimes the case that a theory proposes that the population means on two variables should have the same rank order across a set of experimental conditions. This paper presents a test of this hypothesis. The test statistic is based on the coupled monotonic regression algorithm developed by the authors. The significance of the test statistic is determined by comparison to an empirical distribution specific to each case, obtained via non-parametric or semi-parametric bootstrap. We present an analysis of the power and Type I error control of the test based on numerical simulation. Partial order constraints placed on the variables may sometimes be theoretically justified. These constraints are easily incorporated into the computation of the test statistic and are shown to have substantial effects on power. The test can be applied to any form of data, as long as an appropriate statistical model can be specified.
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| 5. |
- Sysoev, Oleg, et al.
(författare)
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A Smoothed Monotonic Regression via L2 Regularization
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Monotonic Regression (MR) is a standard method for extracting a monotone function from non-monotonic data, and it is used in many applications. However, a known drawback of this method is that its fitted response is a piecewise constant function, while practical response functions are often required to be continuous. The method proposed in this paper achieves monotonicity and smoothness of the regression by introducing an L2 regularization term, and it is shown that the complexity of this method is O(n2). In addition, our simulations demonstrate that the proposed method normally has higher predictive power than some commonly used alternative methods, such as monotonic kernel smoothers. In contrast to these methods, our approach is probabilistically motivated and has connections to Bayesian modeling.
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| 6. |
- Sysoev, Oleg, 1981-, et al.
(författare)
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A smoothed monotonic regression via L2 regularization
- 2019
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Ingår i: Knowledge and Information Systems. - : Springer. - 0219-1377 .- 0219-3116. ; 59:1, s. 197-218
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Tidskriftsartikel (refereegranskat)abstract
- Monotonic regression is a standard method for extracting a monotone function from non-monotonic data, and it is used in many applications. However, a known drawback of this method is that its fitted response is a piecewise constant function, while practical response functions are often required to be continuous. The method proposed in this paper achieves monotonicity and smoothness of the regression by introducing an L2 regularization term. In order to achieve a low computational complexity and at the same time to provide a high predictive power of the method, we introduce a probabilistically motivated approach for selecting the regularization parameters. In addition, we present a technique for correcting inconsistencies on the boundary. We show that the complexity of the proposed method is O(n2). Our simulations demonstrate that when the data are large and the expected response is a complicated function (which is typical in machine learning applications) or when there is a change point in the response, the proposed method has a higher predictive power than many of the existing methods.
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| 7. |
- Sysoev, Oleg, et al.
(författare)
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Bootstrap confidence intervals for large-scale multivariate monotonic regression problems
- 2016
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Ingår i: Communications in statistics. Simulation and computation. - : Taylor & Francis. - 0361-0918 .- 1532-4141. ; 45:3, s. 1025-1040
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Tidskriftsartikel (refereegranskat)abstract
- Recently, the methods used to estimate monotonic regression (MR) models have been substantially improved, and some algorithms can now produce high-accuracy monotonic fits to multivariate datasets containing over a million observations. Nevertheless, the computational burden can be prohibitively large for resampling techniques in which numerous datasets are processed independently of each other. Here, we present efficient algorithms for estimation of confidence limits in large-scale settings that take into account the similarity of the bootstrap or jackknifed datasets to which MR models are fitted. In addition, we introduce modifications that substantially improve the accuracy of MR solutions for binary response variables. The performance of our algorithms isillustrated using data on death in coronary heart disease for a large population. This example also illustrates that MR can be a valuable complement to logistic regression.
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| 8. |
- Källestål, Carina, 1954-, et al.
(författare)
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Predicting poverty : data mining approaches to the health and demographic surveillance system in Cuatro Santos, Nicaragua
- 2019
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Ingår i: International Journal for Equity in Health. - : BioMed Central. - 1475-9276. ; 18:1
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Tidskriftsartikel (refereegranskat)abstract
- BACKGROUND: In order to further identify the needed interventions for continued poverty reduction in our study area Cuatro Santos, northern Nicaragua, we aimed to elucidate what predicts poverty, measured by the Unsatisfied Basic Need index. This analysis was done by using decision tree methodology applied to the Cuatro Santos health and demographic surveillance databases.METHODS: Using variables derived from the health and demographic surveillance update 2014, transferring individual data to the household level we used the decision tree framework Conditional Inference trees to predict the outcome "poverty" defined as two to four unsatisfied basic needs using the Unsatisfied Basic Need Index. We further validated the trees by applying Conditional random forest analyses in order to assess and rank the importance of predictors about their ability to explain the variation of the outcome "poverty." The majority of the Cuatro Santos households provided information and the included variables measured housing conditions, assets, and demographic experiences since the last update (5 yrs), earlier participation in interventions and food security during the last 4 weeks.RESULTS: Poverty was rare in households that have some assets and someone in the household that has a higher education than primary school. For these households participating in the intervention that installed piped water with water meter was most important, but also when excluding this variable, the resulting tree showed the same results. When assets were not taken into consideration, the importance of education was pronounced as a predictor for welfare. The results were further strengthened by the validation using Conditional random forest modeling showing the same variables being important as predicting the outcome in the CI tree analysis. As assets can be a result, rather than a predictor of more affluence our results in summary point specifically to the importance of education and participation in the water installation intervention as predictors for more affluence.CONCLUSION: Predictors of poverty are useful for directing interventions and in the Cuatro Santos area education seems most important to prioritize. Hopefully, the lessons learned can continue to develop the Cuatro Santos communities as well as development in similar poor rural settings around the world.
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| 9. |
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| 10. |
- Svefors, Pernilla, 1985-, et al.
(författare)
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Relative importance of prenatal and postnatal determinants of stunting : data mining approaches to the MINIMat cohort, Bangladesh
- 2019
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Ingår i: BMJ Open. - : BMJ. - 2044-6055. ; 9:8
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Tidskriftsartikel (refereegranskat)abstract
- INTRODUCTION: WHO has set a goal to reduce the prevalence of stunted child growth by 40% by the year 2025. To reach this goal, it is imperative to establish the relative importance of risk factors for stunting to deliver appropriate interventions. Currently, most interventions take place in late infancy and early childhood. This study aimed to identify the most critical prenatal and postnatal determinants of linear growth 0-24 months and the risk factors for stunting at 2 years, and to identify subgroups with different growth trajectories and levels of stunting at 2 years.METHODS: Conditional inference tree-based methods were applied to the extensive Maternal and Infant Nutrition Interventions in Matlab trial database with 309 variables of 2723 children, their parents and living conditions, including socioeconomic, nutritional and other biological characteristics of the parents; maternal exposure to violence; household food security; breast and complementary feeding; and measurements of morbidity of the mothers during pregnancy and repeatedly of their children up to 24 months of age. Child anthropometry was measured monthly from birth to 12 months, thereafter quarterly to 24 months.RESULTS: Birth length and weight were the most critical factors for linear growth 0-24 months and stunting at 2 years, followed by maternal anthropometry and parental education. Conditions after birth, such as feeding practices and morbidity, were less strongly associated with linear growth trajectories and stunting at 2 years.CONCLUSION: The results of this study emphasise the benefit of interventions before conception and during pregnancy to reach a substantial reduction in stunting.
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