Piecewise regression
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This article addresses the topic of extracting logical rules from data by means of artificial neural networks. The approach based on piecewise linear neural networks is revisited, which has already been used for the extraction of Boolean rules in the past, and it is shown that this approach can be important also for the extraction of fuzzy rules. Two important theoretical properties of piecewise-linear neural networks are proved, allowing an elaboration of the basic ideas of the approach into several variants of an algorithm for the extraction of Boolean rules. That algorithm has already been used in two real-world applications. Finally, a connection to the extraction of rules of the Łukasiewicz logic is established, relying on recent results about rational McNaughton functions. Based on one of the constructive proofs of the McNaughton theorem, an algorithm is formulated that in principle allows extracting a particular kind of formulas of the Łukasiewicz predicate logic from piecewise-linear neural networks trained with rational data.
- MeSH
- algoritmy MeSH
- ekologie MeSH
- financování organizované MeSH
- fuzzy logika MeSH
- interpretace statistických dat MeSH
- lidé MeSH
- lineární modely MeSH
- neuronové sítě MeSH
- rozpoznávání automatizované metody MeSH
- umělá inteligence MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- srovnávací studie MeSH
Ranked model in the form of linear transformation of multivariate feature vectors on a line can reflect a causal order between liver diseases. A priori medical knowledge about order between liver diseases and clinical data sets has been used in the definition of the convex and piecewise linear (CPL) criterion function. The linear ranked transformations have been designed here through minimization of such CPL criterion functions.
... He has a Ph.D. in nonlinear regression models and is Doctor of Science based on a thesis on frailty models ... ... distribution 45 -- 2.2.2 The Weibull distribution 47 -- 2.2.3 The Gompertz distribution 54 -- 2.2.4 Piecewise ... ... dependence 236 -- 7.4 Positive stable frailty distributions 237 -- 7.4.1 Updating 238 -- 7.4.2 Regression ... ... models 238 -- 7.4.3 The stable-Weibull model 238 -- 7.4.4 Weibull regression models 240 -- 7.5 PVF frailty ... ... distributions 241 -- 7.5.1 Weibull and regression models 243 -- 7.5.2 Updating 243 -- 7.6 Lognormal ...
Statistics for biology and health
1st ed. xvii, 542 s.
OBJECTIVES: This study aimed at re-evaluating the strength and shape of the dose-response relationship between the combined (or joint) effect of intensity and duration of cigarette smoking and the risk of head and neck cancer (HNC). We explored this issue considering bivariate spline models, where smoking intensity and duration were treated as interacting continuous exposures. MATERIALS AND METHODS: We pooled individual-level data from 33 case-control studies (18,260 HNC cases and 29,844 controls) participating in the International Head and Neck Cancer Epidemiology (INHANCE) consortium. In bivariate regression spline models, exposures to cigarette smoking intensity and duration (compared with never smokers) were modeled as a linear piecewise function within a logistic regression also including potential confounders. We jointly estimated the optimal knot locations and regression parameters within the Bayesian framework. RESULTS: For oral-cavity/pharyngeal (OCP) cancers, an odds ratio (OR) >5 was reached after 30 years in current smokers of ∼20 or more cigarettes/day. Patterns of OCP cancer risk in current smokers differed across strata of alcohol intensity. For laryngeal cancer, ORs >20 were found for current smokers of ≥20 cigarettes/day for ≥30 years. In former smokers who quit ≥10 years ago, the ORs were approximately halved for OCP cancers, and ∼1/3 for laryngeal cancer, as compared to the same levels of intensity and duration in current smokers. CONCLUSION: Referring to bivariate spline models, this study better quantified the joint effect of intensity and duration of cigarette smoking on HNC risk, further stressing the need of smoking cessation policies.
- MeSH
- dospělí MeSH
- kouření cigaret škodlivé účinky MeSH
- lidé středního věku MeSH
- lidé MeSH
- nádory hlavy a krku etiologie patologie MeSH
- rizikové faktory MeSH
- senioři nad 80 let MeSH
- senioři MeSH
- studie případů a kontrol MeSH
- Check Tag
- dospělí MeSH
- lidé středního věku MeSH
- lidé MeSH
- mužské pohlaví MeSH
- senioři nad 80 let MeSH
- senioři MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
- Research Support, N.I.H., Extramural MeSH
AIMS: The aim was to assess trends in incidence of pediatric type 1 diabetes (T1D) using data recorded by the population-based Czech Childhood Diabetes Register over 1989-2009. METHODS: New cases of childhood-onset T1D aged 0-14.9 yr were recorded using the EURODIAB protocol by two independent sources with the combined estimated completeness of 98.6%. The incidence was modeled by Poisson regression, and the effects of age and calendar time on incidence were assessed using piecewise linear functions. RESULTS: A total of 5155 cases was ascertained over 1989-2009 from an average pediatric population of 1.76 million. Two points of change in the incidence trend were identified by the modeling: in 1995 the incidence accelerated, while in 2001 the growth in incidence significantly slowed down in all ages up to 10 yr. In the youngest age category, 0-4 yr at onset, the rapid average annual rise of 15% over 1996-2001 suddenly changed into stagnation over 2002-2009. CONCLUSIONS: Our data contribute to the notion that long- and intermediate-term predictions from the past incidence developments of incidence are difficult, as abrupt changes in the trend can occur. Caution should be exercised against too far-reaching incidence predictions, even if the population has experienced a previous history of a very fast rise in T1D incidence.
- MeSH
- diabetes mellitus 1. typu epidemiologie MeSH
- dítě MeSH
- incidence MeSH
- kojenec MeSH
- lidé MeSH
- mladiství MeSH
- předškolní dítě MeSH
- registrace MeSH
- Check Tag
- dítě MeSH
- kojenec MeSH
- lidé MeSH
- mladiství MeSH
- předškolní dítě MeSH
- Publikační typ
- časopisecké články MeSH
- Geografické názvy
- Česká republika MeSH
Aortic dissection is a life-threatening disease that consists in the development of a tear in the wall of the aorta. The initial tear propagates as a discontinuity leading to separation within the aortic wall, which can result in the creation of a so-called false lumen. A fatal threat occurs if the rupture extends through the whole thickness of the aortic wall, as blood may then leak. It is generally accepted that the dissection, which can sometime extend along the entire length of the aorta, propagates via a delamination mechanism. The aim of the present paper is to provide experimentally validated parameters of a mathematical model for the description of the wall's cohesion. A model of the peeling experiment was built in Abaqus. The delamination interface was described by a piecewise linear traction-separation law. The bulk behavior of the aorta was assumed to be nonlinearly elastic, anisotropic, and incompressible. Our simulations resulted in estimates of the material parameters for the traction-separation law of the human descending thoracic aorta, which were obtained by minimizing the differences between the FEM predictions and the delamination force given by the regression of the peeling experiments. The results show that the stress at damage initiation, Tc, should be understood as an age-dependent quantity, and under the assumptions of our model this dependence can be expressed by linear regression as Tc = - 13.03·10-4·Age + 0.2485 if the crack front advances in the axial direction, and Tc = - 7.58·10-4·Age + 0.1897 if the crack front advances in the direction of the aortic circumference (Tc [MPa], Age [years]). Other model parameters were the stiffness K and the separation at failure, δf-δc (K = 0.5 MPa/mm, δf-δc = 0.1 mm). The material parameters provided by our study can be used in numerical simulations of the biomechanics of dissection propagation through the aorta especially when age-associated phenomena are studied.
- MeSH
- analýza metodou konečných prvků MeSH
- aorta thoracica * fyziologie MeSH
- biomechanika MeSH
- dospělí MeSH
- lidé středního věku MeSH
- lidé MeSH
- mechanický stres MeSH
- modely kardiovaskulární MeSH
- počítačová simulace MeSH
- senioři MeSH
- stárnutí fyziologie MeSH
- trakce MeSH
- Check Tag
- dospělí MeSH
- lidé středního věku MeSH
- lidé MeSH
- senioři MeSH
- Publikační typ
- časopisecké články MeSH