Regression

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  • 文章类型: Journal Article
    分析崩溃数据是一个复杂且劳动密集型的过程,需要仔细考虑多个相互依赖的建模方面。如功能形式,转换,可能的促成因素,相关性,和未观察到的异质性。有限的时间,知识,经验可能会导致过度简化,过度装配,或忽略重要见解的错误指定模型。本文提出了一个广泛的假设检验框架,包括多目标数学规划公式和求解算法,以估计同时考虑可能的影响因素的碰撞频率模型。转换,非线性,和相关的随机参数。数学规划公式最小化样本内拟合和样本外预测。为了解决数学程序的复杂性和非凸性,所提出的解决方案框架利用各种元启发式解决方案算法。具体来说,和声搜索对超参数的敏感性最小,实现对解决方案的有效搜索,而不受超参数选择的影响。使用两个真实世界的数据集和一个合成数据集来评估框架的有效性。使用两个真实世界的数据集和独立团队在文献中发布的相应模型进行比较分析。所提出的框架显示了其查明有效模型规格的能力,产生准确的估计,并为研究人员和从业人员提供有价值的见解。所提出的方法可以发现许多见解,同时最大程度地减少模型开发所花费的时间。通过考虑更广泛的因素,可以生成具有不同质量的模型。例如,当应用于昆士兰州的崩溃数据时,拟议的方法表明,在急剧弯曲的道路上加入中间分隔可以有效减少撞车的发生,当应用于华盛顿的崩溃数据时,同时考虑交通量和道路曲率,导致碰撞差异显着减少,但碰撞手段增加。
    Analyzing crash data is a complex and labor-intensive process that requires careful consideration of multiple interdependent modeling aspects, such as functional forms, transformations, likely contributing factors, correlations, and unobserved heterogeneity. Limited time, knowledge, and experience may lead to over-simplified, over-fitted, or misspecified models overlooking important insights. This paper proposes an extensive hypothesis testing framework including a multi-objective mathematical programming formulation and solution algorithms to estimate crash frequency models considering simultaneously likely contributing factors, transformations, non-linearities, and correlated random parameters. The mathematical programming formulation minimizes both in-sample fit and out-of-sample prediction. To address the complexity and non-convexity of the mathematical program, the proposed solution framework utilizes a variety of metaheuristic solution algorithms. Specifically, Harmony Search demonstrated minimal sensitivity to hyperparameters, enabling an efficient search for solutions without being influenced by the choice of hyperparameters. The effectiveness of the framework was evaluated using two real-world datasets and one synthetic dataset. Comparative analyses were performed using the two real-world datasets and the corresponding models published in literature by independent teams. The proposed framework showed its capability to pinpoint efficient model specifications, produce accurate estimates, and provide valuable insights for both researchers and practitioners. The proposed approach allows for the discovery of numerous insights while minimizing the time spent on model development. By considering a broader set of contributing factors, models with varied qualities can be generated. For instance, when applied to crash data from Queensland, the proposed approach revealed that the inclusion of medians on sharp curved roads can effectively reduce the occurrence of crashes, when applied to crash data from Washington, the simultaneous consideration of traffic volume and road curvature resulted in a notable reduction in crash variances but an increase in crash means.
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  • 文章类型: Journal Article
    本研究旨在开发一种算法,该算法将WHODAS2.0映射到EQ-5D-5L,用于患有精神疾病的患者。
    这项横断面研究于2019年6月至2022年11月在新加坡的心理健康研究所和社区健康诊所进行。我们包括四种回归方法,包括普通最小二乘(OLS)回归,Tobit回归模型(Tobit),具有MM估计器(MM)和调整后的有限因变量混合模型(ALDVMM)的稳健回归,以映射来自WHODAS2.0的EQ-5D-5L效用得分。
    总共包括797名参与者。平均EQ-5D-5L效用和WHODAS2.0总分分别为0.61(SD=0.34)和11.96(SD=8.97),分别。我们发现,EQ-5D-5L效用得分最好通过具有MM估计器的稳健回归模型来预测。我们的发现表明,WHODAS2.0总分与EQ-5D-5L效用得分显着负相关。
    本研究提供了一种映射算法,用于将WHODAS2.0分数转换为EQ-5D-5L实用程序分数,可以在以下Web应用程序中使用简单的在线计算器实现:https://eastats。shinyapps.io/whodas_eq5d/.
    UNASSIGNED: The current study aims to develop an algorithm that mapping the WHODAS 2.0 to the EQ-5D-5 L for patients with mental disorders.
    UNASSIGNED: This cross-sectional study was conducted at the Institute of Mental Health and the Community Wellness Clinics in Singapore between June 2019 and November 2022. We included four regression methods including the Ordinary Least Square (OLS) regression, Tobit regression model (Tobit), the robust regression with MM estimator (MM) and the adjusted limited dependent variable mixture models (ALDVMM) to map EQ-5D-5 L utility scores from the WHODAS 2.0.
    UNASSIGNED: A total of 797 participants were included. The mean EQ-5D-5 L utility and WHODAS 2.0 total scores were 0.61 (SD = 0.34) and 11.96(SD = 8.97), respectively. We found that the EQ-5D-5 L utility score was best predicted by the robust regression model with the MM estimator. Our findings suggest that the WHODAS 2.0 total scores were significantly and inversely associated with the EQ-5D-5 L utility scores.
    UNASSIGNED: This study provides a mapping algorithm for converting the WHODAS 2.0 scores into EQ-5D-5 L utility scores which can be implemented using a simple online calculator in the following web application: https://eastats.shinyapps.io/whodas_eq5d/.
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  • 文章类型: Journal Article
    本文介绍了一种通过将聚类策略与回归模型集成并利用气象数据来模拟尼日利亚疟疾发病率的新方法。通过使用聚类技术将数据集分解为多个子集,我们增加了解释变量的数量,并阐明了天气在预测不同发病率数据范围中的作用.我们的聚类集成回归模型,伴随着最优障碍,提供有关疟疾发病率与降雨和温度等既定影响天气因素之间复杂关系的见解。我们探索两种模式。第一个模型结合了滞后发生率和个体特异性效应。第二个模型只关注天气成分。模型的选择取决于决策者的优先事项。推荐模型一用于更高的预测精度。此外,我们的发现揭示了疟疾发病率的显著差异,特定于某些地理集群,而不仅仅是观测到的天气变量可以解释的。值得注意的是,降雨和温度在不同的发病率集群中表现出不同的边际效应,表明它们对疟疾传播的不同影响。高降雨量与低发病率相关,可能是由于它在冲洗蚊子繁殖场所中的作用。另一方面,温度不能预测高发病例,这表明温度以外的其他因素也会导致高病例。我们的研究解决了疟疾发病率综合模型的需求,特别是在尼日利亚等疾病仍然流行的地区。通过将聚类技术与回归分析相结合,我们对预定的天气因素如何影响疟疾传播提供了细微差别的理解。这种方法有助于公共卫生当局实施有针对性的干预措施。我们的研究强调了在疟疾控制工作中考虑当地环境因素的重要性,并强调了基于天气的预测对主动疾病管理的潜力。
    This paper introduces a novel approach to modeling malaria incidence in Nigeria by integrating clustering strategies with regression modeling and leveraging meteorological data. By decomposing the datasets into multiple subsets using clustering techniques, we increase the number of explanatory variables and elucidate the role of weather in predicting different ranges of incidence data. Our clustering-integrated regression models, accompanied by optimal barriers, provide insights into the complex relationship between malaria incidence and well-established influencing weather factors such as rainfall and temperature.We explore two models. The first model incorporates lagged incidence and individual-specific effects. The second model focuses solely on weather components. Selection of a model depends on decision-makers priorities. The model one is recommended for higher predictive accuracy. Moreover, our findings reveal significant variability in malaria incidence, specific to certain geographic clusters and beyond what can be explained by observed weather variables alone.Notably, rainfall and temperature exhibit varying marginal effects across incidence clusters, indicating their differential impact on malaria transmission. High rainfall correlates with lower incidence, possibly due to its role in flushing mosquito breeding sites. On the other hand, temperature could not predict high-incidence cases, suggesting that other factors other than temperature contribute to high cases.Our study addresses the demand for comprehensive modeling of malaria incidence, particularly in regions like Nigeria where the disease remains prevalent. By integrating clustering techniques with regression analysis, we offer a nuanced understanding of how predetermined weather factors influence malaria transmission. This approach aids public health authorities in implementing targeted interventions. Our research underscores the importance of considering local contextual factors in malaria control efforts and highlights the potential of weather-based forecasting for proactive disease management.
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  • 文章类型: Journal Article
    电解质浓度的不平衡会产生严重的后果,但准确和可访问的测量可以改善患者的结果。基于血液测试的当前测量方法是准确的,但侵入性且耗时,并且通常在例如远程位置或救护车环境中不可用。在本文中,我们探索使用深度神经网络(DNN)进行回归任务,以准确预测来自心电图(ECG)的连续电解质浓度,一个快速和广泛采用的工具。我们在四个主要电解质的超过290,000个ECG的新数据集上分析了我们的DNN模型,并将它们的性能与传统机器学习模型进行了比较。为了提高理解,我们还研究了从连续预测到极端浓度水平的二元分类的全谱。最后,我们研究了概率回归方法,并探索了增强临床有用性的不确定性估计.我们的结果表明,DNN优于传统模型,但不同电解质的模型性能差异显著。虽然离散化导致良好的分类性能,它没有解决连续浓度水平预测的原始问题。概率回归具有实际潜力,但是我们的不确定性估计并没有完全校准。因此,我们的研究是朝着开发一种准确可靠的基于ECG的电解质浓度水平预测方法迈出的第一步,该方法在多种临床场景中具有很高的潜在影响。
    Imbalances in electrolyte concentrations can have severe consequences, but accurate and accessible measurements could improve patient outcomes. The current measurement method based on blood tests is accurate but invasive and time-consuming and is often unavailable for example in remote locations or an ambulance setting. In this paper, we explore the use of deep neural networks (DNNs) for regression tasks to accurately predict continuous electrolyte concentrations from electrocardiograms (ECGs), a quick and widely adopted tool. We analyze our DNN models on a novel dataset of over 290,000 ECGs across four major electrolytes and compare their performance with traditional machine learning models. For improved understanding, we also study the full spectrum from continuous predictions to a binary classification of extreme concentration levels. Finally, we investigate probabilistic regression approaches and explore uncertainty estimates for enhanced clinical usefulness. Our results show that DNNs outperform traditional models but model performance varies significantly across different electrolytes. While discretization leads to good classification performance, it does not address the original problem of continuous concentration level prediction. Probabilistic regression has practical potential, but our uncertainty estimates are not perfectly calibrated. Our study is therefore a first step towards developing an accurate and reliable ECG-based method for electrolyte concentration level prediction-a method with high potential impact within multiple clinical scenarios.
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  • 文章类型: Journal Article
    背景:本研究的目的是探讨中国成年人血清残余胆固醇(RC)水平与代谢功能障碍相关的脂肪变性肝病(MASLD)进展和消退的关系。
    方法:我们对13,903名接受瞬时弹性成像测试的个体进行了横断面研究(队列1),对17,752名接受了至少两次腹部超声检查的个体进行了纵向研究(队列2)。收集人体测量和生化参数。计算血清RC水平。在队列2中评估了非侵入性纤维化指标,例如FIB-4。
    结果:在队列1中,根据逻辑回归分析,血清RC水平与肝脂肪变性和肝纤维化的严重程度呈正相关且独立相关。在队列2中,在随访期间,随着MASLD的发生率,参与者的基线血清RC水平升高,随着MASLD的消退,参与者的基线血清RC水平降低。基线血清RC水平与发展风险增加和MASLD消退可能性降低独立相关:完全调整的风险比(HR)为2.785(95%CI2.332-3.236,P<0.001)和2.925(95%CI2.361-3.623,P<0.001),分别。此外,当我们使用FIB-4评估肝纤维化时,基线血清RC水平与晚期纤维化的高中间概率的发生率呈正相关。然而,我们没有发现血清RC水平与肝纤维化消退之间的关联。
    结论:中国成年人血清RC水平与MASLD的进展和消退独立相关,提示RC可能参与了MASLD的病理生理过程。
    BACKGROUND: The aim of this study was to explore the associations of serum remnant cholesterol (RC) levels with the progression and regression of metabolic dysfunction-associated steatotic liver disease (MASLD) in Chinese adults.
    METHODS: We conducted a cross-sectional study in 13,903 individuals who underwent transient elastography tests (cohort 1) and a longitudinal study in 17,752 individuals who underwent at least two health check-up exams with abdominal ultrasound (cohort 2). Anthropometric and biochemical parameters were collected. Serum RC levels were calculated. Noninvasive fibrosis indices such as FIB-4 were evaluated in cohort 2.
    RESULTS: In cohort 1, serum RC levels were positively and independently associated with the severity of hepatic steatosis and liver fibrosis according to logistic regression analysis. In cohort 2, baseline serum RC levels were increased in participants with the incidence of MASLD and decreased in participants with the regression of MASLD during the follow-up period. Baseline serum RC levels were independently associated with an increased risk of development and a decreased likelihood of regression of MASLD: the fully adjusted hazard ratios (HR) were 2.785 (95 % CI 2.332-3.236, P < 0.001) and 2.925 (95 % CI 2.361-3.623, P < 0.001), respectively. In addition, when we used FIB-4 to evaluate liver fibrosis, baseline serum RC levels were positively correlated with the incidence of high-intermediate probability of advanced fibrosis. However, we did not find an association between serum RC levels and the regression of liver fibrosis.
    CONCLUSIONS: Serum RC levels are independently correlated with the progression and regression of MASLD in Chinese adults, suggesting that RC may participate in the pathophysiological process of MASLD.
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  • 文章类型: Journal Article
    这项研究调查了首尔市每日确诊病例多次接种COVID-19疫苗的有效性。利用来自韩国内政和安全部官方网站的有关接种疫苗的个人和确诊病例的全面数据,我们进行了详细的统计分析,以评估每次疫苗接种剂量的影响.该研究涵盖了2021年4月21日至2022年9月29日的数据。统计多元线性回归分析每日确诊病例(PCR检测阳性结果)与多剂量疫苗之间的关系,使用p值作为确定每个剂量有效性的标准。分析包括来自四个疫苗接种剂量的数据。分析表明,第一,第二,第三剂COVID-19疫苗与每日确诊病例相关,具有统计学显著的正效应。然而,研究发现,第四剂对减少每日确诊病例没有统计学意义。这表明,尽管最初的三个剂量对于建立和维持高水平的免疫力至关重要,后续剂量的增量益处可能会减少。
    This study investigates the effectiveness of multiple COVID-19 vaccinations on daily confirmed cases in Seoul City. Utilizing comprehensive data on vaccinated individuals and confirmed cases sourced from the official website of the Korean Ministry of the Interior and Safety, we conducted detailed statistical analyses to assess the impact of each vaccination dose. The study covers data from April 21, 2021, to September 29, 2022. Statistical multiple linear regression was employed to analyze the relationship between daily confirmed cases (positive outcomes from PCR tests) and multiple vaccine doses, using p-values as the criteria for determining the effectiveness of each dose. The analysis included data from four vaccination doses. The analysis reveals that the first, second, and third doses of the COVID-19 vaccines have a statistically significant positive effect associated with the daily confirmed cases. However, the study finds that the fourth dose does not show a statistically significant impact on the reduction of daily confirmed cases. This suggests that while the initial three doses are crucial for establishing and maintaining high levels of immunity, the incremental benefit of subsequent doses may diminish.
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  • 文章类型: Journal Article
    目标:presenteism,员工生病工作的现象,是一个全球性的重大问题,影响个人福祉和组织效率。这项研究调查了瑞士员工的出勤率,探索它的发生,主要因素,原因,以及对员工健康的影响。
    方法:本研究使用了来自瑞士不同部门的1,521名员工的横截面数据。影响因素和不利影响的描述性统计和多元线性模型,比如倦怠症状,工作满意度,一般健康,和生活质量,进行数据分析计算。presenteism是使用Hägerbäumer多项目量表测量的,范围从1=“在生病的情况下从不”-5=“在生病的情况下非常经常。\"
    结果:员工报告说,如果生病,他们在过去12个月中很少工作M=2.04(SD=1.00)。在团队中,积极的出勤方式与较少的出勤(β=-0.07)和有问题的领导文化有关。除了众所周知的因素,表现为倦怠症状(β=1.49),一般健康状况(β=-1.5),和生活质量(β=-0.01)。
    结论:该研究通过应用多项目的出勤量表,为瑞士各部门员工的出勤现象提供了见解。研究结果表明,积极的团队动态和组织文化可能会显着降低出勤率。表现行为是不良后果的重要因素。这凸显了在职业健康背景下承认出勤的重要性。
    OBJECTIVE: Presenteeism, the phenomenon of employees working despite illness, is a significant issue globally, impacting individual well-being and organizational efficiency. This study examines presenteeism among Swiss employees, exploring its occurrence, primary factors, reasons, and impact on employees\' health.
    METHODS: This study used cross-sectional data from 1,521 employees in different sectors in Switzerland. Descriptive statistics and multiple linear models for influencing factors and detrimental effects, such as burnout symptoms, job satisfaction, general health, and quality of life, were calculated for data analysis. Presenteeism was measured using the Hägerbäumer multi-item scale, ranging from 1 = \"Never in case of illness\" - 5 = \"Very often in case of illness.\"
    RESULTS: The employees reported that in case of illness, they rarely worked in the last 12 months M = 2.04 (SD = 1.00). A positive approach to presenteeism in the team was associated with less presenteeism (β = -0.07) and problematic leadership culture in dealing with presenteeism with increased presenteeism (β = 0.10). In addition to well-known factors, presenteeism was significant for burnout symptoms (β = 1.49), general health status (β = -1.5), and quality of life (β = -0.01).
    CONCLUSIONS: The study offers insights into the phenomenon of presenteeism among Swiss employees in various sectors by applying a multi-item scale for presenteeism. The findings indicate that a positive team dynamic and organizational culture may significantly reduce presenteeism. Presenteeism behavior is a significant factor of adverse outcomes. This highlights the importance of acknowledging presenteeism in the context of occupational health.
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  • 文章类型: Journal Article
    目的:我们旨在探讨基线和累积心血管健康与非酒精性脂肪性肝病(NAFLD)发展和回归的关系,使用新的生命基础8评分。
    方法:来自健康筛查数据库,我们招募了在2012-2022年间至少接受过4次健康检查的参与者,并将其分为两个队列:(a)在第4次考试前无NAFLD病史的NAFLD发展队列和(b)在第4次考试前诊断为NAFLD的NAFLD回归队列.从每个组分计算LE8评分。结果定义为新发生的NAFLD或从检查4到随访结束的现有NAFLD的消退。
    结果:在NAFLD发展队列中,在21,844名参与者中,3,510例经历了NAFLD事件,中位随访时间为2.3年。与累积LE8的最低四分位数相比,最高四分位数的个体在统计学上显着降低了76%的几率(风险比[HR]0.24,95%置信区间[CI],0.21-0.28)NAFLD发病率,基线LE8的相应值为42%(HR0.58,95%CI0.53-0.65).在NAFLD回归队列中,在6,566名参与者中,469例NAFLD消退,中位随访时间为2.4年。累积LE8四分位数最高的受试者的NAFLD消退几率高2.03倍(95%CI,1.51-2.74),基线LE8的相应值为1.61倍(95%CI,1.24-2.10).
    结论:理想心血管健康累积暴露与NAFLD发展减少和NAFLD消退增加相关。改善和保护健康行为和因素应作为NAFLD预防和干预策略的重要组成部分。
    OBJECTIVE: We aimed to explore the associations of baseline and cumulative cardiovascular health with nonalcoholic fatty liver disease (NAFLD) development and regression using the new Life\'s Essential 8 score.
    METHODS: From a health screening database, participants who underwent at least 4 health examinations between 2012 and 2022 were recruited and categorized into two cohorts: (a) the NAFLD development cohort with no history of NAFLD prior to Exam 4 and (b) the NAFLD regression cohort with diagnosed NAFLD prior to Exam 4. The LE8 score was calculated from each component. The outcomes were defined as newly incident NAFLD or regression of existing NAFLD from Exam 4 to the end of follow-up.
    RESULTS: In the NAFLD development cohort, of 21,844 participants, 3,510 experienced incident NAFLD over a median follow-up of 2.3 years. Compared with the lowest quartile of cumulative LE8, individuals in the highest quartile conferred statistically significant 76% lower odds (hazard ratio [HR] 0.24, 95% confidence interval [CI], 0.21-0.28) of NAFLD incidence, and corresponding values for baseline LE8 were 42% (HR 0.58, 95% CI 0.53-0.65). In the NAFLD regression cohort, of 6,566 participants, 469 experienced NAFLD regression over a median follow-up of 2.4 years. Subjects with the highest quartile of cumulative LE8 had 2.03-fold (95% CI, 1.51-2.74) higher odds of NAFLD regression, and corresponding values for baseline LE8 were 1.61-fold (95% CI, 1.24-2.10).
    CONCLUSIONS: Cumulative ideal cardiovascular health exposure is associated with reduced NAFLD development and increased NAFLD regression. Improving and preserving health behaviors and factors should be emphasized as an important part of NAFLD prevention and intervention strategies.
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  • 文章类型: Journal Article
    像印度这样的发展中国家正在迅速从传统能源向可持续能源过渡,由于需求的增加和化石燃料的枯竭。并网光伏(PV)系统吸引了许多投资者,组织,和部署机构。本文研究并比较了安装在教育机构的三个52kW光伏电站的性能评估,SRMIST(SRM科学技术研究所),在泰米尔纳德邦,印度。该站点的年平均温度为28.5°C,全球平均水平辐射为160kWh/m2/m。利用太阳辐射获得了52千瓦发电厂的预测模型,温度,和风速。使用Minitab16.2.1软件推导了基于线性回归模型的预测方程,并将结果与2020年从三个52千瓦电厂获得的实时交流能量产量进行比较。此外,这个52千瓦的工厂是使用PVsystV7.1.8版本软件设计的。将模拟结果与2020年工厂的能源产量进行比较,以确定工厂性能的不足。通过从PVsyst软件获得损失图,对工厂进行损失分析。本研究还提出了一种方法来研究委托光伏电站的性能,并确定直接和扩散太阳辐射等变量之间的相互作用,空气温度,和风速,用于预测每小时产生的功率。本文将激励研究人员使用现代技术工具分析已安装的发电厂。
    Developing countries like India are rapidly transitioning from traditional energy sources to sustainable energy sources, due to the increase in demand and the depletion of fossil fuels. Grid-connected photovoltaic (PV) systems attract many investors, organizations, and institutions for deployment. This article studies and compares the performance evaluations of three 52-kW PV plants installed at an educational institution, SRMIST (SRM Institute of Science and Technology), in Tamil Nadu, India. This site receives an annual average temperature of 28.5°C and an average global horizontal irradiation of 160 kWh/m2/m. The prediction model for the 52-kW power plant is obtained using solar radiation, temperature, and wind speed. Linear regression model-based prediction equations are derived using the Minitab 16.2.1 software, and the results are compared with the real-time AC energy yield acquired from the three 52-kW plants for the year 2020. Furthermore, this 52-kW plant is designed using PVsyst V7.1.8 version software. The simulation results are compared with the energy yield from the plants in 2020 to identify the shortfall in the plant performance. The loss analysis for the plant is performed by obtaining the loss diagram from the PVsyst software. This study also proposes a methodology to study the commissioned PV plant\'s performance and determine the interaction between variables such as direct and diffused solar radiations, air temperature, and wind speed for forecasting hourly produced power. This article will motivate researchers to analyze installed power plants using modern technical tools.
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  • 文章类型: Journal Article
    在本文中,提出了利用约束最小二乘将非线性函数和/或离散数据简化为分段多项式的最优逼近算法。在对时间敏感的应用程序或资源有限的嵌入式系统中,近似函数的运行时间与其准确性一样重要。所提出的算法在确保误差低于指定阈值的同时,以最小的计算成本搜索最佳分段多项式(OPP)。这是通过使用具有最佳顺序和间隔数的平滑分段多项式来实现的。计算成本仅取决于多项式复杂度,即,运行时函数调用的顺序和间隔数。在以往的研究中,用户必须决定一个或所有的订单和间隔的数量。相比之下,OPP近似算法决定了两者。对于最佳逼近,对于特定的目标CPU离线,按升序计算了所有可能的分段多项式组合的计算成本,并将其制成表格。对于给定的样本点,通过约束最小二乘法和随机选择方法对每个组合进行优化。之后,检查近似误差是否低于预定值。如果错误是允许的,该组合被选择为最优近似,或者检查了下一个组合。要验证性能,对几个具有代表性的函数进行了检查和分析。
    In this paper, the optimal approximation algorithm is proposed to simplify non-linear functions and/or discrete data as piecewise polynomials by using the constrained least squares. In time-sensitive applications or in embedded systems with limited resources, the runtime of the approximate function is as crucial as its accuracy. The proposed algorithm searches for the optimal piecewise polynomial (OPP) with the minimum computational cost while ensuring that the error is below a specified threshold. This was accomplished by using smooth piecewise polynomials with optimal order and numbers of intervals. The computational cost only depended on polynomial complexity, i.e., the order and the number of intervals at runtime function call. In previous studies, the user had to decide one or all of the orders and the number of intervals. In contrast, the OPP approximation algorithm determines both of them. For the optimal approximation, computational costs for all the possible combinations of piecewise polynomials were calculated and tabulated in ascending order for the specific target CPU off-line. Each combination was optimized through constrained least squares and the random selection method for the given sample points. Afterward, whether the approximation error was below the predetermined value was examined. When the error was permissible, the combination was selected as the optimal approximation, or the next combination was examined. To verify the performance, several representative functions were examined and analyzed.
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