Knot selection for least-squares and penalized splines

Spiriti, Steven Mark; Eubank, R. L.; Smith, Philip W.; Young, Dennis

doi:10.1080/00949655.2011.647317

Cited by 52 publications

(42 citation statements)

References 40 publications

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“…The approach used in this application was to approximate the step function via a spline of degree 0. Genetic algorithm was used to find the optimal knot locations . The optimal locations are those which minimize the residual sums of squares between the approximation and the data collected.…”

Section: Regularization Approaches For Individual Missionsmentioning

confidence: 94%

“…Genetic algorithm was used to find the optimal knot locations. 5 The optimal locations are those which minimize the residual sums of squares between the approximation and the data collected. Denoting the covariate to be approximated by X ki , the residual sum of squares criterion for r knots for the kth factor on the ith mission is given by the following:…”

Section: Change Point Identificationmentioning

confidence: 99%

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Regularization for Continuously Observed Ordinal Response Variables with Piecewise‐constant Functional Covariates

Avery

Orndorff

Robinson

et al. 2016

Quality & Reliability Eng

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This paper investigates regularization for continuously observed covariates that resemble step functions. The motivating examples come from operational test data from a recent US Department of Defense test of the Shadow Tactical Unmanned Aircraft system. The response variable, quality of video provided by the Shadow to friendly ground units, was measured on an ordinal scale continuously over time. Functional covariates, altitude and distance, can be well approximated by step functions. Two approaches for regularizing these covariates are considered, including a thinning approach commonly used within the Department of Defense to address autocorrelated time series data, and a novel ‘smoothing’ approach, which first approximates the covariates as step functions and then treats each ‘step’ as a uniquely observed data point. Datasets resulting from both approaches are fit using a mixed model cumulative logistic regression, and we compare their results. While the thinning approach identifies altitude as having a significant impact on video quality, the smoothing approach finds no evidence of an effect. This difference is attributable to the larger effective sample size produced by thinning. System characteristics make it unlikely that video quality would degrade at higher altitudes, suggesting that the thinning approach has produced a Type 1 error. By accounting for the functional characteristics of the covariates, the novel smoothing approach has produced a more accurate characterization of the Shadow's ability to provide full motion video to supported units. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Regularization Approaches For Individual Missionsmentioning

confidence: 94%

Section: Change Point Identificationmentioning

confidence: 99%

Regularization for Continuously Observed Ordinal Response Variables with Piecewise‐constant Functional Covariates

Avery

Orndorff

Robinson

et al. 2016

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…In addition, the knots need to be placed in optimal positions for the fit to be accurate. Common knot selection approaches are based on either fit statistics or cross‐validation . To find this set via fit statistics, one can place many equally spaced knots and then find the knot sequence that minimizes a goodness of fit statistic, such as AIC or BIC.…”

Section: Methodsmentioning

confidence: 99%

“…Common knot selection approaches are based on either fit statistics or cross-validation. 9 To find this set via fit statistics, one can place many equally spaced knots and then find the knot sequence that minimizes a goodness of fit statistic, such as AIC or BIC. For cross-validation, a subset of data is fit to each specified knot sequence, and the knot sequence that minimizes some sort of fit criterion, such as the mean squared error, is selected.…”

Section: Modelmentioning

confidence: 99%

Bayesian monotonic errors‐in‐variables models with applications to pathogen susceptibility testing

DePalma

Craig

2017

Statistics in Medicine

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Drug dilution (MIC) and disk diffusion (DIA) are the 2 most common antimicrobial susceptibility assays used by hospitals and clinics to determine an unknown pathogen's susceptibility to various antibiotics. Since only one assay is commonly used, it is important that the 2 assays give similar results. Calibration of the DIA assay to the MIC assay is typically done using the error-rate bounded method, which selects DIA breakpoints that minimize the observed discrepancies between the 2 assays. In 2000, Craig proposed a model-based approach that specifically models the measurement error and rounding processes of each assay, the underlying pathogen distribution, and the true monotonic relationship between the 2 assays. The 2 assays are then calibrated by focusing on matching the probabilities of correct classification (susceptible, indeterminant, and resistant). This approach results in greater precision and accuracy for estimating DIA breakpoints. In this paper, we expand the flexibility of the model-based method by introducing a Bayesian 4-parameter logistic model (extending Craig's original 3-parameter model) as well as a Bayesian nonparametric spline model to describe the relationship between the 2 assays. We propose 2 ways to handle spline knot selection, considering many equally spaced knots but restricting overfitting via a random walk prior and treating the number and location of knots as additional unknown parameters. We demonstrate the 2 approaches via a series of simulation studies and apply the methods to 2 real data sets.

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“…For example, [19], [20], [21]. A stochastic search method was proposed in [22] for optimizing the knot locations by using a continuous genetic algorithm. Bayesian methods for fitting free-knot splines have been considered in some literatures [23], [24], [25],and [26].…”

Section: Introductionmentioning

confidence: 99%

Hit and run ARMS: adaptive rejection Metropolis sampling with hit and run random direction

Zhang

Cheng

et al. 2015

Journal of Statistical Computation and Simulation

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An algorithm for sampling from non-log-concave multivariate distributions is proposed, which improves the adaptive rejection Metropolis sampling (ARMS) algorithm by incorporating the hit and run sampling. It is not rare that the ARMS is trapped away from some subspace with significant probability in the support of the multivariate distribution. While the ARMS updates samples only in the directions that are parallel to dimensions, our proposed method, the hit and run ARMS (HARARMS), updates samples in arbitrary directions determined by the hit and run algorithm, which makes it almost not possible to be trapped in any isolated subspaces. The HARARMS performs the same as ARMS in a single dimension while more reliable in multidimensional spaces. Its performance is illustrated by a Bayesian free-knot spline regression example. We showed that it overcomes the well-known 'lethargy' property and decisively find the global optimal number and locations of the knots of the spline function.

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Knot selection for least-squares and penalized splines

Cited by 52 publications

References 40 publications

Regularization for Continuously Observed Ordinal Response Variables with Piecewise‐constant Functional Covariates

Regularization for Continuously Observed Ordinal Response Variables with Piecewise‐constant Functional Covariates

Bayesian monotonic errors‐in‐variables models with applications to pathogen susceptibility testing

Hit and run ARMS: adaptive rejection Metropolis sampling with hit and run random direction

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