From Data to Assessments and Decisions: Epi-Spline Technology

Røyset, Johannes Ø.; Wets, Roger J.-B.

doi:10.1287/educ.2014.0126

Cited by 7 publications

(8 citation statements)

References 18 publications

(43 reference statements)

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“…In fact, (lsc-fcns(IR n ), dl) is a proper complete separable metric space; [24,Theorem 7.58] and [27,Corollary 3.6]. This example is a motivation for the development due to applications in nonparametric statistics, curve fitting, and stochastic processes; see [26,27,30]. We use the following well-known fact repeatedly.…”

Section: Propositionmentioning

confidence: 99%

“…A class of functions over which such optimal fitting might take place is the collection of lsc functions on IR n , often simply with n = 1; see [30,26,27] for applications. The class of such lsc functions offers obvious modeling flexibility, which is important to practitioners, but under the aw-distance the class is a proper metric space that fails to be linear [24,Theorem 7.58].…”

Section: Introductionmentioning

confidence: 99%

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Approximations and solution estimates in optimization

Røyset

2017

Math. Program.

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Abstract. Approximation is central to many optimization problems and the supporting theory provides insight as well as foundation for algorithms. In this paper, we lay out a broad framework for quantifying approximations by viewing finite-and infinite-dimensional constrained minimization problems as instances of extended real-valued lower semicontinuous functions defined on a general metric space. Since the Attouch-Wets distance between such functions quantifies epi-convergence, we are able to obtain estimates of optimal solutions and optimal values through estimates of that distance. In particular, we show that near-optimal and near-feasible solutions are effectively Lipschitz continuous with modulus one in this distance. We construct a general class of approximations of extended real-valued lower semicontinuous functions that can be made arbitrarily accurate and that involve only a finite number of parameters under additional assumptions on the underlying metric space.

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Section: Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximations and solution estimates in optimization

Røyset

2017

Math. Program.

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“…We also start with a problem of identifying a function that minimizes a criterion and satisfies given constraints, but depart from the traditional focus on smoothness, interpolation, and (least-squares) approximation. Motivated by applications in curve fitting, regression, probability density estimation, variogram computation, financial curve construction, and building of stochastic processes [31,30], we instead consider nearly arbitrary criterion and constraints, which leads to a broad class of function identification problems. Although recent efforts focus on additional constraints, for example related to shape [32,19,15,14,22,23,17], our treatment is more general.…”

Section: Introductionmentioning

confidence: 99%

“…The paper ends with numerical examples in §6. A summary of some results and an exposition of the framework of analysis are given in the forthcoming tutorial [31].…”

Section: Introductionmentioning

confidence: 99%

Multivariate Epi-splines and Evolving Function Identification Problems

Røyset

Wets

2015

Set-Valued Var. Anal

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Abstract. The broad class of extended real-valued lower semicontinuous (lsc) functions on IR n captures nearly all functions of practical importance in equation solving, variational problems, fitting, and estimation. The paper develops piecewise polynomial functions, called epi-splines, that approximate any lsc function to an arbitrary level of accuracy. Epi-splines provide the foundation for the solution of a rich class of function identification problems that incorporate general constraints on the function to be identified including those derived from information about smoothness, shape, proximity to other functions, and so on. As such extrinsic information as well as observed function and subgradient values often evolve in applications, we establish conditions under which the computed epi-splines converge to the function we seek to identify. Numerical examples in response surface building and probability density estimation illustrate the framework.

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“…Motivated by the power of epi-splines to derive term and volatility structures associated with fi markets [47], and their successful applications in numerous areas [48], in this paper epi-splines are applied separately in each segment of a season for each zone to model the complex nonlinear temporal dependence of load and effects of weather on load. Section 2.1 introduces epi-splines.…”

Section: Day-ahead Hourly Load Modelmentioning

confidence: 99%

Day-ahead hourly electricity load modeling by functional regression

Feng

Ryan

2016

Applied Energy

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Short-term load forecasting is important for power system generation planning and operation. For unit commitment and dispatch processes to incorporate uncertainty, a short-term load model must not only provide accurate load predictions but also enable the generation of reasonable probabilistic scenarios or uncertainty sets. This paper proposes a temporal and weather conditional epi-splines based load model (TWE) using functional approximation. TWE models the dependence of load on time and weather separately by functional approximation using epi-splines, conditional on season and area, in each segment of similar weather days. Load data are transformed from various day types to a specified reference day type among similar weather days in the same season and area, in order to enrich the data for capturing the non-weather dependent load pattern. In an instance derived from an Independent System Operator in the U.S., TWE not only provides accurate hourly load prediction and narrow bands of prediction errors, but also yields serial correlations among forecast hourly load values within a day that are similar to those of actual hourly load. KeywordsShort-term load model, Forecasting, Day-ahead scenario, Epi-splines Disciplines Industrial Engineering | Systems EngineeringComments NOTICE: this is the author's version of a work that was accepted for publication in Applied Energy. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Energy, v.170, 15 May (2016) AbstractShort-term load forecasting is important for power system generation planning and operation. For unit commitment and dispatch processes to incorporate uncertainty, a short-term load model must not only provide accurate load predictions but also enable the generation of reasonable probabilistic scenarios or uncertainty sets. This paper proposes a temporal and weather conditional epi-splines based load model (TWE) using functional approximation. TWE models the dependence of load on time and weather separately by functional approximation using epi-splines, conditional on season and area, in each segment of similar weather days. Load data are transformed from various day types to a specified reference day type among similar weather days in the same season and area, in order to enrich the data for capturing the non-weather dependent load pattern. In an instance derived from an Independent System Operator in the U.S., TWE not only provides accurate hourly load prediction and narrow bands of prediction errors, but also yields serial correlations among forecast hourly load values within a day that are similar to those of actual hourly load.

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From Data to Assessments and Decisions: Epi-Spline Technology

Cited by 7 publications

References 18 publications

Approximations and solution estimates in optimization

Approximations and solution estimates in optimization

Multivariate Epi-splines and Evolving Function Identification Problems

Day-ahead hourly electricity load modeling by functional regression

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