Fusion of hard and soft information in nonparametric density estimation

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

doi:10.1016/j.ejor.2015.06.034

Cited by 22 publications

(33 citation statements)

References 51 publications

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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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“…Probability density estimation [29,34] is one of our major incentives for considering problems of the form (F IP ) and constructing evolving approximations (F IP ν ). A density is a nonnegative function that sums up to 1 and an estimate is chosen so as to minimize some appropriate criterion; for further details see §6.2, [29], and references therein.…”

Section: Composite Epi-splinementioning

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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“…We estimate the distribution of these errors by fitting an exponential epi-spline [18,19]. This process is graphically illustrated in Figure 1.…”

Section: Scenario Generationmentioning

confidence: 99%

“…We estimate the probability density function f t * (·) of the temperature scalar t d * by fitting an exponential epi-spline [18,19]. We denote the corresponding cumulative distribution function by F t * (·).…”

Section: Segmentationmentioning

confidence: 99%

Toward scalable stochastic unit commitment. Part 1: load scenario generation

et al. 2015

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Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Tra-ditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load sce-narios, with associated probabilities, that in aggregate capture the range of likely load time-series. The shift from point-based to scenario-based forecasting necessi-tates a shift in forecasting technologies, to provide accurate inputs to stochastic unit commitment. In this paper, we discuss a novel scenario generation method-ology for load forecasting in stochastic unit commitment, with application to real data associated with the Independent System Operator for New England (ISO-NE). The accuracy of the expected scenario generated using our methodology is consistent with that of point forecasting methods. The resulting sets of realistic scenarios serve as input to rigorously test the scalability of stochastic unit com-mitment solvers, as described in the companion paper. The scenarios generated by our method are available as an online supplement to this paper, as part of a novel, publicly available large-scale stochastic unit commitment benchmark. Abstract Unit commitment decisions made in the day-ahead market and during subsequent reliability assessments are critically based on forecasts of load. Traditional, deterministic unit commitment is based on point or expectation-based load forecasts. In contrast, stochastic unit commitment relies on multiple load scenarios, with associated probabilities, that in aggregate capture the range of likely load time-series. The shift from point-based to scenario-based forecasting necessitates a shift in forecasting technologies, to provide accurate inputs to stochastic unit commitment. In this paper, we discuss a novel scenario generation methodology for load forecasting in stochastic unit commitment, with application to real data associated with the Independent System Operator for New England (ISO-NE). The accuracy of the expected scenario generated using our methodology is consistent with that of point forecasting methods. The resulting sets of realistic scenarios serve as input to rigorously test the scalability of stochastic unit commitment solvers, as described in the companion paper. The scenarios generated Disciplines Industrial Engineering | Systems Engineering

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Fusion of hard and soft information in nonparametric density estimation

Cited by 22 publications

References 51 publications

Approximations and solution estimates in optimization

Approximations and solution estimates in optimization

Multivariate Epi-splines and Evolving Function Identification Problems

Toward scalable stochastic unit commitment. Part 1: load scenario generation

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