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1

Stretching the Least Squares to Embed Loss Function Tables

Yoneda K., Moretti A. C., Poker J. Jr.

Decision Making in Manufacturing and Services

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2015

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Vol. 9, no. 2

105--116

EN

The method of least squares is extended to accommodate a class of loss functions specified in the form of function tables. The function tables are embedded into the standard quadratic loss function so that nonlinear least squares algorithms can be adopted for loss minimization. This is an alternative to a more straightforward approach which interpolates the function tables and minimizes the resulting loss function by some generic optimization algorithm. The alternative approach has advantages over the straightforward, such as the wider availability of the least squares programs compared to the generic optimization programs and reduction in computational complexity. Examples are given for its application to multiplicative utility function maximization problems.

2

Maximization of an Asymmetric Utility Function by the Least Squares

Yoneda K., Moretti A. C.

Decision Making in Manufacturing and Services

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2014

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Vol. 8, no. 1-2

5--12

EN

This note points out that a utility maximization procedure proposed in an earlier paper may be reduced to the least squares. The utility function is asymmetric in the sense that for each cue its ideal value and the permissible range are assigned in such a way that the ideal is not necessarily at the center of the range, like "a beer of 350 ml would be ideal, but acceptable if within [100, 500]". A practical consequence of the observation is that very little programming will be needed to deploy the utility maximization since software for the least squares is widely available.

3

A Utility Function to Solve Approximate Linear Equations for Decision Making

Yoneda K., Celaschi W.

Decision Making in Manufacturing and Services

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2013

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Vol. 7, no. 1-2

5--18

EN

Suppose there are a number of decision variables linearly related to a set of outcome variables. There are at least as many outcome variables as the number of decision variables since all decisions are outcomes by themselves. The quality of outcome is evaluated by a utility function. Given desired values for all outcome variables, decision making reduces to “solving” the system of linear equations with respect to the decision variables; the solution being defined as decision variable values such that maximize the utility function. This paper proposes a family of additively separable utility functions which can be defined by setting four intuitive parameters for each outcome variable: the desired value of the outcome, the lower and the upper limits of its admissible interval, and its importance weight. The utility function takes a nonnegative value within the admissible domain and negative outside; permits gradient methods for maximization; is designed to have a small dynamic range for numerical computation. Small examples are presented to illustrate the proposed method.

4

A loss function for box-constrained inverses problems

Yoneda K.

Decision Making in Manufacturing and Services

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2008

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Vol. 2, no. 1-2

79-98

EN

A loss function is proposed for solving box-constrained inverse problems. Given causality mechanisms between inputs and outputs as smooth functions, an inverse problem demands to adjust the input levels to make the output levels as close as possible to the target values; box-constrained refers to the requirement that all outcome levels remain within their respective permissible intervals. A feasible solution is assumed known, which is often the status quo. We propose a loss function which avoids activation of the constraints. A practical advantage of this approach over the usual weighted least squares is that permissible outcome intervals are required in place of target importance weights, facilitating data acquisition. The proposed loss function is smooth and strictly convex with closed-form gradient and Hessian, permitting Newton family algorithms. The author has not been able to locate in the literature the Gibbs distribution corresponding to the loss function. The loss function is closely related to the generalized matching law in psychology.

5

Elevator trip distribution for inconsistent passenger input-output data

Yoneda K.

Decision Making in Manufacturing and Services

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2007

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Vol. 1, no. 1-2

175-190

EN

Accurate traffic data are the basis for group control of elevators and its performance evaluation by trace driven simulation. The present practice estimates a time series of inter-floor passenger traffic based on commonly available elevator sensor data. The method demands that the sensor data be transformed into sets of passenger input-output data which are consistent in the sense that the transportation preserves the number of passengers. Since observation involves various behavioral assumptions, which may actually be violated, as well as measurement errors, it has been necessary to apply data adjustment procedures to secure the consistency. This paper proposes an alternative algorithm which reconstructs elevator passenger origin-destination tables from inconsistent passenger input-output data sets, thus eliminating the ad hoc data adjustment.

6

Modular function spaces and control functions of almost everywhere convergence

Kita H., Miyamoto T., Yoneda K.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2001

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[Z] 41

99-133

EN

The modular spaces have been studied by many authors. In this paper we consider the modular function spaces which provide a generalization of Banach function spaces, and discuss some relations between properties of these spaces and control functions of almost everywhrere convergence of functions in modular function spaces. We give a necessary and sufficient condition for a control function to be in the same modular function space as functions appearing in almost everywhere convergence.