Optimal Value Estimation of Intentional-Value-Substitution for Learning Regression Models
Takuya Fukushima*, Tomoharu Nakashima*, Taku Hasegawa*, and Vicenç Torra**
*Osaka Prefecture University
1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531, Japan
MIT-huset, C444, Umeå universitet, Umeå 901 87, Sweden
This paper focuses on a method to train a regression model from incomplete input values. It is assumed in this paper that there are no missing values in a training dataset while missing values exist during a prediction phase using the trained model. Under this assumption, we propose Intentional-Value-Substitution (IVS) training to obtain a machine learning model that makes the prediction error as minimum as possible. In IVS training, a model is trained to approximate the target function using a modified training dataset in which some feature values are substituted with a certain value even though their values are not missing. It is shown through a series of computational experiments that the substitution values calculated from a mathematical analysis help the models correctly predict outputs for inputs with missing values.
-  A. N. Baraldi, and C. K. Enders, “An introduction to modern missing data analyses,” J. of School Psychology, Vol.48, No.1, pp. 5-37, 2010.
-  R. J. A. Little and D. B. Rubin, “Statistical Analysis with Missing Data,” John Wiley & Sons, Inc., 1986.
-  D. B. Rubin, “Multiple Imputation For Nonresponse In Surveys,” Wiley Series in Probability and Statistics, 1987.
-  D. B. Rubin, “Multiple Imputation After 18+ Years,” J. of the American Statistical Association, Vol.91, No.434, pp. 473-489, 1996.
-  J. L. Schafer and J. W. Graham, “Missing data: our view of the state of the art,” J. of Psychological Methods, Vol.2, No.7, pp. 147-177, 2002.
-  V. Tresp, S. Ahmad, and R. Neuneier, “Training Neural Networks with Deficient Data,” Proc. of the 6th Int. Conf. on Neural Information Processing Systems (NIPS’93), pp. 128-135, 1993.
-  A. C. Acock, “Working With Missing Values,” J. of Marriage and Family, Vol.67, No.4, pp. 1012-1028, 2005.
-  T. Hasegawa, T. Fukushima, and T. Nakashima, “Robust Prediction against Missing Values by Intentional Value Substitution,” Proc. of 7th Int. Symp. on Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM’19), pp. 69-80, 2019.
-  D. P. Kingma and J. Ba, “Adam: A Method for Stochastic Optimization,” Proc of the 3rd Int. Conf. on Learning Representations (ICLR 2015), 2015.
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