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comp.ai.neural-nets FAQ, Part 7 of 7: Hardware
Section - What to do with missing/incomplete data?

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The problem of missing data is very complex. 

For unsupervised learning, conventional statistical methods for missing data
are often appropriate (Little and Rubin, 1987; Schafer, 1997; Schafer and
Olsen, 1998). There is a concise introduction to these methods in the
University of Texas statistics FAQ at 
http://www.utexas.edu/cc/faqs/stat/general/gen25.html. 

For supervised learning, the considerations are somewhat different, as
discussed by Sarle (1998). The statistical literature on missing data deals
almost exclusively with training rather than prediction (e.g., Little,
1992). For example, if you have only a small proportion of cases with
missing data, you can simply throw those cases out for purposes of training;
if you want to make predictions for cases with missing inputs, you don't
have the option of throwing those cases out! In theory, Bayesian methods
take care of everything, but a full Bayesian analysis is practical only with
special models (such as multivariate normal distributions) or small sample
sizes. The neural net literature contains a few good papers that cover
prediction with missing inputs (e.g., Ghahramani and Jordan, 1997; Tresp,
Neuneier, and Ahmad 1995), but much research remains to be done. 

References: 

   Donner, A. (1982), "The relative effectiveness of procedures commonly
   used in multiple regression analysis for dealing with missing values,"
   American Statistician, 36, 378-381. 

   Ghahramani, Z. and Jordan, M.I. (1994), "Supervised learning from
   incomplete data via an EM approach," in Cowan, J.D., Tesauro, G., and
   Alspector, J. (eds.) Advances in Neural Information Processing Systems
   6, San Mateo, CA: Morgan Kaufman, pp. 120-127. 

   Ghahramani, Z. and Jordan, M.I. (1997), "Mixture models for Learning from
   incomplete data," in Greiner, R., Petsche, T., and Hanson, S.J. (eds.) 
   Computational Learning Theory and Natural Learning Systems, Volume IV:
   Making Learning Systems Practical, Cambridge, MA: The MIT Press, pp.
   67-85. 

   Jones, M.P. (1996), "Indicator and stratification methods for missing
   explanatory variables in multiple linear regression," J. of the American
   Statistical Association, 91, 222-230. 

   Little, R.J.A. (1992), "Regression with missing X's: A review," J. of the
   American Statistical Association, 87, 1227-1237. 

   Little, R.J.A. and Rubin, D.B. (1987), Statistical Analysis with Missing
   Data, NY: Wiley. 

   McLachlan, G.J. (1992) Discriminant Analysis and Statistical Pattern
   Recognition, Wiley. 

   Sarle, W.S. (1998), "Prediction with Missing Inputs," in Wang, P.P.
   (ed.), JCIS '98 Proceedings, Vol II, Research Triangle Park, NC, 399-402,
   ftp://ftp.sas.com/pub/neural/JCIS98.ps. 

   Schafer, J.L. (1997), Analysis of Incomplete Multivariate Data, London:
   Chapman & Hall, ISBN 0 412 04061 1. 

   Schafer, J.L., and Olsen, M.K. (1998), "Multiple imputation for
   multivariate missing-data problems: A data analyst's perspective," 
   http://www.stat.psu.edu/~jls/mbr.pdf or 
   http://www.stat.psu.edu/~jls/mbr.ps 

   Tresp, V., Ahmad, S. and Neuneier, R., (1994), "Training neural networks
   with deficient data", in Cowan, J.D., Tesauro, G., and Alspector, J.
   (eds.) Advances in Neural Information Processing Systems 6, San Mateo,
   CA: Morgan Kaufman, pp. 128-135. 

   Tresp, V., Neuneier, R., and Ahmad, S. (1995), "Efficient methods for
   dealing with missing data in supervised learning", in Tesauro, G.,
   Touretzky, D.S., and Leen, T.K. (eds.) Advances in Neural Information
   Processing Systems 7, Cambridge, MA: The MIT Press, pp. 689-696. 

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Top Document: comp.ai.neural-nets FAQ, Part 7 of 7: Hardware
Previous Document: What are some applications of NNs?
Next Document: How to forecast time series (temporal sequences)?

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