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Techniques for dealing with incomplete data: a tutorial and survey. (English) Zbl 1425.68364

Summary: Real-world applications of pattern recognition, or machine learning algorithms, often present situations where the data are partly missing, corrupted by noise, or otherwise incomplete. In spite of that, developments in the machine learning community in the last decade have mostly focused on mathematical analysis of learning machines, making it difficult for practitioners to recollect an overview of major approaches to this issue. Paradoxically, as a consequence, even established methodologies rooted in statistics appear to have long been forgotten. Although the relevant literature on the topic is so wide that no exhaustive coverage is nowadays possible, the first goal of this paper is to provide the reader with a nonetheless significant survey of major, or utterly sound, techniques for dealing with the tasks of pattern recognition, machine learning, and density estimation from incomplete data. Secondly, the paper aims at representing a viable tutorial tool for the interested practitioner, by allowing for self-contained, step-by-step understanding of several approaches. An effort is made to categorize the different techniques as follows: (1) heuristic methods; (2) statistical approaches; (3) connectionist-oriented techniques; (4) other approaches (dynamical systems, adversarial deletion of features, etc.).

MSC:

68T10 Pattern recognition, speech recognition
68T05 Learning and adaptive systems in artificial intelligence

Software:

VIM; impute
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Full Text: DOI

References:

[1] Lee C, Choi SW, Lee J-M, Lee I-B (2004) Sensor fault identification in mspm using reconstructed monitoring statistics. Ind Eng Chem Res 43(15):4293-4304 · doi:10.1021/ie034246z
[2] Lopes VV, Menezes JC (2005) Inferential sensor design in the presence of missing data: a case study. Chemometr Intell Lab Syst 78(1-2):1-10 · doi:10.1016/j.chemolab.2004.11.004
[3] Rendtel U (2006) The 2005 plenary meeting on missing data and measurement error. AStA Adv Stat Anal 90(4):493-499 · Zbl 1417.00079
[4] Mott P, Sammis TW, Southward GM (1994) Climate data estimation using climate information from surrounding climate stations. Appl Eng Agric 10(1):41-44 · doi:10.13031/2013.25825
[5] Li Q, Roxas BAP (2008) Significance analysis of microarray for relative quantitation of lc/ms data in proteomics. BMC Bioinform 9(1):187-197
[6] Green P, Barker J, Cooke M, Josifovski L (2001) Handling missing and unreliable information in speech recognition. In: Proceedings of AISTATS · Zbl 1005.68756
[7] Barker J (2012) Missing-data techniques: recognition with incomplete spectrograms. Wiley, New York, pp 369-398
[8] Pynadath D, Wellman M (2000) Probabilistic state-dependent grammars for plan recognition. In: Proceedings of the conference on uncertainty in artificial intelligence, pp 507-514
[9] Guerreiro RFC, Aguiar PMQ (2002) Factorization with missing data for 3d structure recovery. In: Proceedings of the IEEE workshop on multimedia signal processing, pp 105-108
[10] Jia H, Martinez AM (2009) Support vector machines in face recognition with occlusions. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 136-141
[11] Chapelle O, Schölkopf B, Zien A (eds) (2006) Semi-supervised learning. MIT Press, Cambridge
[12] Chen K, Wang S (2011) Semi-supervised learning via regularized boosting working on multiple semi-supervised assumptions. IEEE Trans Pattern Anal Mach Intell 99(1):129-143
[13] You Z, Yin Z, Han K, Huang D-S, Zhou X (2010) A semi-supervised learning approach to predict synthetic genetic interactions by combining functional and topological properties of functional gene network. BMC Bioinform 11:343 · doi:10.1186/1471-2105-11-343
[14] Schwenker F, Trentin E (2014) Pattern classification and clustering: a review of partially supervised learning approaches. Pattern Recognit Lett 37:4-14 · doi:10.1016/j.patrec.2013.10.017
[15] Gabrys, B.; Foggia, P. (ed.); Sansone, C. (ed.); Vento, M. (ed.), Learning with missing or incomplete data, 1-4 (2009), Berlin, Heidelberg · doi:10.1007/978-3-642-04146-4_1
[16] Vinod NC, Punithavalli M (2011) Classification of incomplete data handling techniques an overview. Int J Comput Sci Eng 3(1):340-344
[17] Richard MD, Lippmann RP (1991) Neural network classifiers estimate Bayesian a posteriori probabilities. Neural Comput 3:461-483 · doi:10.1162/neco.1991.3.4.461
[18] Lee RCT, Slagle JR, Mong CT (1976) Application of clustering to estimate missing data and improve data integrity. In: Proceedings of 2nd international software engineering conference, pp 539-544, San Francisco, October 1976 · Zbl 0362.68117
[19] Lim C-P, Leong J-H, Kuan M-M (2005) A hybrid neural network system for pattern classification tasks with missing features. IEEE Trans Pattern Anal Mach Intell 27(4):648-653 · doi:10.1109/TPAMI.2005.64
[20] Zhang S, Qin Y, Zhu X, Zhang J, Zhang C (2006) Optimized parameters for missing data imputation. In: PRICAI, pp 1010-1016
[21] Pelckmans KA, De Brabanter JB, Suykens JAKA, De Moor BA (2005) Handling missing values in support vector machine classifiers. Neural Netw 18(5-6):684-692 · Zbl 1077.68777 · doi:10.1016/j.neunet.2005.06.025
[22] Su X, Khoshgoftaar TM, Zhu X, Greiner R (2008) Imputation-boosted collaborative filtering using machine learning classifiers. In: SAC ’08: Proceedings of the 2008 ACM symposium on applied computing. ACM, New York, pp 949-950
[23] Su X, Greiner R, Khoshgoftaar TM, Napolitano A (2011) Using classifier-based nominal imputation to improve machine learning. In: Huang JZ, Cao L, Srivastava J (eds) PAKDD (1). Springer, pp 124-135
[24] Little RJA, Rubin DB (2002) Statistical analysis with missing data. Wiley, New York · Zbl 1011.62004 · doi:10.1002/9781119013563
[25] Dixon JK (1979) Pattern recognition with partly missing data. IEEE Trans Syst Man Cybern 9(10):617-621 · doi:10.1109/TSMC.1979.4310090
[26] Dudani SA (1976) The distance-weighted \[k\] k-nearest-neighbor rule. IEEE Trans Syst Man Cybern 6:325-327 · doi:10.1109/TSMC.1976.5408784
[27] Bailey T, Jain AK (1978) A note on distance-weighted \[k\] k-nearest neighbor rules. IEEE Trans Syst Man Cybern 8:311-313 · Zbl 0383.68067 · doi:10.1109/TSMC.1978.4309958
[28] Morin RL, Raeside DE (1981) A reappraisal of distance-weighted \[k\] k-nearest neighbor classification for pattern recognition with missing data. IEEE Trans Syst Man Cybern 11(3):241-243 · doi:10.1109/TSMC.1981.4308660
[29] Schafer JL, Graham JW (2002) Missing data: our view of the state of the art. Psychol Methods 7:147-177 · doi:10.1037/1082-989X.7.2.147
[30] Ghahramani Z, Jordan MI (1994) Learning from incomplete data. AI Memo 1509, CBCL paper 108. MIT, Cambridge
[31] Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 39:1-38 · Zbl 0364.62022
[32] Rao CR (1972) Linear statistical inference and its applications. Wiley, New York
[33] Wu CFJ (1983) On the convergence properties of the EM algorithm. Ann Stat 11(1):95-103 · Zbl 0517.62035 · doi:10.1214/aos/1176346060
[34] Redner RA, Walker HF (1984) Mixture densities, maximum likelihood and the EM algorithm. SIAM Rev 26:195-239 · Zbl 0536.62021 · doi:10.1137/1026034
[35] Xu L, Jordan MI (1996) On convergence properties of the EM algorithm for Gaussian mixtures. Neural Comput 8:129-151 · doi:10.1162/neco.1996.8.1.129
[36] Duda RO, Hart PE (1973) Pattern classification and scene analysis. Wiley, New York · Zbl 0277.68056
[37] Walter RG, Richardson S, Spiegelhalter D (1996) Markov chain Monte Carlo in practice. Chapman & Hall/CRC, New York · Zbl 0832.00018
[38] Ramoni M, Sebastiani P (2001) Robust learning with missing data. Machine Learn 45(2):147-170 · Zbl 1007.68154 · doi:10.1023/A:1010968702992
[39] Beaton AE (1964) The use of special matrix operations in statistical calculus. Educational Testing Service Research Bulletin, RB-64-51
[40] Dempster AP (1969) Elements of continuous multivariate analysis. Addison-Wesley, Reading · Zbl 0197.44904
[41] McLachlan G, Basford K (1988) Mixture models: inference and applications to clustering. Marcel Dekker, New York · Zbl 0697.62050
[42] Ghahramani Z (1994) Solving inverse problems using an EM approach to density estimation. In: Mozer MC, Smolensky P, Touretzky DS, Elman JL, Weigend AS (eds) Proceedings of the 1993 Connectionist Models Summer School. Erlbaum Associates, Hillsdale, pp 316-323
[43] Ghahramani, Z.; Jordan, MI; Cowan, JD (ed.); Tesauro, G. (ed.); Alspector, J. (ed.), Supervised learning from incomplete data via an EM approach (1994), San Mateo
[44] Moss S, Hancock ER (1997) Registering incomplete radar images using the EM algorithm. Image Vis Comput 15:637-648 · doi:10.1016/S0262-8856(97)00014-0
[45] Breiman L, Friedman JH, Olshen RA, Stone CJ (1984) Classification and Regression Trees. Wadsworth International Group, Belmont · Zbl 0541.62042
[46] Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat 19:1-141 · Zbl 0765.62064 · doi:10.1214/aos/1176347963
[47] Tresp, V.; Hollatz, J.; Ahmad, S.; Hanson, SJ (ed.); Cowan, JD (ed.); Giles, CL (ed.), Network structuring and training using rule-based knowledge, 871-878 (1993), San Mateo
[48] Jordan MI, Jacobs RA (1994) Hierarchical mixtures of experts and the EM algorithm. Neural Comput 6:181-214 · doi:10.1162/neco.1994.6.2.181
[49] Tresp, V.; Ahmad, S.; Neuneier, R.; Cowan, JD (ed.); Tesauro, G. (ed.); Alspector, J. (ed.), Training neural networks with deficient data, 128-135 (1994), San Mateo
[50] Streit RL, Luginbuhl TE (1994) Maximum likelihood training of probabilistic neural networks. IEEE Trans Neural Netw 5(5):764-783 · doi:10.1109/72.317728
[51] Tanaka M, Kotokawa Y, Tanino T (1996) Pattern classification by stochastic neural networks with missing data. In: IEEE international conference on systems, man and cybernetics, Beijing, China, pp 690-695, 14-17 October 1996
[52] Vellido A (2006) Missing data imputation through GTM as a mixture of t-distributions. Neural Netw 19(10):1624-1635 · Zbl 1178.68472 · doi:10.1016/j.neunet.2005.11.003
[53] Hwang JN, Wang CJ (1994) Classification of incomplete data with missing elements. In: International symposium on artificial neural networks, Tainan, Taiwan, December 1994, pp 471-477
[54] Schafer JL (2010) Analysis of incomplete multivariate data. Chapmann and Hall-CRC Press, London
[55] Linden A, Kindermann J (1989) Inversion of multilayer nets. In: Proceedings of the international joint conference on neural networks, II, Washington DC, June 1989, pp 425-430
[56] Ahmad, S.; Tresp, V.; Hanson, SJ (ed.); Cowan, JD (ed.); Giles, CL (ed.), Some solutions to the missing feature problem in vision, 393-400 (1993), San Mateo
[57] Tresp, V.; Neuneier, R.; Ahmad, S.; Tesauro, G. (ed.); Touretzky, D. (ed.); Leen, T. (ed.), Efficient methods for dealing with missing data in supervised learning, 689-696 (1995), San Mateo
[58] Graham BS, Keisuke H (2011) Robustness to parametric assumptions in missing data models. Am Econ Rev 101(3):538-543 · doi:10.1257/aer.101.3.538
[59] Ahmad S, Tresp V (1993) Classification with missing and uncertain inputs. In: Proceedings of the IEEE international conference on neural networks, San Francisco
[60] Moody J, Darken C (1988) Learning with localized receptive fields. In: Hinton G, Sejnowski T (eds) Proceedings of the 1988 Connectionist Models Summer School. Morgan-Kauffmann
[61] Nowlan S (1990) Maximum likelihood competitive learning. In: Advances in neural information processing systems 2. Morgan Kaufmann Publishers, pp 574-582
[62] Moody J, Darken C (1989) Fast learning in networks of locally-tuned processing units. Neural Comput 1:281-294 · doi:10.1162/neco.1989.1.2.281
[63] Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33:1065-1076 · Zbl 0116.11302 · doi:10.1214/aoms/1177704472
[64] Breiman L, Meisel W, Purcell E (1977) Variable kernel estimates of multivariate densities. Technometrics 19(2):135-144 · Zbl 0379.62023
[65] Hwang JN, Lay SR, Lippman A (1994) Nonparametric multivariate density estimation: a comparative study. IEEE Trans Signal Process 42(10):2795-2810 · doi:10.1109/78.324744
[66] Ahmad, S.; Cowan, JD (ed.); Tesauro, G. (ed.); Alspector, J. (ed.), Feature densities are required for computing feature correspondence, 961-968 (1994), San Mateo
[67] Fielding S, Fayers PM, McDonald A, McPherson G, Campbell MK (2008) Simple imputation methods were inadequate for missing not at random (MNAR) quality of life data. Health Qual Life Outcomes 6(57)
[68] Molenberghs G, Thijs H, Jansen I, Beunckens C, Kenward MG, Mallinckrodt C, Carroll RJ (2004) Analyzing incomplete longitudinal clinical trial data. Biostatistics 5(3):445-464 · Zbl 1154.62398 · doi:10.1093/biostatistics/kxh001
[69] Congdon P (2006) Bayesian statistical modelling, 2nd edn. Wiley, New York · Zbl 1193.62034 · doi:10.1002/9780470035948
[70] Collins LM, Schafer JL, Kam CM (2001) A comparison of inclusive and restrictive strategies in modern missing-data procedures. Psychol Methods 6:330-351 · doi:10.1037/1082-989X.6.4.330
[71] Heckman JJ (1976) The common structure of statistical models of truncation, sample selection and limited dependent variables and a simple estimator for such models. In: Annals of economic and social measurement, vol 5, number 4. National Bureau of Economic Research, Inc, pp 475-492
[72] Berndt ER, Hall BH, Hall RE, Hausman JA (1974) Estimation and inference in nonlinear structural models. Ann Econ Soc Meas 3:653-665
[73] Marlin B, Roweis S, Zemel R (2005) Unsupervised learning with non-ignorable missing data. In: Proceedings of the tenth international workshop on artificial intelligence and statistics (AISTATS), pp 222-229
[74] Little RJA (1993) Pattern-mixture models for multivariate incomplete data. J Am Stat Assoc 88:125-134 · Zbl 0775.62134
[75] Molenberghs G, Kenward M (2007) Missing data in clinical studies. Wiley, New York · doi:10.1002/9780470510445
[76] Vonesh EF, Greene T, Schluchter MD (2006) Shared parameter models for the joint analysis of longitudinal data and event times. Stat Med 25(1):143-163 · doi:10.1002/sim.2249
[77] Little RJ (2006) Selection and pattern-mixture models. CRC Press, London, pp 409-431
[78] Gad AM, Darwish NMM (2013) A shared parameter model for longitudinal data with missing values. Am J Appl Math Stat 1(2):30-35 · doi:10.12691/ajams-1-2-3
[79] Rubin DB (1987) Multiple imputation for nonresponse in surveys. Wiley, New York · Zbl 1070.62007 · doi:10.1002/9780470316696
[80] Harel O, Zhou XH (2007) Multiple imputation: review of theory, implementation and software. Stat Med 26:3057-3077 · doi:10.1002/sim.2787
[81] Kenward MG, Carpenter JC (2009) Multiple Imputation. CRC Press, London, pp 477-500
[82] Saltelli A, Chan K, Scott EM (2000) Sensitivity analysis. Wiley, New York · Zbl 0961.62091
[83] White IR, Royston P, Wood AM (2011) Multiple imputation using chained equations: issues and guidance for practice. Stat Med 30(4):377-399 · doi:10.1002/sim.4067
[84] Daniel Rhian M, Kenward Michael G (2012) A method for increasing the robustness of multiple imputation. Comput Stat Data Anal 56(6):1624-1643 · Zbl 1243.62073 · doi:10.1016/j.csda.2011.10.006
[85] Jansen I, Hens N, Molenberghs G, Aerts M, Verbeke G, Kenward MG (2006) The nature of sensitivity in monotone missing not at random models. Comput Stat Data Anal 50(3):830-858 · Zbl 1431.62497 · doi:10.1016/j.csda.2004.10.009
[86] Park J-S, Qian GQ, Jun Y (2008) Monte Carlo EM algorithm in logistic linear models involving non-ignorable missing data. Appl Math Comput 197(1):440-450 · Zbl 1135.65305 · doi:10.1016/j.amc.2007.07.080
[87] Stubbendick AL, Ibrahim JG (2003) Maximum likelihood methods for nonignorable missing responses and covariates in random effects models. Biometrics 59(4):1140-50 · Zbl 1274.62174 · doi:10.1111/j.0006-341X.2003.00131.x
[88] Jolani S (2012) Dual imputation strategies for analyzing incomplete data. Utrecht University, Utrecht
[89] Enders CK (2011) Missing not at random models for latent growth curve analyses. Psychol Methods 16(1):1-16 · doi:10.1037/a0022640
[90] Molenberghs G, Beunckens C, Sotto C, Kenward MG (2008) Every missingness not at random model has a missingness at random counterpart with equal fit. J R Stat Soc Ser B 70(Part 2):371-388 · Zbl 1148.62046 · doi:10.1111/j.1467-9868.2007.00640.x
[91] Vamplew P, Adams A (1992) Missing values in a backpropagation neural net. In: Leong S, Jabri M (eds) Proceedings of the third Australian conference on neural networks, Sidney, February 1992, pp 64-67
[92] Vamplew P, Clark D, Adams A, Muench J (1996) Techniques for dealing with missing values in feedforward networks. In: Proceedings of the seventh Australian conference on neural networks, Canberra, 10-12 April 1996
[93] Southcott ML, Bogner RE (1993) Classification of incomplete data using neural networks. In: Proceedings of the fourth Australian conference on neural networks, Melbourne, 3-5 February 1993, pp 220-223
[94] Hwang JN, Wang CJ (1994) Neural network inversion techniques for missing data applications. In: IEEE neural network workshop on signal processing, Ermioni, Greece, September 1994, pp 22-31
[95] Specht DF (1990) Probabilistic neural networks. Neural Netw 3(1):109-118 · doi:10.1016/0893-6080(90)90049-Q
[96] Vapnik V (1982) Estimation of dependences based on empirical data. Springer, Berlin · Zbl 0499.62005
[97] Buntine WL, Weigend AS (1991) Bayesian back-propagation. Complex Syst 5(6):603-643 · Zbl 0761.62031
[98] Arrowsmith DK, Place CM (1990) An introduction to dynamical systems. Cambridge University Press, Cambridge · Zbl 0702.58002
[99] Rabiner LR (1989) A tutorial on Hidden Markov Models and selected applications in speech recognition. Proc IEEE 77(2):267-296 · doi:10.1109/5.18626
[100] Jain LC, Medsker LR (1999) Recurrent neural networks: design and applications. CRC Press Inc, Boca Raton
[101] Jurafsky D, Martin JH (2009) Speech and language processing, 2nd edn. Prentice-Hall Inc, Upper Saddle River
[102] Trentin E, Gori M (2003) Robust combination of neural networks and hidden Markov models for speech recognition. IEEE Trans Neural Netw 14(6):1519-1531
[103] Bertolami R, Bunke H (2008) Hidden markov model-based ensemble methods for offline handwritten text line recognition. Pattern Recogn 41(11):3452-3460 · Zbl 1154.68478 · doi:10.1016/j.patcog.2008.04.003
[104] Baldi P, Brunak S (2001) Bioinformatics: the machine learning approach, 2nd edn. MIT Press, Cambridge · Zbl 0992.92024
[105] Hinton GE, Sejnowski TJ (1986) Learning and relearning in Boltzmann machines. In: Rumelhart DE, McClelland J (eds) Parallel distributed processing, vol 1, chapter 7. MIT Press
[106] Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. In: Proceedings of the National Academy of Sciences, vol 79, pp 2554-2558 · Zbl 1369.92007
[107] Hertz J, Krogh A, Palmer RG (1991) Introduction to the theory of neural computation. Addison-Wesley, Redwood City
[108] Almeida L (1987) A learning rule for asynchronous perceptrons with feedback in a combinatorial environment. In: Caudill M, Butler C (eds) Proceedings of the IEEE first international conference on neural networks, vol 2. IEEE, San Diego, pp 609-618
[109] Pineda F (1989) Recurrent backpropagation and the dynamical approach to adaptive neural computation. Neural Comput 1:161-172 · doi:10.1162/neco.1989.1.2.161
[110] Bengio, Y.; Gingras, F.; Touretzky, DS (ed.); Mozer, MC (ed.); Hasselmo, ME (ed.), Recurrent neural networks for missing or asynchronous data, 395-401 (1996), Cambridge
[111] Minsky ML, Papert SA (1969) Perceptrons. MIT Press, Cambridge · Zbl 0197.43702
[112] Rumelhart DE, Hinton GE, Williams RJ (1986) Learning internal representations by error propagation. In: Rumelhart DE, McClelland J (eds) Parallel distributed processing, vol 1, chapter 8. MIT Press, pp 318-362
[113] Globerson A, Roweis ST (2006) Nightmare at test time: robust learning by feature deletion. In: ICML ’06: Proceedings of the 23th international conference on machine learning, pp 353-360
[114] Dekel O, Shamir O (2008) Learning to classify with missing and corrupted features. In: ICML ’08: Proceedings of the 25th international conference on machine learning. ACM, New York, pp 216-223
[115] Ding Y, Simonoff JS (2010) An investigation of missing data methods for classification trees applied to binary response data. J Mach Learn Res 11:131-170 · Zbl 1242.62052
[116] Twala B (2009) An empirical comparison of techniques for handling incomplete data using decision trees. Appl Artif Intell 23:373-405 · doi:10.1080/08839510902872223
[117] Luengo J, García S, Herrera F (2010) A study on the use of imputation methods for experimentation with radial basis function network classifiers handling missing attribute values: The good synergy between RBFs and event covering method. Neural Netw 23:406-418 · doi:10.1016/j.neunet.2009.11.014
[118] Corani G, Zaffalon M (2008) Learning reliable classifiers from small or incomplete data sets: the naive credal classifier 2. J Mach Learn Res 9:581-621 · Zbl 1225.62082
[119] Chierichetti, F.; Kleinberg, J.; Liben-Nowell, D.; Shawe-Taylor, J. (ed.); Zemel, RS (ed.); Bartlett, P. (ed.); Pereira, FCN (ed.); Weinberger, KQ (ed.), Reconstructing patterns of information diffusion from incomplete observations, 792-800 (2011), Cambridge
[120] Greenwald, A.; Li, J.; Sodomka, E.; Bartlett, P. (ed.); Pereira, FCN (ed.); Burges, CJC (ed.); Bottou, L. (ed.); Weinberger, KQ (ed.), Approximating equilibria in sequential auctions with incomplete information and multi-unit demand, 2330-2338 (2012), Cambridge
[121] Ghannad-Rezaie M, Soltanian-Zadeh H, Ying H, Dong M (2010) Selection-fusion approach for classification of data sets with missing values. Pattern Recognit 43:2340-2350 · Zbl 1191.68573 · doi:10.1016/j.patcog.2009.12.003
[122] Farhangfar A, Kurgan L, Dy J (2008) Impact of imputation of missing values on classification error for discrete data. Pattern Recognit 41:3692-3705 · Zbl 1173.68479 · doi:10.1016/j.patcog.2008.05.019
[123] Saar-Tsechansky M, Provost F (2007) Handling missing values when applying classification models. J Mach Learn Res 8:1623-1657 · Zbl 1222.68295
[124] Troyanskaya O, Cantor M, Sherlock G, Brown P, Hastie T, Tibshirani R, Botstein D, Altman RB (2001) Missing value estimation methods for DNA microarrays. Bioinformatics 17(6):520-525 · doi:10.1093/bioinformatics/17.6.520
[125] Oba SA, Sato MA, Takemasa IC, Monden MC, Matsubara KI, Ishii SA (2003) A bayesian missing value estimation method for gene expression profile data. Bioinformatics 19(16):2088-2096 · doi:10.1093/bioinformatics/btg287
[126] Kim HA, Golub GHB, Park HA (2005) Missing value estimation for DNA microarray gene expression data: Local least squares imputation. Bioinformatics 21(2):187-198 · doi:10.1093/bioinformatics/bth499
[127] Scheel IA, Aldrin MB, Glad IKA, Sorum RA, Lyng HC, Frigessi AB (2005) The influence of missing value imputation on detection of differentially expressed genes from microarray data. Bioinformatics 21(23):4272-4279 · doi:10.1093/bioinformatics/bti708
[128] Wang X, Jiang Z, Feng H (2006) Missing value estimation for DNA microarray gene expression data by support vector regression imputation and orthogonal coding scheme. BMC Bioinform 7(32):1-10 · Zbl 1085.92050
[129] Wong DSV, Wong FK, Wood GR (2007) A multi-stage approach to clustering and imputation of gene expression profiles. Bioinformatics 23(8):998-1005 · doi:10.1093/bioinformatics/btm053
[130] Yoon D, Lee EK, Park T (2007) Robust imputation method for missing values in microarray data. BMC Bioinform 8(2):1-7
[131] Roure B, Baurain D, Philippe H (2013) Impact of missing data on phylogenies inferred from empirical phylogenomic data sets. Mol Biol Evol 30(1):197-214 · doi:10.1093/molbev/mss208
[132] Nutt W, Razniewski S, Vegliach G (2012) Incomplete databases: missing records and missing values. In: Proceedings of the 17th international conference on database systems for advanced applications, DASFAA’12. Springer, pp 298-310
[133] Kaambwa B, Bryan S, Billingham L (2012) Do the methods used to analyse missing data really matter? An examination of data from an observational study of Intermediate Care patients. BMC Res Notes 5(1):330 · doi:10.1186/1756-0500-5-330
[134] David M, Little RJA, Samuhel ME, Triest RK (1986) Alternative methods for CPS income imputation. J Am Stat Assoc 81(393):29-41 · doi:10.1080/01621459.1986.10478235
[135] Foster EM, Fang GY (2004) Alternative methods for handling attrition: an illustration using data from the fast track evaluation. Eval Rev 28(5):434-464 · doi:10.1177/0193841X04264662
[136] Horton NJ, Kleinman KP (2007) Much ado about nothing: a comparison of missing data methods and software to fit incomplete data regression models. Am Stat 61(1):79-90 · doi:10.1198/000313007X172556
[137] Dong Y, Peng C-YJ (2013) Principled missing data methods for researchers. Springerplus 2(1):222 · doi:10.1186/2193-1801-2-222
[138] Ali AMG, Dawson SJ, Blows FM, Provenzano E, Ellis IO, Baglietto L, Huntsman D, Caldas C, Pharoah PD (2011) Comparison of methods for handling missing data on immunohistochemical markers in survival analysis of breast cancer. Br J Cancer 104(4):693-699 · doi:10.1038/sj.bjc.6606078
[139] Fielding S, Fayers P, Ramsay C (2010) Predicting missing quality of life data that were later recovered: an empirical comparison of approaches. Clin Trials 7(4):333-342 · doi:10.1177/1740774510374626
[140] Marshall A, Altman D, Royston P, Holder R (2010) Comparison of techniques for handling missing covariate data within prognostic modelling studies: a simulation study. BMC Med Res Methodol 10(1):7 · Zbl 1187.51015 · doi:10.1186/1471-2288-10-7
[141] Hedden S, Woolson R, Malcolm R (2008) A comparison of missing data methods for hypothesis tests of the treatment effect in substance abuse clinical trials: a Monte-Carlo simulation study. Subst Abuse Treatm Prev Policy 3(1):1-9 · doi:10.1186/1747-597X-3-1
[142] Ding Y, Simonoff JS (2010) An investigation of missing data methods for classification trees applied to binary response data. J Mach Learn Res 11:131-170 · Zbl 1242.62052
[143] Roda C, Nicolis I, Momas I, Guihenneuc-Jouyaux C (2013) Comparing methods for handling missing data. Epidemiology 24(3):469-471 · doi:10.1097/EDE.0b013e31828c4a44
[144] Graham JW (2009) Missing data analysis: making it work in the real world. Annu Rev Psychol 60:549-576 · doi:10.1146/annurev.psych.58.110405.085530
[145] Schwartz T, Zeig-Owens R (2013) Knowledge (of your missing data) is power: handling missing values in your SAS dataset. In: Proceedings of SAS global forum SUGI 31: statistics, data analysis and data mining, San Francisco, California, 28 April-1 May 2013
[146] Templ M, Alfons A, Filzmoser P (2012) Exploring incomplete data using visualization techniques. Adv Data Anal Classif 6(1):29-47 · doi:10.1007/s11634-011-0102-y
[147] Heitjan DF (2011) Incomplete data: what you don’t know might hurt you. Cancer Epidemiol Biomark Prev 20(8):1567-1570 · doi:10.1158/1055-9965.EPI-11-0505
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