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Genetic alterations, such as chromosomal gains and losses, are key causes of tumorigenesis. Comparative Genomic Hybridization (CGH) is a molecular method for detecting such DNA copy number alterations in tumor cells. Recent observations have reported that in many tumors, the mRNA transcript changes measured by gene expression profiling (GEP) are correlated with corresponding DNA copy number alterations, supporting the possibility of predicting DNA copy number alterations from GEP data. In this paper, contrary to the traditional use of GEP, we present a new analytical approach utilizing GEP data for predicting DNA copy number alterations. The proposed approach is built on a hidden Markov model and trained in the light of paired GEP and CGH data on a sufficient number of tumor cases of the same tumor type. Then it can be applied to new cases of that tumor type to predict the CGH profiles from their GEP profiles.