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An adaptation algorithm using the theoretically optimal maximum a posteriori (MAP) formulation, and at the same time accounting for parameter correlation between different classes is desirable, especially when using sparse adaptation data. However, a direct implementation of such an approach may be prohibitive in many practical situations. We present an algorithm that approximates the above mentioned correlated MAP algorithm by iteratively maximizing the set of posterior marginals. With some simplifying assumptions, expressions for these marginals are then derived, using the principle of minimum cross-entropy. The resulting algorithm is simple, and includes conventional MAP estimation as a special case. The utility of the proposed method is tested in adaptation experiments for an alphabet recognition task.