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In speech recognition research, transformation-based adaptation algorithms provide an effective way of adapting acoustic models to improve the recognition accuracy. However, when only limited amounts of adaptation data are available, the transformation is often poorly estimated, which may cause performance degradation. This paper presents the Markov Random Field Linear Regression (MRFLR) algorithm, which constrains the transformation-based adaptation by the correlations among acoustic parameters. The Markov Random Field theory is used to model the correlations. The correlations are estimated from the training corpus and hypothesized as prior knowledge of acoustic models. By explicitly incorporating them into adaptation, robust and fast adaptation can be achieved. The hypothesis is tested by comparing MRFLR with MLLR (Maximum Likelihood Linear Regression), a widely used transformation-based adaptation algorithm. Experimental results show that MRFLR outperforms MLLR when adaptation data are sparse, and converges to the MLLR performance when more adaptation data are available.