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This paper deals with detecting change of distribution in multi-dimensional data sets. For a given baseline data set and a set of newly observed data points, we define a statistical test called the density test for deciding if the observed data points are sampled from the underlying distribution that produced the baseline data set. We define a test statistic that is strictly distribution-free under the null hypothesis. Our experimental results show that the density test has substantially more power than the two existing methods for multi-dimensional change detection.