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We consider the problem of detecting a change in mean in a sequence ofGaussian vectors. Under the alternative hypothesis, the change occurs only insome subset of the components of the vector. We propose a test of the presenceof a change-point that is adaptive to the number of changing components. Underthe assumption that the vector dimension tends to infinity and the length ofthe sequence grows slower than the dimension of the signal, we obtain thedetection boundary for this problem and prove its rate-optimality.

High-dimensional change-point detection with sparse alternatives