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Abstract:
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The talk will summarize some recent results in multiple change-point detection. In the first part of the talk, we introduce the concept of 'tail-greediness' and discuss a new tail-greedy, bottom-up transform for one-dimensional data, which results in a nonlinear but conditionally orthonormal, multiscale decomposition of the data with respect to an adaptively chosen Unbalanced Haar wavelet basis. The resulting agglomerative change-point detection method avoids the disadvantages of the classical divisive binary segmentation, and offers very good practical performance.
In the second part, we discuss a new, generic methodology for nonparametric function estimation, in which we first estimate the number and locations of any features that may be present in the function. The method is general in character due to the use of a new multiple generalised change-point detection device, termed Narrowest-Over-Threshold (NOT). The key ingredient of NOT is its focus on the smallest local sections of the data on which the existence of a feature is suspected. The NOT estimators are easy to implement and rapid to compute. The NOT approach is easy to extend by the user to tailor to their own needs.
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