Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they have undesirable scaling behavior in the high-dimensional setting. Hover, many high-dimensional signals encountered in practice frequently possess latent low-dimensional structure. Motivated by this observation,  propose a technique for high-dimensional change-point estimation that combines the filtered derivative approach from previous work with convex optimization methods based on atomic norm regularization, which are useful for exploiting structure in high-dimensional data. Our algorithm is applicable in online settings as it operates on small portions of the sequence of observations at a time, and it is ll-suited to the high-dimensional setting both in terms of computational scalability and of statistical efficiency. The main result of this paper shows that our method performs change-point estimation reliably as long as the product of the smallest-sized change (the Euclidean-norm-squared of the difference beten signals at a change-point) and the smallest distance beten change-points (number of time instances) is larger than a Gaussian width parameter that characterizes the low-dimensional complexity of the underlying signal sequence.
['Yong Sheng Soh', 'Venkat Chandrasekaran']
I am writing a research paper on a idea High-dimensional change-point estimation: Combining filtering with convex optimization
[{"from": "human", "value": "I am writing a research paper on a idea High-dimensional change-point estimation: Combining filtering with convex optimization"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider change-point estimation in a sequence of high-dimensional signals given noisy observations. Classical approaches to this problem such as the filtered derivative method are useful for sequences of scalar-valued signals, but they have undesirable scaling behavior in the high-dimensional setting. Hover, many high-dimensional signals encountered in practice frequently possess latent low-dimensional structure. Motivated by this observation,  propose a technique for high-dimensional change-point estimation that combines the filtered derivative approach from previous work with convex optimization methods based on atomic norm regularization, which are useful for exploiting structure in high-dimensional data. Our algorithm is applicable in online settings as it operates on small portions of the sequence of observations at a time, and it is ll-suited to the high-dimensional setting both in terms of computational scalability and of statistical efficiency. The main result of this paper shows that our method performs change-point estimation reliably as long as the product of the smallest-sized change (the Euclidean-norm-squared of the difference beten signals at a change-point) and the smallest distance beten change-points (number of time instances) is larger than a Gaussian width parameter that characterizes the low-dimensional complexity of the underlying signal sequence."}]