Matrix Mean Confidence Sequence
A generalization of confidence sequences from scalar random variables to the means of matrix-valued random variables. It requires handling concentration inequalities under matrix norms and ensuring validity at arbitrary stopping times, with application prospects in quantum information and high-dimensional statistics.
Timeline (last 90 days)
The paper proposes a new algorithm for constructing confidence sequences for the mean of matrix-valued random variables, which can dynamically give confidence intervals for the matrix mean without relying on a fixed sample size.
In numerical experiments, the confidence sequence width given by the new matrix mean confidence sequence algorithm is comparable to that of methods specifically designed for matrix concentration inequalities, but it is more computationally efficient.
The paper points out that the construction of the matrix mean confidence sequence depends on a specific matrix norm, and whether it can be generalized to more general norms is worth exploring.
All Facts (3)
The paper proposes a new algorithm for constructing confidence sequences for the mean of matrix-valued random variables, which can dynamically give confidence intervals for the matrix mean without relying on a fixed sample size.
50%UnverifiedIn numerical experiments, the confidence sequence width given by the new matrix mean confidence sequence algorithm is comparable to that of methods specifically designed for matrix concentration inequalities, but it is more computationally efficient.
50%UnverifiedThe paper points out that the construction of the matrix mean confidence sequence depends on a specific matrix norm, and whether it can be generalized to more general norms is worth exploring.
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