A Proof of the Fisher Information Inequality via a Data Processing Argument

By Ram Zamir. 1998

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Citations in the corpus

Learning Distributions from their Samples under Communication Constraints (2019, methodology): “The upper bound Tr ( I M ( θ )) ≤ Tr ( I X ( θ )) follows easily from the data processing inequality for Fisher information [11].”
Bounding Training Data Reconstruction in Private (Deep) Learning (2022, background): “…model h ← A ( D train ) is a deterministic function of only the initial parameters w 0 and the observed gradients ¯ g 1 , . . . any , ¯ g T without other access to z , hence by the post-processing inequality for Fisher information (Zamir, 1998), we get I h ( z ) I w 0 , ¯ g 1 ,..., ¯ g T ( z ) .”
Lower Bounds for Learning Distributions under Communication Constraints via Fisher Information (2019, methodology): “To finish the proof of Theorem 1, note that the upper bound Tr(IM (θ)) ≤ Tr(IX(θ)) follows easily from the data processing inequality for Fisher information Zamir (1998).”
Ridge regression and asymptotic minimax estimation over spheres of growing dimension (2016, background): “Lemma B.5 (Stam’s inequality; this version due to Zamir [53]).”
An Extremal Inequality Motivated by Multiterminal Information-Theoretic Problems (2007, methodology): “An interesting estimation-theoretic proof using the data processing inequality for Fisher information was given by Zamir [11].”
Subdiffraction incoherent optical imaging via spatial-mode demultiplexing (2016, background): “[42] Ram Zamir, “A proof of the Fisher information inequality via a data processing argument,” IEEE Transactions on Information Theory 44, 1246–1250 (1998).”
Minimax Bounds for Distributed Logistic Regression (2019, background): “The first term in the max term of each lemma is a simple consequence of the data processing inequality for Fisher information (Zamir, 1998), so we will focus on the other terms.”
An Extremal Inequality Motivated by Multiterminal Information Theoretic Problems (2006, background): “An interesting estimation theoretic proof of FII was given by Zamir [13].”