Empirical non-parametric estimation of the Fisher Information

Alfred O. Hero; Visar Berisha

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Empirical non-parametric estimation of the Fisher Information

Visar Berisha, Alfred O. Hero

Computation · Submitted 6 Aug 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Thus we obtain an empirical estimator of the FIM that does not require density estimation and is asymptotically consistent.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.05 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.30 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM require estimating the probability distribution function (PDF), or its parameters, along with its gradient or Hessian. However, in many practical situations the PDF of the data is not known but the statistician has access to an observation sample for any parameter value. Here we propose a method of estimating the FIM directly from sampled data that does not require knowledge of the underlying PDF. The method is based on non-parametric estimation of an $f$-divergence over a local neighborhood of the parameter space and a relation between curvature of the $f$-divergence and the FIM. Thus we obtain an empirical estimator of the FIM that does not require density estimation and is asymptotically consistent. We empirically evaluate the validity of our approach using two experiments.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The Fisher information matrix (FIM) is a foundational concept in statistical signal processing.	background 1.00	0.04	0.02	asserted 1.00
s1	The FIM depends on the probability distribution, assumed to belong to a smooth parametric family.	background 1.00	0.04	0.02	asserted 1.00
s2	Traditional approaches to estimating the FIM require estimating the probability distribution function (PDF), or its parameters, along with its gradient or Hessian.	background 0.97	0.05	0.02	asserted 1.00
s3	However, in many practical situations the PDF of the data is not known but the statistician has access to an observation sample for any parameter value.	gap 0.69	0.08	0.03	asserted 0.85
s4	Here we propose a method of estimating the FIM directly from sampled data that does not require knowledge of the underlying PDF.	contribution 1.00	0.89	0.56	asserted 0.99
s5	The method is based on non-parametric estimation of an $f$-divergence over a local neighborhood of the parameter space and a relation between curvature of the $f$-divergence and the FIM.	method 0.98	0.83	0.18	asserted 1.00
s6	Thus we obtain an empirical estimator of the FIM that does not require density estimation and is asymptotically consistent.	result 0.50	0.92	0.71	asserted 1.00
s7	We empirically evaluate the validity of our approach using two experiments.	method 0.49	0.95	0.06	asserted 0.92

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.51.

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Original abstract

The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM require estimating the probability distribution function (PDF), or its parameters, along with its gradient or Hessian. However, in many practical situations the PDF of the data is not known but the statistician has access to an observation sample for any parameter value. Here we propose a method of estimating the FIM directly from sampled data that does not require knowledge of the underlying PDF. The method is based on non-parametric estimation of an $f$-divergence over a local neighborhood of the parameter space and a relation between curvature of the $f$-divergence and the FIM. Thus we obtain an empirical estimator of the FIM that does not require density estimation and is asymptotically consistent. We empirically evaluate the validity of our approach using two experiments.

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