# Reparametrization Invariant Statistical Inference and Gravity

@article{Periwal1997ReparametrizationIS, title={Reparametrization Invariant Statistical Inference and Gravity}, author={Vipul Periwal}, journal={Physical Review Letters}, year={1997}, volume={78}, pages={4671-4674} }

Bialek, Callan and Strong have recently given a solution of the problem of determining a continuous probability distribution from a finite set of experimental measurements by formulating it as a one-dimensional quantum field theory. This letter gives a reparametrization-invariant solution of the problem, obtained by coupling to gravity. The case of a large number of dimensions may involve quantum gravity restricted to metrics of vanishing Weyl curvature.

## 11 Citations

### Recognition and geometrical on-line learning algorithm of probability distributions

- Computer ScienceProceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium
- 2000

An online learning algorithm for probability distributions is constructed in a reparameterization invariant form and can be optimal, since conformal gauge reduces the problem to a noncovariant case.

### Information theory and learning: a physical approach

- Computer ScienceArXiv
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It is proved that predictive information provides the unique measure for the complexity of dynamics underlying the time series and there are classes of models characterized by {\em power-law growth of the predictive information} that are qualitatively more complex than any of the systems that have been investigated before.

### Predictability, Complexity, and Learning

- Computer ScienceNeural Computation
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It is argued that the divergent part of Ipred(T) provides the unique measure for the complexity of dynamics underlying a time series.

### Predictability , Complexity , and Learning

- Computer Science
- 2002

It is argued that the divergent part of Ipred(T), the mutual information between the past and the future of a time series, provides the unique measure for the complexity of dynamics underlying aTime series.

### Self‐consistent method for density estimation

- Computer Science, Mathematics
- 2009

The self‐consistent estimate is defined as a prior candidate density that precisely reproduces itself and is applied to artificial data generated from various distributions and reaches the theoretical limit for the scaling of the square error with the size of the data set.

### ec 2 01 0 Self-consistent method for density estimation

- Computer Science, Mathematics
- 2013

The self-consistent estimate is defined as a prior candidate density that precisely reproduces itself and is applied to artificial data generated from various distributions and reaches the theoretical limit for the scaling of the square error with the dataset size.

### Thinking About The Brain

- Psychology
- 2002

A central theme in this work is the matching of the coding and computational strategies of the brain to the statistical structure of the world around us, and extension of these principles to the problem of learning leads to interesting theoretical questions about how to measure the complexity of the data from which the authors learn.

### Can Gaussian Process Regression Be Made Robust Against Model Mismatch?

- Computer ScienceDeterministic and Statistical Methods in Machine Learning
- 2004

In lower-dimensional learning scenarios, the theory predicts—in excellent qualitative and good quantitative accord with simulations—that evidence maximization eliminates logarithmically slow learning and recovers the optimal scaling of the decrease of generalization error with training set size.

## References

SHOWING 1-5 OF 5 REFERENCES

### Pattern theory: a unifying perspective

- Art
- 1996

The term “Pattern Theory” was introduced by Ulf Grenander in the 70s as a name for a field of applied mathematics which gave a theoretical setting for a large number of related ideas, techniques and…

### Phys

- Rev. Lett. 77
- 1996

### Bayes or Bust?-A Critical Examination of Bayesian Confirmation Theory.

- Philosophy
- 1994

Bayes' Bayesianism the machinery of modern Bayesianism success stories challenges met the problem of old evidence the rationality and objectivity of scientific inference a plea for eliminative…

### explained to me the biophysical applications in pattern recognition which motivated the investigation in Ref

- First European Congress of Mathematicians,
- 1992