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Carlos C. Rodriguez

Publications and source records attributed to Carlos C. Rodriguez.

9 recordsLinked to original sources
arXiv2026

Robust Sequential Tracking via Bounded Information Geometry and Non-Parametric Field Actions

Standard sequential inference architectures are compromised by a normalizability crisis when confronted with extreme, structured outliers. By operating on unbounded parameter spaces, state-of-the-art estimators lack the intrinsic geometry required to appropriately sever anomalies, resulting in unbounded covariance inflation and mean divergence. This paper resolves this structural failure by analyzing the abstraction sequence of inference at the meta-prior level (S_2). We demonstrate that extremizing the action over an infinite-dimensional space requires a non-parametric field anchored by a pre-prior, as a uniform volume element mathematically does not exist. By utilizing strictly invariant Delta (or \nu) Information Separations on the statistical manifold, we physically truncate the infinite tails of the spatial distribution. When evaluated as a Radon-Nikodym derivative against the base measure, the active parameter space compresses into a strictly finite, normalizable probability droplet. Empirical benchmarks across three domains--LiDAR maneuvering target tracking, high-frequency cryptocurrency order flow, and quantum state tomography--demonstrate that this bounded information geometry analytically truncates outliers, ensuring robust estimation without relying on infinite-tailed distributional assumptions.

stat.ML↗
arXiv2026

Quantization of Ricci Curvature in Information Geometry

In 2004, while studying the information geometry of binary Bayesian networks (bitnets), the author conjectured that the volume-averaged Ricci scalar computed with respect to the Fisher information metric is universally quantized to positive half-integers: in (1/2)Z. This paper resolves the conjecture after 20 years. We prove it for tree-structured and complete-graph bitnets via a universal Beta function cancellation mechanism, and disprove it in general by exhibiting explicit loop counterexamples. We extend the program to Gaussian DAG networks, where a sign dichotomy holds: discrete bitnets have positive curvature, while Gaussian networks form solvable Lie groups with negative curvature.

cs.IT↗
arXiv2007

Wrong Priors

All priors are not created equal. There are right and there are wrong priors. That is the main conclusion of this contribution. I use, a cooked-up example designed to create drama, and a typical textbook example to show the pervasiveness of wrong priors in standard statistical practice.

physics.data-an↗
arXiv2002

Entropic Priors for Discrete Probabilistic Networks and for Mixtures of Gaussians Models

The ongoing unprecedented exponential explosion of available computing power, has radically transformed the methods of statistical inference. What used to be a small minority of statisticians advocating for the use of priors and a strict adherence to bayes theorem, it is now becoming the norm across disciplines. The evolutionary direction is now clear. The trend is towards more realistic, flexible and complex likelihoods characterized by an ever increasing number of parameters. This makes the old question of: What should the prior be? to acquire a new central importance in the modern bayesian theory of inference. Entropic priors provide one answer to the problem of prior selection. The general definition of an entropic prior has existed since 1988, but it was not until 1998 that it was found that they provide a new notion of complete ignorance. This paper re-introduces the family of entropic priors as minimizers of mutual information between the data and the parameters, as in [rodriguez98b], but with a small change and a correction. The general formalism is then applied to two large classes of models: Discrete probabilistic networks and univariate finite mixtures of gaussians. It is also shown how to perform inference by efficiently sampling the corresponding posterior distributions.

physics.data-an↗
arXiv2000

Optimal Recovery of Local Truth

Probability mass curves the data space with horizons. Let f be a multivariate probability density function with continuous second order partial derivatives. Consider the problem of estimating the true value of f(z) > 0 at a single point z, from n independent observations. It is shown that, the fastest possible estimators (like the k-nearest neighbor and kernel) have minimum asymptotic mean square errors when the space of observations is thought as conformally curved. The optimal metric is shown to be generated by the Hessian of f in the regions where the Hessian is definite. Thus, the peaks and valleys of f are surrounded by singular horizons when the Hessian changes signature from Riemannian to pseudo-Riemannian. Adaptive estimators based on the optimal variable metric show considerable theoretical and practical improvements over traditional methods. The formulas simplify dramatically when the dimension of the data space is 4. The similarities with General Relativity are striking but possibly illusory at this point. However, these results suggest that nonparametric density estimation may have something new to say about current physical theory.

physics.data-an↗
arXiv1998

Are We Cruising a Hypothesis Space?

This paper is about Information Geometry, a relatively new subject within mathematical statistics that attempts to study the problem of inference by using tools from modern differential geometry. This paper provides an overview of some of the achievements and possible future applications of this subject to physics.

physics.data-an↗
arXiv1997

Cross Validated Non parametric Bayesianism by Markov Chain Monte Carlo

Completely automatic and adaptive non-parametric inference is a pie in the sky. The frequentist approach, best exemplified by the kernel estimators, has excellent asymptotic characteristics but it is very sensitive to the choice of smoothness parameters. On the other hand the Bayesian approach, best exemplified by the mixture of gaussians models, is optimal given the observed data but it is very sensitive to the choice of prior. In 1984 the author proposed to use the Cross-Validated gaussian kernel as the likelihood for the smoothness scale parameter h, and obtained a closed formula for the posterior mean of h based on Jeffreys's rule as the prior. The practical operational characteristics of this bayes' rule for the smoothness parameter remained unknown for all these years due to the combinatorial complexity of the formula. It is shown in this paper that a version of the metropolis algorithm can be used to approximate the value of h producing remarkably good completely automatic and adaptive kernel estimators. A close study of the form of the cross validated likelihood suggests a modification and a new approach to Bayesian Non-parametrics in general.

physics.data-an↗
arXiv1995

Confidence Intervals from One One Observation

Robert Machol's surprising result, that from a single observation it is possible to have finite length confidence intervals for the parameters of location-scale models, is re-produced and extended. Two previously unpublished modifications are included. First, Herbert Robbins nonparametric confidence interval is obtained. Second, I introduce a technique for obtaining confidence intervals for the scale parameter of finite length in the logarithmic metric. Keywords: Theory/Foundations , Estimation, Prior Distributions, Non-parametrics & Semi-parametrics Geometry of Inference, Confidence Intervals, Location-Scale models

bayes-an↗