arXiv subjects

Carlos E. Rodríguez

Publications and source records attributed to Carlos E. Rodríguez.

3 recordsLinked to original sources

arXiv2026

Exact two-stage finite-mixture representations for species sampling processes

Discrete random probability measures are central to Bayesian inference, particularly as priors for mixture modeling and clustering. A broad and unifying class is that of proper species sampling processes (SSPs), encompassing many Bayesian nonparametric priors. We show that any proper SSP admits an exact two-stage finite-mixture representation built from a latent truncation index and a simple reweighting of the atoms. For each realized truncation index, the representation has finitely many atoms, and averaging over the induced law of that index recovers the original SSP setwise. This yields at least two consequences: (i) an exact two-stage finite construction for arbitrary SSPs, without user-chosen truncation levels; and (ii) posterior inference in SSP mixture models via standard finite-mixture machinery, leading to tractable MCMC algorithms without ad hoc truncations. We explore these consequences by deriving explicit total-variation bounds for the approximation error when the truncation level is fixed, and by studying practical performance in mixture modeling, with emphasis on Dirichlet and geometric SSPs.

stat.ME↗

arXiv2025

Weighted Support Points from Random Measures: An Interpretable Alternative for Generative Modeling

Support points summarize a large dataset through a smaller set of representative points that can be used for data operations, such as Monte Carlo integration, without requiring access to the full dataset. In this sense, support points offer a compact yet informative representation of the original data. We build on this idea to introduce a generative modeling framework based on random weighted support points, where the randomness arises from a weighting scheme inspired by the Dirichlet process and the Bayesian bootstrap. The proposed method generates diverse and interpretable sample sets from a fixed dataset, without relying on probabilistic modeling assumptions or neural network architectures. We present the theoretical formulation of the method and develop an efficient optimization algorithm based on the Convex--Concave Procedure (CCP). Empirical results on the MNIST and CelebA-HQ datasets show that our approach produces high-quality and diverse outputs at a fraction of the computational cost of black-box alternatives such as Generative Adversarial Networks (GANs) or Denoising Diffusion Probabilistic Models (DDPMs). These results suggest that random weighted support points offer a principled, scalable, and interpretable alternative for generative modeling. A key feature is their ability to produce genuinely interpolative samples that preserve underlying data structure.

stat.ML↗

arXiv2021

COVID-19 Clinical footprint to infer about mortality

Information of 1.6 million patients identified as SARS-CoV-2 positive in Mexico is used to understand the relationship between comorbidities, symptoms, hospitalizations and deaths due to the COVID-19 disease. Using the presence or absence of these latter variables a clinical footprint for each patient is created. The risk, expected mortality and the prediction of death outcomes, among other relevant quantities, are obtained and analyzed by means of a multivariate Bernoulli distribution. The proposal considers all possible footprint combinations resulting in a robust model suitable for Bayesian inference.

stat.AP↗