arXiv subjects

Bernardo Flores

Publications and source records attributed to Bernardo Flores.

5 recordsLinked to original sources

arXiv2026

Newton's Algorithm as a Gradient Flow: A Geometric Framework for Recursive Mixture Estimation

Bayesian nonparametric mixture models provide a flexible framework for data analysis but are often hindered by the computational expense of traditional inference methods like MCMC. A fast, recursive algorithm proposed by Newton (2002) offers a practical alternative, yet its formal connection to Bayesian inference and its theoretical properties remain only partially understood. This paper reveals a new geometric interpretation of this class of predictive recursions. We demonstrate that Newton's recursion is a discrete-time approximation of a gradient flow on the space of probability measures governed by the Fisher-Rao geometry, providing the first rigorous dynamical characterisation of this family of estimators. This geometric perspective provides a principled theoretical foundation for studying these recursions: it clarifies their convergence behaviour, situates them within the variational Bayes literature, and yields a systematic basis for generalisation by modifying the underlying geometry and discretisation. In contrast to approaches that construct gradient flows from a prescribed variational objective, this work proceeds in the reverse direction: beginning from an existing recursive estimator and uncovering the variational problem it implicitly solves, it opens a pathway for the systematic analysis and extension of a broad class of sequential Bayesian estimators.

stat.ME↗

arXiv2025

A Dependent Feature Allocation Model Based on Random Fields

We introduce a flexible framework for modeling dependent feature allocations. Our approach addresses limitations in traditional nonparametric methods by directly modeling the logit-probability surface of the feature paintbox, enabling the explicit incorporation of covariates and complex but tractable dependence structures. The core of our model is a Gaussian Markov Random Field (GMRF), which we use to robustly decompose the latent field, separating a structural component based on the baseline covariates from intrinsic, unstructured heterogeneity. This structure is not a rigid grid but a sparse k-nearest neighbors graph derived from the latent geometry in the data, ensuring high-dimensional tractability. We extend this framework to a dynamic spatio-temporal process, allowing item effects to evolve via an Ornstein-Uhlenbeck process. Feature correlations are captured using a low-rank factorization of their joint prior. We demonstrate our model's utility by applying it to a polypharmacy dataset, successfully inferring latent health conditions from patient drug profiles.

stat.ME↗

arXiv2025

Posterior Consistency in Parametric Models via a Tighter Notion of Identifiability

We study Bayesian posterior consistency in parametric density models with proper priors, challenging the perception that the problem is settled. Classical results established consistency via MLE convergence under regularity and identifiability assumptions, with the latter taken for granted and rarely examined. We refocus attention on identifiability, showing that inconsistency arises only when the true distribution coincides with a weak limit of model densities in a way that violates identifiability. While such failures occur naturally in nonparametric settings, they are implausible and effectively self-inflicted in parametric models. Our analysis shows that classical regularity conditions are unnecessary: a mild strengthening of identifiability suffices to ensure consistency in parametric models, even when the MLE is inconsistent. We also demonstrate that parametric inconsistency requires carefully engineered, oscillatory model features aligned with the true distribution, which is unlikely to occur without adversarial design. Our findings also clarify the distinct mechanisms behind Bayesian and frequentist inconsistency and advocate for separate theoretical treatments.

math.ST↗

arXiv2025

Predictive Coresets

Modern data analysis often involves massive datasets with hundreds of thousands of observations, making traditional inference algorithms computationally prohibitive. Coresets are selection methods designed to choose a smaller subset of observations while maintaining similar learning performance. Conventional coreset approaches determine these weights by minimizing the Kullback-Leibler (KL) divergence between the likelihood functions of the full and weighted datasets; as a result, this makes them ill-posed for nonparametric models, where the likelihood is often intractable. We propose an alternative variational method which employs randomized posteriors and finds weights to match the unknown posterior predictive distributions conditioned on the full and reduced datasets. Our approach provides a general algorithm based on predictive recursions suitable for nonparametric priors. We evaluate the performance of the proposed coreset construction on diverse problems, including random partitions and density estimation.

stat.CO↗

arXiv2024

Clustering and Meta-Analysis Using a Mixture of Dependent Linear Tail-Free Priors

We propose a novel nonparametric Bayesian approach for meta-analysis with event time outcomes. The model is an extension of linear dependent tail-free processes. The extension includes a modification to facilitate (conditionally) conjugate posterior updating and a hierarchical extension with a random partition of studies. The partition is formalized as a Dirichlet process mixture. The model development is motivated by a meta-analysis of cancer immunotherapy studies. The aim is to validate the use of relevant biomarkers in the design of immunotherapy studies. The hypothesis is about immunotherapy in general, rather than about a specific tumor type, therapy and marker. This broad hypothesis leads to a very diverse set of studies being included in the analysis and gives rise to substantial heterogeneity across studies

stat.ME↗