11 papers
Partial Differential Equation Barriers to Identifiability in Infinite Mixture Models
Dung Le, Nicola Bariletto, Alessandro Rinaldo +1
We study identifiability of mixing measures in infinite mixture models. We show that, in many common cases, lack of identifiability can be characterized in terms of certain differe…
On the geometry of weak convergence without total variation convergence
Nicola Bariletto, Stephen G. Walker
We study some geometric consequences of the discrepancy between weak and total variation convergence of probability measures. We consider a sequence of probability measures on $\ma…
Convergence Rates for Latent Mixing Measures in Infinite Homoscedastic Location-Scale Mixture Models
Nicola Bariletto, Dung Le, Alessandro Rinaldo +1
We study posterior contraction rates for mixing measures in homoscedastic location-scale mixture models with infinitely many components. While posterior convergence at the level of…
On Bayesian Softmax-Gated Mixture-of-Experts Models
Nicola Bariletto, Huy Nguyen, Nhat Ho +1
Mixture-of-experts models provide a flexible framework for learning complex probabilistic input-output relationships by combining multiple expert models through an input-dependent…
Scalable Posterior Uncertainty for Flexible Density-Based Clustering
Nicola Bariletto, Stephen G. Walker
Density-based clustering is a well-established framework that defines clusters through topological or geometric features of the data-generating density, yielding flexible procedure…
Conformalized Bayesian Inference, with Applications to Random Partition Models
Nicola Bariletto, Nhat Ho, Alessandro Rinaldo
Bayesian posterior distributions naturally represent parameter uncertainty informed by data. However, when the parameter space is complex, as in many nonparametric settings where i…
On A Necessary Condition For Posterior Inconsistency: New Insights From A Classic Counterexample
Nicola Bariletto, Stephen G. Walker
The consistency of posterior distributions in density estimation is at the core of Bayesian statistical theory. Classical work established sufficient conditions, typically combinin…
Posterior Consistency in Parametric Models via a Tighter Notion of Identifiability
Nicola Bariletto, Bernardo Flores, Stephen G. Walker
We study Bayesian posterior consistency in parametric density models with proper priors, challenging the perception that the problem is settled. Classical results established consi…
Data-Driven DRO and Economic Decision Theory: An Analytical Synthesis With Bayesian Nonparametric Advancements
Nicola Bariletto, Khai Nguyen, Nhat Ho
We develop an analytical synthesis that bridges data-driven Distributionally Robust Optimization (DRO) and Economic Decision Theory under Ambiguity (DTA). By reinterpreting standar…
Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimization
Nicola Bariletto, Nhat Ho
Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distributio…
Quasi-Monte Carlo for 3D Sliced Wasserstein
Khai Nguyen, Nicola Bariletto, Nhat Ho
Monte Carlo (MC) integration has been employed as the standard approximation method for the Sliced Wasserstein (SW) distance, whose analytical expression involves an intractable ex…