Searcharxiv⌕ Search

arXiv subjects

Juan Felipe Carmona

Publications and source records attributed to Juan Felipe Carmona.

4 recordsLinked to original sources
arXiv2025

Definably amenable groups in Continuous logic

We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both notions using fixed-point properties. We show that stable and ultracompact groups are definably amenable and prove that, for groups definable in dependent theories, definable amenability is equivalent to the existence of an f-generic type. Finally, we show the randomizations of first-order definably amenable groups are extremely definably amenable.

math.LO↗
arXiv2023

Improving the Inference of Topic Models via Infinite Latent State Replications

In text mining, topic models are a type of probabilistic generative models for inferring latent semantic topics from text corpus. One of the most popular inference approaches to topic models is perhaps collapsed Gibbs sampling (CGS), which typically samples one single topic label for each observed document-word pair. In this paper, we aim at improving the inference of CGS for topic models. We propose to leverage state augmentation technique by maximizing the number of topic samples to infinity, and then develop a new inference approach, called infinite latent state replication (ILR), to generate robust soft topic assignment for each given document-word pair. Experimental results on the publicly available datasets show that ILR outperforms CGS for inference of existing established topic models.

cs.CL↗
arXiv2018

Supersimple structures with a dense independent subset

Based on the work done in \cite{BV-Tind,DMS} in the o-minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking-independent elements that is dense inside a partial type $\mathcal{G}(x)$, which we call $H$-structures. We show that any two such expansions have the same theory and that under some technical conditions, the saturated models of this common theory are again $H$-structures. We prove that under these assumptions the expansion is supersimple and characterize forking and canonical bases of types in the expansion. We also analyze the effect these expansions have on one-basedness and CM-triviality. In the one-based case, when $T$ has $SU$-rank $ω^α$ and the $SU$-rank is continuous, we take $\mathcal{G}(x)$ to be the type of elements of $SU$-rank $ω^α$ and we describe a natural "geometry of generics modulo $H$" associated with such expansions and show it is modular.

math.LO↗