Search for: All records

Tree-based methods are popular nonparametric tools for capturing spatial heterogeneity and making predictions in multivariate problems. In unsupervised learning, trees and their ensembles have also been applied to a wide range of statistical inference tasks, such as multi-resolution sketching of distributional variations, localization of high-density regions, and design of efficient data compression schemes. In this paper, we study the spatial adaptation property of Bayesian tree-based methods in the unsupervised setting, with a focus on the density estimation problem. We characterize spatial heterogeneity of the underlying density function by using anisotropic Besov spaces, region-wise anisotropic Besov spaces, and two novel function classes as their extensions. For two types of commonly used prior distributions on trees under the context of unsupervised learning—the optional P{ó}lya tree (Wong and Ma, 2010) and the Dirichlet prior (Lu et al., 2013)—we calculate posterior concentration rates when the density function exhibits different types of heterogeneity. In specific, we show that the posterior concentration rate for trees is near minimax over the anisotropic Besov space. The rate is adaptive in the sense that to achieve such a rate we do not need any prior knowledge of the parameters of the Besov space. 

Tree-based methods are popular nonparametric tools for capturing spatial heterogeneity and making predictions in multivariate problems. In unsupervised learning, trees and their ensembles have also been applied to a wide range of statistical inference tasks, such as multi-resolution sketching of distributional variations, localization of high-density regions, and design of efficient data compression schemes. In this paper, we study the spatial adaptation property of Bayesian tree-based methods in the unsupervised setting, with a focus on the density estimation problem. We characterize spatial heterogeneity of the underlying density function by using anisotropic Besov spaces, region-wise anisotropic Besov spaces, and two novel function classes as their extensions. For two types of commonly used prior distributions on trees under the context of unsupervised learning—the optional P{ó}lya tree (Wong and Ma, 2010) and the Dirichlet prior (Lu et al., 2013)—we calculate posterior concentration rates when the density function exhibits different types of heterogeneity. In specific, we show that the posterior concentration rate for trees is near minimax over the anisotropic Besov space. The rate is adaptive in the sense that to achieve such a rate we do not need any prior knowledge of the parameters of the Besov space. 

Abstract BackgroundX chromosome inactivation (XCI) is a female-specific process in which one X chromosome is silenced to balance X-linked gene expression between the sexes. XCI is initiated in early development by upregulation of the lncRNAXiston the future inactive X (Xi). A subset of X-linked genes escape silencing and thus have higher expression in females, suggesting female-specific functions. One of these genes is the highly conserved geneKdm6a, which encodes a histone demethylase that removes methyl groups at H3K27 to facilitate gene expression.KDM6Amutations have been implicated in congenital disorders such as Kabuki Syndrome, as well as in sex differences in development and cancer. MethodsKdm6awas knocked out (KO) using CRISPR/Cas9 gene editing in hybrid female mouse embryonic stem (ES) cells derived either from a 129 × Mus castaneus(cast) cross or a BL6 xcastcross. In one of the lines a transcriptional stop signal inserted inTsixresults in completely skewed X silencing upon differentiation. The effects of both homozygous and heterozygousKdm6aKO onXistexpression during the onset of XCI were measured by RT-PCR and RNA-FISH. Changes in gene expression and in H3K27me3 enrichment were investigated using allele-specific RNA-seq and Cut&Run, respectively. KDM6A binding to theXistgene was characterized by Cut&Run. ResultsWe observed impaired upregulation ofXistand reduced coating of the Xi during early stages of differentiation inKdm6aKO cells, both homozygous and heterozygous, suggesting a threshold effect of KDM6A. This was associated with aberrant overexpression of genes from the Xi after differentiation, indicating loss of X inactivation potency. Consistent with KDM6A having a direct role inXistregulation, we found that the histone demethylase binds to theXistpromoter and KO cells show an increase in H3K27me3 atXist, consistent with reduced expression. ConclusionsThese results reveal a novel female-specific role for the X-linked histone demethylase, KDM6A in the initiation of XCI through histone demethylase-dependent activation ofXistduring early differentiation. Plain language summaryX chromosome inactivation is a female-specific mechanism that evolved to balance sex-linked gene dosage between females (XX) and males (XY) by silencing one X chromosome in females. X inactivation begins with the upregulation of the long noncoding RNAXiston the future inactive X chromosome. While most genes become silenced on the inactive X chromosome some genes escape inactivation and thus have higher expression in females compared to males, suggesting that escape genes may have female-specific functions. One such gene encodes the histone demethylase KDM6A which function is to turn on gene expression by removing repressive histone modifications. In this study, we investigated the role of KDM6A in the regulation ofXistexpression during the onset of X inactivation. We found that KDM6A binds to theXistgene to remove repressive histone marks and facilitate its expression in early development. Indeed, depletion of KDM6A prevents upregulation ofXistdue to abnormal persistence of repressive histone modifications. In turn, this results in aberrant overexpression of genes from the inactive X chromosome. Our findings point to a novel mechanism ofXistregulation during the initiation of X inactivation, which may lead to new avenues of treatment to alleviate congenital disorders such as Kabuki syndrome and sex-biased immune disorders where X-linked gene dosage is perturbed. 

Bone marrow mesenchymal stem cells (BM MSCs) play a tumor-supportive role in promoting drug resistance and disease relapse in multiple myeloma (MM). Recent studies have discovered a sub-population of MSCs, known as inflammatory MSCs (iMSCs), exclusive to the MM BM microenvironment and implicated in drug resistance. Through a sophisticated analysis of public expression data from unexpanded BM MSCs, we uncovered a positive association between iMSC signature expression and minimal residual disease. While in vitro expansion generally results in the loss of the iMSC signature, our meta-analysis of additional public expression data demonstrated that cytokine stimulation, including IL1-β and TNF-α, as well as immune cells such as neutrophils, macrophages, and MM cells, can reactivate the signature expression of iMSCs to varying extents. These findings underscore the importance and potential utility of cytokine stimulation in mimicking the gene expression signature of early passage of iMSCs for functional characterizations of their tumor-supportive roles in MM.