We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient conditions on the prior specification that guarantee convergence to a true density at a rate that is optimal minimax for the smoothness class W. SHEN, S.T. TOKDAR AND S. GHOSAL to which the true density belongs. No prior knowledge of smoothness is assumed. The sufficient conditions are shown to hold for the Dirichlet location mixture of normals prior with a Gaussian base measure and an inverse-Wishart prior on the covariance matrix parameter. Locally Hölder smoothness classes and their anisotropic extensions are considered. Our study involves several technical novelties, including sharp approximation of finitely differentiable multivariate densities by normal mixtures and a new sieve on the space of such densities.

Summary Direct lineage conversion offers a new strategy for tissue regeneration and disease modeling. Despite recent success in directly reprogramming fibroblasts into various cell types, the precise changes that occur as fibroblasts progressively convert to target cell fates remain unclear. The inherent heterogeneity and asynchronous nature of the reprogramming process renders it difficult to study using bulk genomic techniques. Here, to overcome this limitation, we applied single-cell RNA-seq to analyze global transcriptome changes at early stages of induced cardiomyocyte (iCM) reprogramming1–4. Using unsupervised dimensionality reduction and clustering algorithms, we identified molecularly distinct subpopulations of cells along reprogramming. We also constructed routes of iCM formation, and delineated the relationship between cell proliferation and iCM induction. Further analysis of global gene expression changes during reprogramming revealed an unexpected down-regulation of factors involved in mRNA processing and splicing. Detailed functional analysis of the top candidate splicing factor Ptbp1 revealed that it is a critical barrier to the acquisition of CM-specific splicing patterns in fibroblasts. Concomitantly, Ptbp1 depletion promoted cardiac transcriptome acquisition and increased iCM reprogramming efficiency. Additional quantitative analysis of our dataset revealed a strong correlation between the expression of each reprogramming factor and the progress of individual cells through the reprogramming process, and led to the discovery of novel surface markers for enrichment of iCMs. In summary, our single cell transcriptomics approaches enabled us to reconstruct the reprogramming trajectory and to uncover heretofore unrecognized intermediate cell populations, gene pathways and regulators involved in iCM induction.

Highlights d Single-cell transcriptomics reveals a bifurcated trajectory of hiCM reprogramming d Discovery of a decision point for a cell to enter reprogramming or refractory route d Identification of hiCM-specific features when compared to miCM d Development of cell fate index to evaluate the progression of cell fate conversion

We consider a general class of prior distributions for nonparametric Bayesian estimation which uses finite random series with a random number of terms. A prior is constructed through distributions on the number of basis functions and the associated coefficients. We derive a general result on adaptive posterior contraction rates for all smoothness levels of the target function in the true model by constructing an appropriate ‘sieve’ and applying the general theory of posterior contraction rates. We apply this general result on several statistical problems such as density estimation, various nonparametric regressions, classification, spectral density estimation and functional regression. The prior can be viewed as an alternative to the commonly used Gaussian process prior, but properties of the posterior distribution can be analysed by relatively simpler techniques. An interesting approximation property of B‐spline basis expansion established in this paper allows a canonical choice of prior on coefficients in a random series and allows a simple computational approach without using Markov chain Monte Carlo methods. A simulation study is conducted to show that the accuracy of the Bayesian estimators based on the random series prior and the Gaussian process prior are comparable. We apply the method on Tecator data using functional regression models.

We propose a novel regularized mixture model for clustering matrix-valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (e.g., low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix-normal distributions with regularization terms, and then develop an EM-type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of the solution.