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Plasma cell-free DNA (cfDNA) is a noninvasive biomarker for cell death of all organs. Deciphering the tissue origin of cfDNA can reveal abnormal cell death because of diseases, which has great clinical potential in disease detection and monitoring. Despite the great promise, the sensitive and accurate quantification of tissue-derived cfDNA remains challenging to existing methods due to the limited characterization of tissue methylation and the reliance on unsupervised methods. To fully exploit the clinical potential of tissue-derived cfDNA, here we present one of the largest comprehensive and high-resolution methylation atlas based on 521 noncancer tissue samples spanning 29 major types of human tissues. We systematically identified fragment-level tissue-specific methylation patterns and extensively validated them in orthogonal datasets. Based on the rich tissue methylation atlas, we develop the first supervised tissue deconvolution approach, a deep-learning-powered model, cfSort , for sensitive and accurate tissue deconvolution in cfDNA. On the benchmarking data, cfSort showed superior sensitivity and accuracy compared to the existing methods. We further demonstrated the clinical utilities of cfSort with two potential applications: aiding disease diagnosis and monitoring treatment side effects. The tissue-derived cfDNA fraction estimated from cfSort reflected the clinical outcomes of the patients. In summary, the tissue methylation atlas and cfSort enhanced the performance of tissue deconvolution in cfDNA, thus facilitating cfDNA-based disease detection and longitudinal treatment monitoring. 

Density estimation is a building block for many other statistical methods, such as classification, nonparametric testing, and data compression. In this paper, we focus on a non-parametric approach to multivariate density estimation, and study its asymptotic properties under both frequentist and Bayesian settings. The estimated density function is obtained by considering a sequence of approximating spaces to the space of densities. These spaces consist of piecewise constant density functions supported by binary partitions with increasing complexity. To obtain an estimate, the partition is learned by maximizing either the likelihood of the corresponding histogram on that partition, or the marginal posterior probability of the partition under a suitable prior. We analyze the convergence rate of the maximum likelihood estimator and the posterior concentration rate of the Bayesian estimator, and conclude that for a relatively rich class of density functions the rate does not directly depend on the dimension. We also show that the Bayesian method can adapt to the unknown smoothness of the density function. The method is applied to several specific function classes and explicit rates are obtained. These include spatially sparse functions, functions of bounded variation, and Holder continuous functions. We also introduce an ensemble approach, obtained by aggregating multiple density estimates fit under carefully designed perturbations, and show that for density functions lying in a Holder space (H^(1,β),0<β≤1), the ensemble method can achieve minimax convergence rate up to a logarithmic term, while the corresponding rate of the density estimator based on a single partition is suboptimal for this function class. 

Density estimation is a building block for many other statistical methods, such as classification, nonparametric testing, and data compression. In this paper, we focus on a nonparametric approach to multivariate density estimation, and study its asymptotic properties under both frequentist and Bayesian settings. The estimated density function is obtained by considering a sequence of approximating spaces to the space of densities. These spaces consist of piecewise constant density functions supported by binary partitions with increasing complexity. To obtain an estimate, the partition is learned by maximizing either the likelihood of the corresponding histogram on that partition, or the marginal posterior probability of the partition under a suitable prior. We analyze the convergence rate of the maximum likelihood estimator and the posterior concentration rate of the Bayesian estimator, and conclude that for a relatively rich class of density functions the rate does not directly depend on the dimension. We also show that the Bayesian method can adapt to the unknown smoothness of the density function. The method is applied to several specific function classes and explicit rates are obtained. These include spatially sparse functions, functions of bounded variation, and Holder continuous functions. We also introduce an ensemble approach, obtained by aggregating multiple density estimates fit under carefully designed perturbations, and show that for density functions lying in a Holder space (H^(1,β), 0 < β ≤ 1), the ensemble method can achieve minimax convergence rate up to a logarithmic term, while the corresponding rate of the density estimator based on a single partition is suboptimal for this function class. 

Density estimation is one of the fundamental problems in both statistics and machine learning. In this study, we propose Roundtrip, a computational framework for general-purpose density estimation based on deep generative neural networks. Roundtrip retains the generative power of deep generative models, such as generative adversarial networks (GANs) while it also provides estimates of density values, thus supporting both data generation and density estimation. Unlike previous neural density estimators that put stringent conditions on the transformation from the latent space to the data space, Roundtrip enables the use of much more general mappings where target density is modeled by learning a manifold induced from a base density (e.g., Gaussian distribution). Roundtrip provides a statistical framework for GAN models where an explicit evaluation of density values is feasible. In numerical experiments, Roundtrip exceeds state-of-the-art performance in a diverse range of density estimation tasks.