arXiv subjects

Hanyu Song

Publications and source records attributed to Hanyu Song.

4 recordsLinked to original sources

arXiv2023

Curved factor analysis with the Ellipsoid-Gaussian distribution

There is a need for new models for characterizing dependence in multivariate data. The multivariate Gaussian distribution is routinely used, but cannot characterize nonlinear relationships in the data. Most non-linear extensions tend to be highly complex; for example, involving estimation of a non-linear regression model in latent variables. In this article, we propose a relatively simple class of Ellipsoid-Gaussian multivariate distributions, which are derived by using a Gaussian linear factor model involving latent variables having a von Mises-Fisher distribution on a unit hyper-sphere. We show that the Ellipsoid-Gaussian distribution can flexibly model curved relationships among variables with lower-dimensional structures. Taking a Bayesian approach, we propose a hybrid of gradient-based geodesic Monte Carlo and adaptive Metropolis for posterior sampling. We derive basic properties and illustrate the utility of the Ellipsoid-Gaussian distribution on a variety of simulated and real data applications. An accompanying R package is also available.

stat.ME↗

arXiv2023

A Survey of Mathematical Models on Somitogenesis

This paper presents a comprehensive survey of various established mathematical models pertaining to Somitogenesis, a biological process. The study begins by revisiting and replicating the findings from prominent research papers in this domain, subsequently offering a critical evaluation of the strengths and weaknesses inherent in each approach. By synthesizing this knowledge, the paper aims to contribute to a deeper understanding of Somitogenesis, and pave the way for further advancements in the development of enhanced mathematical models for this intricate biological process. The concluding section offers valuable insights and directions for prospective research in this field.

math.DS↗

arXiv2021

Deep Clustering based Fair Outlier Detection

In this paper, we focus on the fairness issues regarding unsupervised outlier detection. Traditional algorithms, without a specific design for algorithmic fairness, could implicitly encode and propagate statistical bias in data and raise societal concerns. To correct such unfairness and deliver a fair set of potential outlier candidates, we propose Deep Clustering based Fair Outlier Detection (DCFOD) that learns a good representation for utility maximization while enforcing the learnable representation to be subgroup-invariant on the sensitive attribute. Considering the coupled and reciprocal nature between clustering and outlier detection, we leverage deep clustering to discover the intrinsic cluster structure and out-of-structure instances. Meanwhile, an adversarial training erases the sensitive pattern for instances for fairness adaptation. Technically, we propose an instance-level weighted representation learning strategy to enhance the joint deep clustering and outlier detection, where the dynamic weight module re-emphasizes contributions of likely-inliers while mitigating the negative impact from outliers. Demonstrated by experiments on eight datasets comparing to 17 outlier detection algorithms, our DCFOD method consistently achieves superior performance on both the outlier detection validity and two types of fairness notions in outlier detection.

cs.LG↗

arXiv2020

Distributed Bayesian clustering using finite mixture of mixtures

In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering. Existing distributed clustering algorithms are mostly distance or density based without a likelihood specification, precluding the possibility of formal statistical inference. Model-based clustering allows statistical inference, yet research on distributed inference has emphasized nonparametric Bayesian mixture models over finite mixture models. To fill this gap, we introduce a nearly embarrassingly parallel algorithm for clustering under a Bayesian overfitted finite mixture of Gaussian mixtures, which we term distributed Bayesian clustering (DIB-C). DIB-C can flexibly accommodate data sets with various shapes (e.g. skewed or multi-modal). With data randomly partitioned and distributed, we first run Markov chain Monte Carlo in an embarrassingly parallel manner to obtain local clustering draws and then refine across workers for a final clustering estimate based on any loss function on the space of partitions. DIB-C can also estimate cluster densities, quickly classify new subjects and provide a posterior predictive distribution. Both simulation studies and real data applications show superior performance of DIB-C in terms of robustness and computational efficiency.

stat.CO↗