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Text analysis is an interesting research area in data science and has various applications, such as in artificial intelligence, biomedical research, and engineering. We review popular methods for text analysis, ranging from topic modeling to the recent neural language models. In particular, we review Topic-SCORE, a statistical approach to topic modeling, and discuss how to use it to analyze the Multi-Attribute Data Set on Statisticians (MADStat), a data set on statistical publications that we collected and cleaned. The application of Topic-SCORE and other methods to MADStat leads to interesting findings. For example, we identified 11 representative topics in statistics. For each journal, the evolution of topic weights over time can be visualized, and these results are used to analyze the trends in statistical research. In particular, we propose a new statistical model for ranking the citation impacts of 11 topics, and we also build a cross-topic citation graph to illustrate how research results on different topics spread to one another. The results on MADStat provide a data-driven picture of the statistical research from 1975 to 2015, from a text analysis perspective.

 

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the sim- plex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). How- ever, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest. 

Subject clustering (i.e., the use of measured features to cluster subjects, such as patients or cells, into multiple groups) is a problem of significant interest. In recent years, many approaches have been proposed, among which unsupervised deep learning (UDL) has received much attention. Two interesting questions are 1) how to combine the strengths of UDL and other approaches and 2) how these approaches compare to each other. We combine the variational auto-encoder (VAE), a popular UDL approach, with the recent idea of influential feature-principal component analysis (IF-PCA) and propose IF-VAE as a new method for subject clustering. We study IF-VAE and compare it with several other methods (including IF-PCA, VAE, Seurat, and SC3) on 10 gene microarray data sets and eight single-cell RNA-seq data sets. We find that IF-VAE shows significant improvement over VAE, but still underperforms compared to IF-PCA. We also find that IF-PCA is quite competitive, slightly outperforming Seurat and SC3 over the eight single-cell data sets. IF-PCA is conceptually simple and permits delicate analysis. We demonstrate that IF-PCA is capable of achieving phase transition in a rare/weak model. Comparatively, Seurat and SC3 are more complex and theoretically difficult to analyze (for these reasons, their optimality remains unclear). 

The SNP-set analysis is a powerful tool for dissecting the genetics of complex human diseases. There are three fundamental genetic association approaches to SNR-set analysis: the marginal model fitting approach, the joint model fitting approach, and the decorrelation approach. A problem of primary interest is how these approaches compare with each other. To address this problem, we develop a theoretical platform to compare the signal-to-noise ratio (SNR) of these approaches under the generalized linear model. We elaborate on how causal genetic effects give rise to statistically detectable association signals, and show that when causal effects spread over blocks of strong linkage disequilibrium (LD), the SNR of the marginal model fitting is usually higher than that of the decorrelation approach, which in turn is higher than that of the unbiased joint model fitting approach. We also scrutinize dense effects and LDs by a bivariate model and extensive simulations using the 1000 Genome Project data. Last, we compare the statistical power of two generic types of SNP-set tests (summation-based and supremum-based) by simulations and an osteoporosis study using large data from UK Biobank. Our results help develop powerful tools for SNP-set analysis and understand the signal detection problem in the presence of colored noise. 

SCORE was introduced as a spectral approach to network community detection. Since many networks have severe degree heterogeneity, the ordinary spectral clustering (OSC) approach to community detection may perform unsatisfactorily. SCORE alleviates the effect of degree heterogeneity by introducing a new normalization idea in the spectral domain and makes OSC more effective. SCORE is easy to use and computationally fast. It adapts easily to new directions and sees an increasing interest in practice. In this paper, we review the basics of SCORE, the adaption of SCORE to network mixed membership estimation and topic modeling, and the application of SCORE in real data, including two datasets on the publications of statisticians. We also review the theoretical “ideology” underlying SCORE. We show that in the spectral domain, SCORE converts a simplicial cone to a simplex and provides a simple and direct link between the simplex and network memberships. SCORE attains an exponential rate and a sharp phase transition in community detection, and achieves optimal rates in mixed membership estimation and topic modeling.