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1. On the Number of Edges of the Frechet Mean and Median Graphs

   https://doi.org/10.1007/978-3-030-97240-0_3  

   Ferguson, Daniel; Meyer, Francois G. (February 2022, Network Science)

   Ribeiro, Pedro; Silva, Fernando; Mendes, José Fernando; Laureano, Rosário (Ed.)

   The availability of large datasets composed of graphs creates an unprecedented need to invent novel tools in statistical learning for graph-valued random variables. To characterize the average of a sample of graphs, one can compute the sample Frechet mean and median graphs. In this paper, we address the following foundational question: does a mean or median graph inherit the structural properties of the graphs in the sample? An important graph property is the edge density; we establish that edge density is an hereditary property, which can be transmitted from a graph sample to its sample Frechet mean or median graphs, irrespective of the method used to estimate the mean or the median. Because of the prominence of the Frechet mean in graph-valued machine learning, this novel theoretical result has some significant practical consequences. 

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2. A tail-based test to detect differential expression in RNA-sequencing data

   https://doi.org/10.1177/0962280220951907  

   Chen, Jiong; Mi, Xinlei; Ning, Jing; He, Xuming; Hu, Jianhua (January 2021, Statistical Methods in Medical Research)

   null (Ed.)

   RNA sequencing data have been abundantly generated in biomedical research for biomarker discovery and other studies. Such data at the exon level are usually heavily tailed and correlated. Conventional statistical tests based on the mean or median difference for differential expression likely suffer from low power when the between-group difference occurs mostly in the upper or lower tail of the distribution of gene expression. We propose a tail-based test to make comparisons between groups in terms of a specific distribution area rather than a single location. The proposed test, which is derived from quantile regression, adjusts for covariates and accounts for within-sample dependence among the exons through a specified correlation structure. Through Monte Carlo simulation studies, we show that the proposed test is generally more powerful and robust in detecting differential expression than commonly used tests based on the mean or a single quantile. An application to TCGA lung adenocarcinoma data demonstrates the promise of the proposed method in terms of biomarker discovery. 

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3. Distributed Partial Clustering

   https://doi.org/10.1145/3087556.3087568  

   Guha, Sudipto; Li, Yi; Zhang, Qin (July 2017, The 29th ACM Symposium on Parallelism in Algorithms and Architectures)

   Recent years have witnessed an increasing popularity of algorithm design for distributed data, largely due to the fact that massive datasets are often collected and stored in different locations. In the distributed setting communication typically dominates the query processing time. Thus it becomes crucial to design communication efficient algorithms for queries on distributed data. Simultaneously, it has been widely recognized that partial optimizations, where we are allowed to disregard a small part of the data, provide us significantly better solutions. The motivation for disregarded points often arise from noise and other phenomena that are pervasive in large data scenarios. In this paper we focus on partial clustering problems, k-center, k-median and k-means, in the distributed model, and provide algorithms with communication sublinear of the input size. As a consequence we develop the first algorithms for the partial k-median and means objectives that run in subquadratic running time. We also initiate the study of distributed algorithms for clustering uncertain data, where each data point can possibly fall into multiple locations under certain probability distribution. 

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4. Dwarf AGNs from Optical Variability for the Origins of Seeds (DAVOS): insights from the dark energy survey deep fields

   https://doi.org/10.1093/mnras/stac2262  

   Burke, Colin J; Liu, Xin; Shen, Yue; Phadke, Kedar A; Yang, Qian; Hartley, Will G; Harrison, Ian; Palmese, Antonella; Guo, Hengxiao; Zhang, Kaiwen; et al (September 2022, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We present a sample of 706, z < 1.5 active galactic nuclei (AGNs) selected from optical photometric variability in three of the Dark Energy Survey (DES) deep fields (E2, C3, and X3) over an area of 4.64 deg2. We construct light curves using difference imaging aperture photometry for resolved sources and non-difference imaging PSF photometry for unresolved sources, respectively, and characterize the variability significance. Our DES light curves have a mean cadence of 7 d, a 6-yr baseline, and a single-epoch imaging depth of up to g ∼ 24.5. Using spectral energy distribution (SED) fitting, we find 26 out of total 706 variable galaxies are consistent with dwarf galaxies with a reliable stellar mass estimate ($$M_{\ast }\lt 10^{9.5}\, {\rm M}_\odot$$; median photometric redshift of 0.9). We were able to constrain rapid characteristic variability time-scales (∼ weeks) using the DES light curves in 15 dwarf AGN candidates (a subset of our variable AGN candidates) at a median photometric redshift of 0.4. This rapid variability is consistent with their low black hole (BH) masses. We confirm the low-mass AGN nature of one source with a high S/N optical spectrum. We publish our catalogue, optical light curves, and supplementary data, such as X-ray properties and optical spectra, when available. We measure a variable AGN fraction versus stellar mass and compare to results from a forward model. This work demonstrates the feasibility of optical variability to identify AGNs with lower BH masses in deep fields, which may be more ‘pristine’ analogues of supermassive BH seeds. 

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5. Comparing traditional and Bayesian approaches to ecological meta‐analysis

   https://doi.org/10.1111/2041-210X.13445  

   Pappalardo, Paula; Ogle, Kiona; Hamman, Elizabeth A.; Bence, James R.; Hungate, Bruce A.; Osenberg, Craig W.; O'Hara, ed., Robert B. (July 2020, Methods in Ecology and Evolution)

   Abstract Despite the wide application of meta‐analysis in ecology, some of the traditional methods used for meta‐analysis may not perform well given the type of data characteristic of ecological meta‐analyses.We reviewed published meta‐analyses on the ecological impacts of global climate change, evaluating the number of replicates used in the primary studies (n_i) and the number of studies or records (k) that were aggregated to calculate a mean effect size. We used the results of the review in a simulation experiment to assess the performance of conventional frequentist and Bayesian meta‐analysis methods for estimating a mean effect size and its uncertainty interval.Our literature review showed thatn_iandkwere highly variable, distributions were right‐skewed and were generally small (mediann_i = 5, mediank = 44). Our simulations show that the choice of method for calculating uncertainty intervals was critical for obtaining appropriate coverage (close to the nominal value of 0.95). Whenkwas low (<40), 95% coverage was achieved by a confidence interval (CI) based on thetdistribution that uses an adjusted standard error (the Hartung–Knapp–Sidik–Jonkman, HKSJ), or by a Bayesian credible interval, whereas bootstrap orzdistribution CIs had lower coverage. Despite the importance of the method to calculate the uncertainty interval, 39% of the meta‐analyses reviewed did not report the method used, and of the 61% that did, 94% used a potentially problematic method, which may be a consequence of software defaults.In general, for a simple random‐effects meta‐analysis, the performance of the best frequentist and Bayesian methods was similar for the same combinations of factors (kand mean replication), though the Bayesian approach had higher than nominal (>95%) coverage for the mean effect whenkwas very low (k < 15). Our literature review suggests that many meta‐analyses that usedzdistribution or bootstrapping CIs may have overestimated the statistical significance of their results when the number of studies was low; more appropriate methods need to be adopted in ecological meta‐analyses. 

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