An Empirical Bayes Approach for Constructing the Confidence Intervals of Clonality and Entropy

This paper is motivated by the need to quantify human immune responses to environmental challenges. Specifically, the genome of the selected cell population from a blood sample is amplified by the well-known PCR process of successive heating and cooling, producing a large number of reads. They number roughly 30,000 to 300,000. Each read corresponds to a particular rearrangement of so-called V(D)J sequences. In the end, the observation consists of a set of numbers of reads corresponding to different V(D)J sequences. The underlying relative frequencies of distinct V(D)J sequences can be summarized by a probability vector, with the cardinality being the number of distinct V(D)J rearrangements present in the blood. Statistical question is to make inferences on a summary parameter of the probability vector based on a single multinomial-type observation of a large dimension. Popular summary of the diversity of a cell population includes clonality and entropy, or more generally, is a suitable function of the probability vector. A point estimator of the clonality based on multiple replicates from the same blood sample has been proposed previously. After obtaining a point estimator of a particular function, the remaining challenge is to construct a confidence interval of the parameter to appropriately reflect its uncertainty. In this paper, we have proposed to couple the empirical Bayes method with a resampling-based calibration procedure to construct a robust confidence interval for different population diversity parameters. The method has been illustrated via extensive numerical study and real data examples

CausalEGM: a general causal inference framework by encoding generative modeling

Although understanding and characterizing causal effects have become essential in observational studies, it is challenging when the confounders are high-dimensional. In this article, we develop a general framework $\textit{CausalEGM}$ for estimating causal effects by encoding generative modeling, which can be applied in both binary and continuous treatment settings. Under the potential outcome framework with unconfoundedness, we establish a bidirectional transformation between the high-dimensional confounders space and a low-dimensional latent space where the density is known (e.g., multivariate normal distribution). Through this, CausalEGM simultaneously decouples the dependencies of confounders on both treatment and outcome and maps the confounders to the low-dimensional latent space. By conditioning on the low-dimensional latent features, CausalEGM can estimate the causal effect for each individual or the average causal effect within a population. Our theoretical analysis shows that the excess risk for CausalEGM can be bounded through empirical process theory. Under an assumption on encoder-decoder networks, the consistency of the estimate can be guaranteed. In a series of experiments, CausalEGM demonstrates superior performance over existing methods for both binary and continuous treatments. Specifically, we find CausalEGM to be substantially more powerful than competing methods in the presence of large sample sizes and high dimensional confounders. The software of CausalEGM is freely available at https://github.com/SUwonglab/CausalEGM.Comment: Corrected typo

On a problem of Henning and Yeo about the transversal number of uniform linear systems whose 2-packing number is fixed

For $r\geq2$, let $(P,\mathcal{L})$ be an $r$-uniform linear system. The transversal number $\tau(P,\mathcal{L})$ of $(P,\mathcal{L})$ is the minimum number of points that intersect every line of $(P,\mathcal{L})$. The 2-packing number $\nu_2(P,\mathcal{L})$ of $(P,\mathcal{L})$ is the maximum number of lines such that the intersection of any three of them is empty. In [Discrete Math. 313 (2013), 959--966] Henning and Yeo posed the following question: Is it true that if $(P,\mathcal{L})$ is a $r$-uniform linear system then $\tau(P,\mathcal{L})\leq\displaystyle\frac{|P|+|\mathcal{L}|}{r+1}$ holds for all $k\geq2$?. In this paper, some results about of $r$-uniform linear systems whose 2-packing number is fixed which satisfies the inequality are given

Subgraph Frequency Distribution Estimation using Graph Neural Networks

Small subgraphs (graphlets) are important features to describe fundamental units of a large network. The calculation of the subgraph frequency distributions has a wide application in multiple domains including biology and engineering. Unfortunately due to the inherent complexity of this task, most of the existing methods are computationally intensive and inefficient. In this work, we propose GNNS, a novel representational learning framework that utilizes graph neural networks to sample subgraphs efficiently for estimating their frequency distribution. Our framework includes an inference model and a generative model that learns hierarchical embeddings of nodes, subgraphs, and graph types. With the learned model and embeddings, subgraphs are sampled in a highly scalable and parallel way and the frequency distribution estimation is then performed based on these sampled subgraphs. Eventually, our methods achieve comparable accuracy and a significant speedup by three orders of magnitude compared to existing methods.Comment: accepted by KDD 2022 Workshop on Deep Learning on Graph

Neurochemical Mechanism of Electroacupuncture: Anti-injury Effect on Cerebral Function after Focal Cerebral Ischemia in Rats†

We explored the neurochemical mechanism of electroacupuncture's (EA) protective effect on brain function in focal cerebral ischemia rats, using cerebral ischemia/reperfusion rats established by the middle cerebral artery occlusion (MCAO) method. Adult male Sprague–Dawley rats were randomly divided into four groups: Sham, Sham+EA, MCAO and MCAO+EA. The rats in Sham+EA and MCAO+EA were accepted EA treatment at ‘GV26’ and ‘GV20’ acupoints for 30 min. Electric stimulation was produced by a G-6805 generator and neurological deficit scores were recorded. Mitochondria respiratory function and the activities of respiratory enzymes were measured by a computer-aided Clark oxygen electrode system. Results showed that EA treatment might reduce the neurological deficit score, and significantly improve respiratory control ratio (RCR), the index of mitochondrial respiratory function, and increase the activities of succinic dehydrogenase, NADH dehydrogenase and cytochrome C oxidase in the MCAO rats. Results suggest that EA might markedly decrease the neurological deficit score, promote the activities of respiratory enzymes and reduce the generation of reactive oxygen species (ROS), resulting in improvement of respiratory chain function and anti-oxidative capability of brain tissues in the infarct penumbra zone. This be a mechanism of EA's anti-injury effect on brain function in MCAO rats