arXiv subjects

Shai Gorsky

Publications and source records attributed to Shai Gorsky.

3 recordsLinked to original sources

arXiv2021

Multiscale Fisher's Independence Test for Multivariate Dependence

Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them to massive data. Moreover, resampling is usually necessary to evaluate the statistical significance of the resulting test statistics at finite sample sizes, further worsening the computational burden. We introduce a scalable, resampling-free approach to testing the independence between two random vectors by breaking down the task into simple univariate tests of independence on a collection of 2x2 contingency tables constructed through sequential coarse-to-fine discretization of the sample space, transforming the inference task into a multiple testing problem that can be completed with almost linear complexity with respect to the sample size. To address increasing dimensionality, we introduce a coarse-to-fine sequential adaptive procedure that exploits the spatial features of dependency structures to more effectively examine the sample space. We derive a finite-sample theory that guarantees the inferential validity of our adaptive procedure at any given sample size. In particular, we show that our approach can achieve strong control of the family-wise error rate without resampling or large-sample approximation. We demonstrate the substantial computational advantage of the procedure in comparison to existing approaches as well as its decent statistical power under various dependency scenarios through an extensive simulation study, and illustrate how the divide-and-conquer nature of the procedure can be exploited to not just test independence but to learn the nature of the underlying dependency. Finally, we demonstrate the use of our method through analyzing a large data set from a flow cytometry experiment.

stat.ME↗

arXiv2020

Coarsened mixtures of hierarchical skew normal kernels for flow cytometry analyses

Flow cytometry (FCM) is the standard multi-parameter assay for measuring single cell phenotype and functionality. It is commonly used for quantifying the relative frequencies of cell subsets in blood and disaggregated tissues. A typical analysis of FCM data involves cell classification---that is, the identification of cell subgroups in the sample---and comparisons of the cell subgroups across samples or conditions. While modern experiments often necessitate the collection and processing of samples in multiple batches, analysis of FCM data across batches is challenging because differences across samples may occur due to either true biological variation or technical reasons such as antibody lot effects or instrument optics across batches. Thus a critical step in comparative analyses of multi-sample FCM data---yet missing in existing automated methods for analyzing such data---is cross-sample calibration, whose goal is to align corresponding cell subsets across multiple samples in the presence of technical variations, so that biological variations can be meaningfully compared. We introduce a Bayesian nonparametric hierarchical modeling approach for accomplishing both calibration and cell classification simultaneously in a unified probabilistic manner. Three important features of our method make it particularly effective for analyzing multi-sample FCM data: a nonparametric mixture avoids prespecifying the number of cell clusters; a hierarchical skew normal kernel that allows flexibility in the shapes of the cell subsets and cross-sample variation in their locations; and finally the "coarsening" strategy makes inference robust to departures from the model such as heavy-tailness not captured by the skew normal kernels. We demonstrate the merits of our approach in simulated examples and carry out a case study in the analysis of two multi-sample FCM data sets.

stat.AP↗

arXiv2014

Modeling the Heart as a Communication System

Electrical communication between cardiomyocytes can be perturbed during arrhythmia, but these perturbations are not captured by conventional electrocardiographic metrics. We developed a theoretical framework to quantify electrical communication using information theory metrics in 2-dimensional cell lattice models of cardiac excitation propagation. The time series generated by each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon entropy for each cell was calculated from the time series during four clinically important heart rhythms: normal heartbeat, anatomical reentry, spiral reentry, and multiple reentry. We also used mutual information to perform spatial profiling of communication during these cardiac arrhythmias. We found that information sharing between cells was spatially heterogeneous. In addition, cardiac arrhythmia significantly impacted information sharing within the heart. Entropy localized the path of the drifting core of spiral reentry, which could be an optimal target of therapeutic ablation. We conclude that information theory metrics can quantitatively assess electrical communication among cardiomyocytes. The traditional concept of the heart as a functional syncytium sharing electrical information cannot predict altered entropy and information sharing during complex arrhythmia. Information theory metrics may find clinical application in the identification of rhythm-specific treatments which are currently unmet by traditional electrocardiographic techniques.

q-bio.QM↗