Feature Extraction Involving Multichannel Time Series

研究人员推导了一个对数样条法来估计服从随机截断的响应变量的密度和条件密度(对于回归类型的应用)函数。除了随机截断引起的偏差调整外，估计器将被证明具有最优的收敛速度，与高维解释变量相关的重要问题将通过ANOVA类型的分解来解决。对于功能磁共振成像(FMRI)数据，PI和他的合作者通过去卷积估计血流动力学响应函数(HRF)，并开发大脑区域激活的统计推断。他们还考虑了使用独立分量分析(ICA)进行时空特征提取的问题。在适当的条件下，可以得到混合矩阵和潜在时间信号的参数和非参数统计推断。最后，对于同时记录一组神经元的数据，通过使用对数样条法估计条件强度函数，研究了识别与目标神经元相互作用的一组神经元的特征提取问题。PI通过建立最优收敛速度和估计量的渐近分布来研究射击概率的统计推断。所有项目所需的软件都会开发和分发给公众使用。计算机技术的进步为许多令人兴奋的研究机会提供了肥沃的土壤。一个深刻的例子是，科学家现在如何利用基因组数据来研究影响我们健康的疾病。另一个是脑部疾病和认知研究中的生物医学成像。为了根据这些类型的数据进行有效的统计推断，重要的是要考虑到数据采集阶段的抽样不足问题。首席调查员(PI)开发了一个灵活的统计框架来解决这个问题，并调查了模型在现实世界应用中的有效性。特别是，PI和他的同事们研究了他们的血流信息统计模型如何帮助科学家解释医疗应用的功能磁共振成像数据。他们还构建大脑图像，捕捉特定任务的神经生理活动或电路，作为了解大脑如何运作的途径。最后，PI使用高效和有效的统计方法，通过对特定任务的神经元集合的电势或神经放电概率进行建模，以更高的时间分辨率研究大脑的动力学。这些结果帮助医学研究人员提高他们在相关领域的知识，以便开发各种影响我们健康的遗传或中枢神经系统疾病的治疗方法。

The investigator derives a logspline procedure to estimate the density and conditional density (for regression type of applications) functions for response variable subject to random truncation. In addition to bias adjustment due to random truncation, the estimators will be shown to possess optimal rates of convergence and important issues related to high-dimensional explanatory variables will be addressed via ANOVA type of decomposition. For functional magnetic resonance imaging (fMRI) data, the PI and his collaborators estimate the hemodynamic response function(HRF) via deconvolution and develop statistical inference for brain region activation. They also consider the problem of spatial-temporal feature extraction using independent component analysis (ICA). Under appropriate conditions, both parametric and non-parametric statistical inference for the mixing matrix and the latent temporal signals will be derived. Finally, for data involving simultaneous recording of an ensemble of neurons, the problem of feature extraction in identify a group of neurons that interact with the target neuron is examined by using a logspline methodology to estimate the conditional intensity function. The PI studies the statistical inference for firing probability by establishing optimal rates of convergence and the asymptotic distribution of the estimator. Software for all the projects will be developed and disseminated for public use.Advance in computer technology has provided a fertile ground for many exciting research opportunities. A profound example is how scientists now use genomic data to study diseases that affect our health. Another is biomedical imaging in brain disease and cognitive studies. In order to conduct valid statistical inferences based on these types of data, it is important to account for the under-sampling issue during the data acquisition stage. The Principle Investigator (PI) develops a flexible statistical framework to address this problem and investigates the modelling validity in real world applications. In particular, the PI and his colleagues investigate how their statistical modelling of blood flow information can help scientists interpret the functional magnetic resonant imaging data for medical applications. They also construct brain images that capture the neural physiological activity or circuitry of a specific task, as a pathway to understand how the brain functions. Finally, the PI uses efficient and effective statistical methods to study the dynamics of the brain at a much higher temporal resolution by modelling the electro-potential or neuro-firing probability of a task-specific ensemble of neurons. These results help medical researchers advance their knowledge in their related fields so that treatments to various genetic or central nervous system diseases that affect our health can be developed.