Learning Graphical Models of Multivariate Functional Data with Applications to Neuroimaging

This dissertation investigates the functional graphical models that infer the functional connectivity based on neuroimaging data, which is noisy, high dimensional and has limited samples. The dissertation provides two recipes to infer the functional graphical model: 1) a fully Bayesian framework 2) an end-to-end deep model. We first propose a fully Bayesian regularization scheme to estimate functional graphical models. We consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019).. We then propose a regularization strategy via the graphical horseshoe. We compare both Bayesian approaches to the frequentist functional graphical lasso, and compare the Bayesian functional graphical lasso to the functional graphical horseshoe. We applied the proposed methods with electroencephalography (EEG) data and diffusion tensor imaging (DTI) data. We find that the Bayesian methods tend to outperform the standard functional graphical lasso, and that the functional graphical horseshoe performs best overall, a procedure for which there is no direct frequentist analog. Then we consider a deep neural network architecture to estimate functional graphical models, by combining two simple off-the-shelf algorithms: adaptive functional principal components analysis (FPCA) Yao et al., 2021a) and convolutional graph estimator (Belilovsky et al., 2016). We train our proposed model with synthetic data which emulate the real world observations and prior knowledge. Based on synthetic data generation process, our model convert an inference problem as a supervised learning problem. Compared with other framework, our proposed deep model which offers a general recipe to infer the functional graphical model based on data-driven approach, take the raw functional dataset as input and avoid deriving sophisticated closed-form. Through simulation studies, we find that our deep functional graph model trained on synthetic data generalizes well and outperform other popular baselines marginally. In addition, we apply deep functional graphical model in the real world EEG data, and our proposed model discover meaningful brain connectivity. Finally, we are interested in estimating casual graph with functional input. In order to process functional covariates in causal estimation, we leverage the similar strategy as our deep functional graphical model. We extend popular deep causal models to infer causal effects with functional confoundings within the potential outcomes framework. Our method is simple yet effective, where we validate our proposed architecture in variety of simulation settings. Our work offers an alternative way to do causal inference with functional data

Advances in Hyperspectral Image Classification Methods for Vegetation and Agricultural Cropland Studies

Hyperspectral data are becoming more widely available via sensors on airborne and unmanned aerial vehicle (UAV) platforms, as well as proximal platforms. While space-based hyperspectral data continue to be limited in availability, multiple spaceborne Earth-observing missions on traditional platforms are scheduled for launch, and companies are experimenting with small satellites for constellations to observe the Earth, as well as for planetary missions. Land cover mapping via classification is one of the most important applications of hyperspectral remote sensing and will increase in significance as time series of imagery are more readily available. However, while the narrow bands of hyperspectral data provide new opportunities for chemistry-based modeling and mapping, challenges remain. Hyperspectral data are high dimensional, and many bands are highly correlated or irrelevant for a given classification problem. For supervised classification methods, the quantity of training data is typically limited relative to the dimension of the input space. The resulting Hughes phenomenon, often referred to as the curse of dimensionality, increases potential for unstable parameter estimates, overfitting, and poor generalization of classifiers. This is particularly problematic for parametric approaches such as Gaussian maximum likelihoodbased classifiers that have been the backbone of pixel-based multispectral classification methods. This issue has motivated investigation of alternatives, including regularization of the class covariance matrices, ensembles of weak classifiers, development of feature selection and extraction methods, adoption of nonparametric classifiers, and exploration of methods to exploit unlabeled samples via semi-supervised and active learning. Data sets are also quite large, motivating computationally efficient algorithms and implementations. This chapter provides an overview of the recent advances in classification methods for mapping vegetation using hyperspectral data. Three data sets that are used in the hyperspectral classification literature (e.g., Botswana Hyperion satellite data and AVIRIS airborne data over both Kennedy Space Center and Indian Pines) are described in Section 3.2 and used to illustrate methods described in the chapter. An additional high-resolution hyperspectral data set acquired by a SpecTIR sensor on an airborne platform over the Indian Pines area is included to exemplify the use of new deep learning approaches, and a multiplatform example of airborne hyperspectral data is provided to demonstrate transfer learning in hyperspectral image classification. Classical approaches for supervised and unsupervised feature selection and extraction are reviewed in Section 3.3. In particular, nonlinearities exhibited in hyperspectral imagery have motivated development of nonlinear feature extraction methods in manifold learning, which are outlined in Section 3.3.1.4. Spatial context is also important in classification of both natural vegetation with complex textural patterns and large agricultural fields with significant local variability within fields. Approaches to exploit spatial features at both the pixel level (e.g., co-occurrencebased texture and extended morphological attribute profiles [EMAPs]) and integration of segmentation approaches (e.g., HSeg) are discussed in this context in Section 3.3.2. Recently, classification methods that leverage nonparametric methods originating in the machine learning community have grown in popularity. An overview of both widely used and newly emerging approaches, including support vector machines (SVMs), Gaussian mixture models, and deep learning based on convolutional neural networks is provided in Section 3.4. Strategies to exploit unlabeled samples, including active learning and metric learning, which combine feature extraction and augmentation of the pool of training samples in an active learning framework, are outlined in Section 3.5. Integration of image segmentation with classification to accommodate spatial coherence typically observed in vegetation is also explored, including as an integrated active learning system. Exploitation of multisensor strategies for augmenting the pool of training samples is investigated via a transfer learning framework in Section 3.5.1.2. Finally, we look to the future, considering opportunities soon to be provided by new paradigms, as hyperspectral sensing is becoming common at multiple scales from ground-based and airborne autonomous vehicles to manned aircraft and space-based platforms

An original framework for understanding human actions and body language by using deep neural networks

The evolution of both fields of Computer Vision (CV) and Artificial Neural Networks (ANNs) has allowed the development of efficient automatic systems for the analysis of people's behaviour. By studying hand movements it is possible to recognize gestures, often used by people to communicate information in a non-verbal way. These gestures can also be used to control or interact with devices without physically touching them. In particular, sign language and semaphoric hand gestures are the two foremost areas of interest due to their importance in Human-Human Communication (HHC) and Human-Computer Interaction (HCI), respectively. While the processing of body movements play a key role in the action recognition and affective computing fields. The former is essential to understand how people act in an environment, while the latter tries to interpret people's emotions based on their poses and movements; both are essential tasks in many computer vision applications, including event recognition, and video surveillance. In this Ph.D. thesis, an original framework for understanding Actions and body language is presented. The framework is composed of three main modules: in the first one, a Long Short Term Memory Recurrent Neural Networks (LSTM-RNNs) based method for the Recognition of Sign Language and Semaphoric Hand Gestures is proposed; the second module presents a solution based on 2D skeleton and two-branch stacked LSTM-RNNs for action recognition in video sequences; finally, in the last module, a solution for basic non-acted emotion recognition by using 3D skeleton and Deep Neural Networks (DNNs) is provided. The performances of RNN-LSTMs are explored in depth, due to their ability to model the long term contextual information of temporal sequences, making them suitable for analysing body movements. All the modules were tested by using challenging datasets, well known in the state of the art, showing remarkable results compared to the current literature methods