MODEL-FORM UNCERTAINTY QUANTIFICATION FOR PREDICTIVE PROBABILISTIC GRAPHICAL MODELS

In this thesis, we focus on Uncertainty Quantification and Sensitivity Analysis, which can provide performance guarantees for predictive models built with both aleatoric and epistemic uncertainties, as well as data, and identify which components in a model have the most influence on predictions of our quantities of interest. In the first part (Chapter 2), we propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, are correlated and are limited in size (small data). The proposed mathematical methodology employs gradient-based methods to compute sensitivity indices. We observe that ranking influential parameters depend critically on whether or not correlations between parameters are taken into account. The impact of uncertainty in the correlation and the necessity of the proposed non-parametric perspective are demonstrated. In the second part (Chapter 3-4), we develop new information-based uncertainty quantification and sensitivity analysis methods for Probabilistic Graphical Models. Probabilistic graphical models are an important class of methods for probabilistic modeling and inference, probabilistic machine learning, and probabilistic artificial intelligence. Its hierarchical structure allows us to bring together in a systematic way statistical and multi-scale physical modeling, different types of data, incorporating expert knowledge, correlations, and causal relationships. However, due to multi-scale modeling, learning from sparse data, and mechanisms without full knowledge, many predictive models will necessarily have diverse sources of uncertainty at different scales. The new model-form uncertainty quantification indices we developed can handle both parametric and non-parametric probabilistic graphical models, as well as small and large model/parameter perturbations in a single, unified mathematical framework and provide an envelope of model predictions for our quantities of interest. Moreover, we propose a model-form Sensitivity Index, which allows us to rank the impact of each component of the probabilistic graphical model, and provide a systematic methodology to close the experiment - model - simulation - prediction loop and improve the computational model iteratively based on our new uncertainty quantification and sensitivity analysis methods. To illustrate our ideas, we explore a physicochemical application on the Oxygen Reduction Reaction (ORR) in Chapter 4, whose optimization was identified as a key to the performance of fuel cells. In the last part (Chapter 5), we complete our discussion for the uncertainty quantification and sensitivity analysis methods on probabilistic graphical models by introducing a new sensitivity analysis method for the case where we know the real model sits in a certain parametric family. Note that the uncertainty indices above may be too pessimistic (as they are inherently non-parametric) when studying uncertainty/sensitivity questions for models confined within a given parametric family. Therefore, we develop a method using likelihood ratio and fisher information matrix, which can capture correlations and causal dependencies in the graphical models, and we show it can provide us more accurate results for the parametric probabilistic graphical models

Intelligent Breast Cancer Diagnosis with Heuristic-assisted Trans-Res-U-Net and Multiscale DenseNet using Mammogram Images

Breast cancer (BC) significantly contributes to cancer-related mortality in women, underscoring the criticality of early detection for optimal patient outcomes. A mammography is a key tool for identifying and diagnosing breast abnormalities; however, accurately distinguishing malignant mass lesions remains challenging. To address this issue, we propose a novel deep learning approach for BC screening utilizing mammography images. Our proposed model comprises three distinct stages: data collection from established benchmark sources, image segmentation employing an Atrous Convolution-based Attentive and Adaptive Trans-Res-UNet (ACA-ATRUNet) architecture, and BC identification via an Atrous Convolution-based Attentive and Adaptive Multi-scale DenseNet (ACA-AMDN) model. The hyperparameters within the ACA-ATRUNet and ACA-AMDN models are optimised using the Modified Mussel Length-based Eurasian Oystercatcher Optimization (MML-EOO) algorithm. Performance evaluation, leveraging multiple metrics, is conducted, and a comparative analysis against conventional methods is presented. Our experimental findings reveal that the proposed BC detection framework attains superior precision rates in early disease detection, demonstrating its potential to enhance mammography-based screening methodologies.Comment: 22 pages, 17 figures, 4 Tables and Appendix A: Supplementary Materia

Learning Interaction Variables and Kernels from Observations of Agent-Based Systems

Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of the state of pairs of agents. Yet, these interaction rules can generate self-organized dynamics, with complex emergent behaviors (clustering, flocking, swarming, etc.). We propose a learning technique that, given observations of states and velocities along trajectories of the agents, yields both the variables upon which the interaction kernel depends and the interaction kernel itself, in a nonparametric fashion. This yields an effective dimension reduction which avoids the curse of dimensionality from the high-dimensional observation data (states and velocities of all the agents). We demonstrate the learning capability of our method to a variety of first-order interacting systems

Weighting Function Effects in a Direct Regularization Method for Image-Guided Near-Infrared Spectral Tomography of Breast Cancer.

Structural image-guided near-infrared spectral tomography (NIRST) has been developed as a way to use diffuse NIR spectroscopy within the context of image-guided quantification of tissue spectral features. A direct regularization imaging (DRI) method for NIRST has the value of not requiring any image segmentation. Here, we present a comprehensive investigational study to analyze the impact of the weighting function implied when weighting the recovery of optical coefficients in DRI based NIRST. This was done using simulations, phantom and clinical patient exam data. Simulations where the true object is known indicate that changes to this weighting function can vary the contrast by 10%, the contrast to noise ratio by 20% and the full width half maximum (FWHM) by 30%. The results from phantoms and human images show that a linear inverse distance weighting function appears optimal, and that incorporation of this function can generally improve the recovered total hemoglobin contrast of the tumor to the normal surrounding tissue by more than 15% in human cases

Cone Beam Micro-CT System for Small Animal Imaging and Performance Evaluation

A prototype cone-beam micro-CT system for small animal imaging has been developed by our group recently, which consists of a microfocus X-ray source, a three-dimensional programmable stage with object holder, and a flat-panel X-ray detector. It has a large field of view (FOV), which can acquire the whole body imaging of a normal-size mouse in a single scan which usually takes about several minutes or tens of minutes. FDK method is adopted for 3D reconstruction with Graphics Processing Unit (GPU) acceleration. In order to reconstruct images with high spatial resolution and low artifacts, raw data preprocessing and geometry calibration are implemented before reconstruction. A method which utilizes a wire phantom to estimate the residual horizontal offset of the detector is proposed, and 1D point spread function is used to assess the performance of geometric calibration quantitatively. System spatial resolution, image uniformity and noise, and low contrast resolution have been studied. Mouse images with and without contrast agent are illuminated in this paper. Experimental results show that the system is suitable for small animal imaging and is adequate to provide high-resolution anatomic information for bioluminescence tomography to build a dual modality system

Minimizing the Bag-of-Ngrams Difference for Non-Autoregressive Neural Machine Translation

Non-Autoregressive Neural Machine Translation (NAT) achieves significant decoding speedup through generating target words independently and simultaneously. However, in the context of non-autoregressive translation, the word-level cross-entropy loss cannot model the target-side sequential dependency properly, leading to its weak correlation with the translation quality. As a result, NAT tends to generate influent translations with over-translation and under-translation errors. In this paper, we propose to train NAT to minimize the Bag-of-Ngrams (BoN) difference between the model output and the reference sentence. The bag-of-ngrams training objective is differentiable and can be efficiently calculated, which encourages NAT to capture the target-side sequential dependency and correlates well with the translation quality. We validate our approach on three translation tasks and show that our approach largely outperforms the NAT baseline by about 5.0 BLEU scores on WMT14 En$\leftrightarrow$De and about 2.5 BLEU scores on WMT16 En$\leftrightarrow$Ro.Comment: AAAI 202

Cultivation of Artificial Algal Crust and Its Effect on Soil Improvement in Sandy Area

Algae are the pioneer species of biological soil crusts. Cyanobacteria, microschwannophyta and pseudocladophyta can form fixed quicksand algae crusts on the surface of sand surface. Through artificial culture, soil crusts can be formed in a short time. The development and succession of algeal-sand crust promoted the enrichment of nutrients in the sand surface layer, and created conditions for the reproduction of micro-soil organisms and the colonization of herbaceous plants, thus promoting the desert ecosystem to enter a virtuous cycle. This chapter will focus on the cultivation process of artificial soil crust and its effect on soil improvement (soil organic matter and nitrogen) in sandy areas. In conclusion, the application of algal solution can rapidly form algal crusts, and according to the research results, the formation of algal crusts can significantly improve the chemical and biological properties of soil