We study the community detection problem on a Gaussian mixture model, in which (1) vertices are divided into $k\geq 2$ distinct communities that are not necessarily equally-sized; (2) the Gaussian perturbations for different entries in the observation matrix are not necessarily independent or identically distributed. We prove necessary and sufficient conditions for the exact recovery of the maximum likelihood estimation (MLE), and discuss the cases when these necessary and sufficient conditions give sharp threshold. Applications include the community detection on a graph where the Gaussian perturbations of observations on each edge is the sum of i.i.d.~Gaussian random variables on its end vertices, in which we explicitly obtain the threshold for the exact recovery of the MLE.

Recently, hyperspectral imaging (HSI) has attracted increasing research attention, especially for the ones based on a coded aperture snapshot spectral imaging (CASSI) system. Existing deep HSI reconstruction models are generally trained on paired data to retrieve original signals upon 2D compressed measurements given by a particular optical hardware mask in CASSI, during which the mask largely impacts the reconstruction performance and could work as a "model hyperparameter" governing on data augmentations. This mask-specific training style will lead to a hardware miscalibration issue, which sets up barriers to deploying deep HSI models among different hardware and noisy environments. To address this challenge, we introduce mask uncertainty for HSI with a complete variational Bayesian learning treatment and explicitly model it through a mask decomposition inspired by real hardware. Specifically, we propose a novel Graph-based Self-Tuning (GST) network to reason uncertainties adapting to varying spatial structures of masks among different hardware. Moreover, we develop a bilevel optimization framework to balance HSI reconstruction and uncertainty estimation, accounting for the hyperparameter property of masks. Extensive experimental results and model discussions validate the effectiveness (over 33/30 dB) of the proposed GST method under two miscalibration scenarios and demonstrate a highly competitive performance compared with the state-of-the-art well-calibrated methods. Our code and pre-trained model are available at https://github.com/Jiamian-Wang/mask_uncertainty_spectral_SCI

Applied mathematics and machine computations have raised a lot of hope since the recent success of supervised learning. Many practitioners in industries have been trying to switch from their old paradigms to machine learning. Interestingly, those data scientists spend more time scrapping, annotating and cleaning data than fine-tuning models. This thesis is motivated by the following question: can we derive a more generic framework than the one of supervised learning in order to learn from clutter data? This question is approached through the lens of weakly supervised learning, assuming that the bottleneck of data collection lies in annotation. We model weak supervision as giving, rather than a unique target, a set of target candidates. We argue that one should look for an ``optimistic'' function that matches most of the observations. This allows us to derive a principle to disambiguate partial labels. We also discuss the advantage to incorporate unsupervised learning techniques into our framework, in particular manifold regularization approached through diffusion techniques, for which we derived a new algorithm that scales better with input dimension then the baseline method. Finally, we switch from passive to active weakly supervised learning, introducing the ``active labeling'' framework, in which a practitioner can query weak information about chosen data. Among others, we leverage the fact that one does not need full information to access stochastic gradients and perform stochastic gradient descent.

The rapid progress in clinical data management systems and artificial intelligence approaches enable the era of personalized medicine. Intensive care units (ICUs) are the ideal clinical research environment for such development because they collect many clinical data and are highly computerized environments. We designed a retrospective clinical study on a prospective ICU database using clinical natural language to help in the early diagnosis of heart failure in critically ill children. The methodology consisted of empirical experiments of a learning algorithm to learn the hidden interpretation and presentation of the French clinical note data. This study included 1386 patients' clinical notes with 5444 single lines of notes. There were 1941 positive cases (36 % of total) and 3503 negative cases classified by two independent physicians using a standardized approach. The multilayer perceptron neural network outperforms other discriminative and generative classifiers. Consequently, the proposed framework yields an overall classification performance with 89 % accuracy, 88 % recall, and 89 % precision. This study successfully applied learning representation and machine learning algorithms to detect heart failure from clinical natural language in a single French institution. Further work is needed to use the same methodology in other institutions and other languages.

Over the last ten years, we have seen a significant increase in industrial data, tremendous improvement in computational power, and major theoretical advances in machine learning. This opens up an opportunity to use modern machine learning tools on large-scale nonlinear monitoring and control problems. This article provides a survey of recent results with applications in the process industry.

This paper presents recent methodological advances to perform simulation-based inference (SBI) of a general class of Bayesian hierarchical models (BHMs), while checking for model misspecification. Our approach is based on a two-step framework. First, the latent function that appears as second layer of the BHM is inferred and used to diagnose possible model misspecification. Second, target parameters of the trusted model are inferred via SBI. Simulations used in the first step are recycled for score compression, which is necessary to the second step. As a proof of concept, we apply our framework to a prey-predator model built upon the Lotka-Volterra equations and involving complex observational processes.

Multiclass probability estimation is the problem of estimating conditional probabilities of a data point belonging to a class given its covariate information. It has broad applications in statistical analysis and data science. Recently a class of weighted Support Vector Machines (wSVMs) has been developed to estimate class probabilities through ensemble learning for $K$-class problems (Wu, Zhang and Liu, 2010; Wang, Zhang and Wu, 2019), where $K$ is the number of classes. The estimators are robust and achieve high accuracy for probability estimation, but their learning is implemented through pairwise coupling, which demands polynomial time in $K$. In this paper, we propose two new learning schemes, the baseline learning and the One-vs-All (OVA) learning, to further improve wSVMs in terms of computational efficiency and estimation accuracy. In particular, the baseline learning has optimal computational complexity in the sense that it is linear in $K$. Though not being most efficient in computation, the OVA offers the best estimation accuracy among all the procedures under comparison. The resulting estimators are distribution-free and shown to be consistent. We further conduct extensive numerical experiments to demonstrate finite sample performance.

Leak detection in gas pipelines is an important and persistent problem in the Oil and Gas industry. This is particularly important as pipelines are the most common way of transporting natural gas. This research aims to study the ability of data-driven intelligent models to detect small leaks for a natural gas pipeline using basic operational parameters and then compare the intelligent models among themselves using existing performance metrics. This project applies the observer design technique to detect leaks in natural gas pipelines using a regressoclassification hierarchical model where an intelligent model acts as a regressor and a modified logistic regression model acts as a classifier. Five intelligent models (gradient boosting, decision trees, random forest, support vector machine and artificial neural network) are studied in this project using a pipeline data stream of four weeks. The results shows that while support vector machine and artificial neural networks are better regressors than the others, they do not provide the best results in leak detection due to their internal complexities and the volume of data used. The random forest and decision tree models are the most sensitive as they can detect a leak of 0.1% of nominal flow in about 2 hours. All the intelligent models had high reliability with zero false alarm rate in testing phase. The average time to leak detection for all the intelligent models was compared to a real time transient model in literature. The results show that intelligent models perform relatively well in the problem of leak detection. This result suggests that intelligent models could be used alongside a real time transient model to significantly improve leak detection results.

Various structures in human physiology follow a treelike morphology, which often expresses complexity at very fine scales. Examples of such structures are intrathoracic airways, retinal blood vessels, and hepatic blood vessels. Large collections of 2D and 3D images have been made available by medical imaging modalities such as magnetic resonance imaging (MRI), computed tomography (CT), Optical coherence tomography (OCT) and ultrasound in which the spatial arrangement can be observed. Segmentation of these structures in medical imaging is of great importance since the analysis of the structure provides insights into disease diagnosis, treatment planning, and prognosis. Manually labelling extensive data by radiologists is often time-consuming and error-prone. As a result, automated or semi-automated computational models have become a popular research field of medical imaging in the past two decades, and many have been developed to date. In this survey, we aim to provide a comprehensive review of currently publicly available datasets, segmentation algorithms, and evaluation metrics. In addition, current challenges and future research directions are discussed.

Most of the popular Big Data analytics tools evolved to adapt their working environment to extract valuable information from a vast amount of unstructured data. The ability of data mining techniques to filter this helpful information from Big Data led to the term Big Data Mining. Shifting the scope of data from small-size, structured, and stable data to huge volume, unstructured, and quickly changing data brings many data management challenges. Different tools cope with these challenges in their own way due to their architectural limitations. There are numerous parameters to take into consideration when choosing the right data management framework based on the task at hand. In this paper, we present a comprehensive benchmark for two widely used Big Data analytics tools, namely Apache Spark and Hadoop MapReduce, on a common data mining task, i.e., classification. We employ several evaluation metrics to compare the performance of the benchmarked frameworks, such as execution time, accuracy, and scalability. These metrics are specialized to measure the performance for classification task. To the best of our knowledge, there is no previous study in the literature that employs all these metrics while taking into consideration task-specific concerns. We show that Spark is 5 times faster than MapReduce on training the model. Nevertheless, the performance of Spark degrades when the input workload gets larger. Scaling the environment by additional clusters significantly improves the performance of Spark. However, similar enhancement is not observed in Hadoop. Machine learning utility of MapReduce tend to have better accuracy scores than that of Spark, like around 3%, even in small size data sets.