his talk reviews some fundamental and practical issues related to the formulation and analysis of joint models of mixed types of outcomes with latent variables, with particular emphasis on both several case-studies in applied statistics and their computational implementation

The qualitative study of PDEs often relies on integral identities and inequalities. For example, for time-dependent  PDEs, conserved integral quantities or quantities that are dissipated play an important role. In particular, if these integral quantities have a definite sign, they are of great interest as they may provide control on the solutions to establish well-posedness.

The overarching goal of Prof. Michels' Computational Sciences Group within KAUST's Visual Computing Center is enabling accurate and efficient simulations for applications in Scientific and Visual Computing. Towards this goal, the group develops new principled computational methods based on solid theoretical foundations.

Abstract

For over 30 years, Bayesian image analysis has provided an imp

Assessing the effectiveness of cancer treatments in clinical trials raises multiple methodological challenges that need to be properly addressed in order to produce a reliable estimate of treatment effects.

We consider the problem of parameter estimation for a McKean stochastic differential equation, and the associated system of weakly interacting particles. The problem is motivated by many applications in areas such as neuroscience, social sciences (opinion dynamics, cooperative behaviours), financial mathematics, statistical physics. We will first survey some model properties related to propagation of chaos and ergodicity and then move on to discuss the problem of parameter estimation both in offline and on-line settings. In the on-line case, we propose an online estimator, which evolves according to a continuous-time stochastic gradient descent algorithm on the asymptotic log-likelihood of the interacting particle system. The talk will present our convergence results and then show some numerical results for two examples, a linear mean field model and a stochastic opinion dynamics model. This is joint work with Louis Sharrock, Panos Parpas and Greg Pavliotis. Preprint: https://arxiv.org/abs/2106.13751

We develop a data-driven methodology based on parametric Itô's Stochastic Differential Equations (SDEs) to capture forecast errors' asymmetric dynamics, including the forecast's uncertainty at time zero.

Despite the recent advances in big data processing, enabled by the emergence of large-scale machine learning techniques, several statistical questions regarding the behavior in the regime of high dimensions of well-established and fundamental methods have remained unresolved.

Often in the context of data centric science and engineering applications, one endeavours to learn complex systems in order to make more informed predictions and high stakes decisions under uncertainty. Some key challenges which must be met in this context are robustness, generalizability, and interpretability.

The talk will present our efforts to develop the next generation operational systems for the Red Sea and the Arabian Gulf, as part of Aramco’s resolution toward the Fourth Industrial Revolution. These integrated systems, we refer to as iReds and iGulf, have been built around state-of-the-art ocean-atmosphere-wave general circulation models that have been specifically developed for the region and nested within the global weather systems.

As a fundamental problem in both machine learning and privacy, Empirical Risk Minimization in the Differential Privacy Model (DP-ERM) received much attentions. However, most of the previous studies are either in the central DP model or interactive LDP model. In this talk, I will discuss some recent developments of DP-ERM in the non-interactive LDP model.

Modeling, estimation and prediction of spatial extremes is key for risk assessment in a wide range of geo-environmental, geo-physical, and climate science applications. In this work, we propose a flexible approach for modeling and estimating extreme sea surface temperature (SST) hotspots, i.e., high threshold exceedance regions, for the whole Red Sea, a vital region of high biodiversity.

We consider statistical inference for a class of agent-based SIS and SIR models. In these models, agents infect one another according to random contacts made over a social network, with an infection rate that depends on individual attributes. Infected agents might recover according to another random mechanism that also depends on individual attributes, and observations might involve occasional noisy measurements of the number of infected agents. Likelihood-based inference for such models presents various computational challenges. In this talk, I will present various sequential Monte Carlo algorithms to address these challenges.

In this talk, I will describe three use cases that highlight present challenges and opportunities for the development of machine learning methodology for applications in healthcare. First, I will describe the development of simple word embedding approaches for bag of-documents classification and its applications to diagnosis of peripheral artery disease from clinical narratives. Second, I will present an approach for volumetric image classification that leverages attention mechanisms, contrastive learning and feature-encoding sharing for geographic atrophy prognosis from optical coherence tomography images. Third, I will discuss machine learning approaches for multi-modal and multi-dataset integration for biomarker discovery from molecular (omics) data. To conclude, I will summarize the contributions and insights in each of these different directions in which relatively low sample sizes are the common denominator.

In geostatistical analysis, we are faced with the formidable challenge of specifying a valid spatio-temporal covariance function, either directly or through the construction of processes. This task is difficult as these functions should yield positive definite covariance matrices. In recent years, we have seen a flourishing of methods and theories on constructing spatio-temporal covariance functions satisfying the positive definiteness requirement. The current state-of-the-art when modeling environmental processes are those that embed the associated physical laws of the system. The class of Lagrangian spatio-temporal covariance functions fulfills this requirement. Moreover, this class possesses the allure that they turn already established purely spatial covariance functions into spatio-temporal covariance functions by a direct application of the concept of Lagrangian reference frame. In this dissertation, several developments are proposed and new features are provided to this special class.

Due essentially to the difficulties associated with obtaining explicit forms of stationary marginal distributions of non-linear stationary processes, appropriate characterizations of such processes are worked upon little. After discussing an elaborate motivation behind this thesis and presenting preliminaries in Chapter 1, we characterize, in Chapter 2, the stationary marginal distributions of certain non-linear multivariate stationary processes. To do so, we show that the stationary marginal distributions of these processes belong to specific skew-distribution families, and for a given skew-distribution from the corresponding family, a process, with stationary marginal distribution identical to that given skew-distribution, can be found.

The modeling of spatio-temporal and multivariate spatial random fields has been an important and growing area of research due to the increasing availability of space-time-referenced data in a large number of scientific applications. In geostatistics, the covariance function plays a crucial role in describing the spatio-temporal dependence in the data and is key to statistical modeling, inference, stochastic simulation, and prediction. Therefore, the development of flexible covariance models, which can accommodate the inherent variability of the real data, is necessary for advantageous modeling of random fields. This thesis is composed of four significant contributions in the development and applications of new covariance models for stationary multivariate spatial processes, and nonstationary spatial and spatio-temporal processes. Firstly, this thesis proposes a semiparametric approach for multivariate covariance function estimation with flexible specification of the cross-covariance functions via their spectral representations. The flexibility in the proposed cross-covariance function arises due to B-spline based specification of the underlying coherence functions, which in turn allows for capturing non-trivial cross-spectral features. The proposed method is applied to model and predict the bivariate data of particulate matter concentration and wind speed in the United States. Secondly, this thesis introduces a parametric class of multivariate covariance functions with asymmetric cross-covariance functions. The proposed covariance model is applied to analyze the asymmetry and perform prediction in a trivariate data of particulate matter concentration, wind speed and relative humidity in the United States.
 Thirdly, the thesis presents a space deformation method which imparts nonstationarity to any stationary covariance function. The proposed method utilizes the functional data registration algorithm and classical multidimensional scaling to estimate the spatial deformation. The application of the proposed method is demonstrated on precipitation data from Colorado, United States. Finally, this thesis proposes a parametric class of time-varying spatio-temporal covariance functions, which are stationary in space but nonstationary in time. The proposed time-varying spatio-temporal covariance model is applied to study the seasonality effect and perform space-time predictions in the daily particulate matter concentration data from Oregon, United States.

Abstract

As simulation and analytics enter the exascale era, numerical algorithms must span a wide

Explosive volcanic eruptions are magnificent events that in many ways affect the Earth’s natural processes and climate. They cause sporadic perturbations of the planet’s energy balance, activating complex climate feedbacks and providing unique opportunities to better quantify those processes. We know that explosive eruptions cause cooling in the atmosphere for a few years, but we have just recently realized that they affect the major climate variability modes and volcanic signals can be seen in the subsurface ocean for decades. The volcanic forcing of the previous two centuries offsets the ocean heat uptake and diminishes global warming by about 30%. In the future, explosive volcanism could slightly delay the pace of global warming and has to be accounted for in long-term climate predictions. The recent interest in dynamic, microphysical, chemical and climate impacts of volcanic eruptions is also excited by the fact these impacts provide a natural analog for climate geoengineering schemes involving the deliberate development of an artificial aerosol layer in the lower stratosphere to counteract global warming. In this talk, I will discuss these recently discovered volcanic effects and specifically pay attention to how we can learn about the hidden Earth-system mechanisms activated by explosive volcanic eruptions.

In low-resource settings, disease registries do not exist, and prevalence mapping relies on data collected form surveys of disease prevalence taken in a sample of the communities at risk within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model, Yᵢ ~ Binomial(mᵢ; P(xᵢ)) log [P(x)/{(1- P(xᵢ)}] = d(x)β + S(x), where Yᵢ is the number of positives in a sample of mi individuals at location xᵢ, d(x) is a vector of spatially referenced explanatory variables available at any location x within the region of interest, and S(x) is a Gaussian process.

In this talk, I will first review statistical methods and software associated with this standard model, then consider several methodological extensions and their applications to some Africa-wide control programmes for Neglected Tropical Diseases to demonstrate the very substantial gains in efficiency that can be obtained by comparison with currently used methods.

We develop several new communication-efficient second-order methods for distributed optimization. Our first method, NEWTON-STAR, is a variant of Newton's method from which it inherits its fast local quadratic rate. However, unlike Newton's method, NEWTON-STAR enjoys the same per iteration communication cost as gradient descent. While this method is impractical as it relies on the use of certain unknown parameters characterizing the Hessian of the objective function at the optimum, it serves as the starting point which enables us to design practical variants thereof with strong theoretical guarantees. In particular, we design a stochastic sparsification strategy for learning the unknown parameters in an iterative fashion in a communication efficient manner. Applying this strategy to NEWTON-STAR leads to our next method, NEWTON-LEARN, for which we prove local linear and superlinear rates independent of the condition number. When applicable, this method can have dramatically superior convergence behavior when compared to state-of-the-art methods. Finally, we develop a globalization strategy using cubic regularization which leads to our next method, CUBIC-NEWTON-LEARN, for which we prove global sublinear and linear convergence rates, and a fast superlinear rate. Our results are supported with experimental results on real datasets, and show several orders of magnitude improvement on baseline and state-of-the-art methods in terms of communication complexity.

COVID-19 has caused a global pandemic and become the most urgent threat to the entire world. Tremendous efforts and resources have been invested in developing diagnosis. Despite the various, urgent advances in developing artificial intelligence (AI)-based computer-aided systems for CT-based COVID-19 diagnosis, most of the existing methods can only perform classification, whereas the state-of-the-art segmentation method requires a high level of human intervention. In this talk, I will introduce our recent work on a fully-automatic, rapid, accurate, and machine-agnostic method that can segment and quantify the infection regions on CT scans from different sources. Our method is founded upon three innovations: 1) an embedding method that projects any arbitrary CT scan to a same, standard space, so that the trained model becomes robust and generalizable; 2) the first CT scan simulator for COVID-19, by fitting the dynamic change of real patients’ data measured at different time points, which greatly alleviates the data scarcity issue; and 3) a novel deep learning algorithm to solve the large-scene-small-object problem, which decomposes the 3D segmentation problem into three 2D ones, and thus reduces the model complexity by an order of magnitude and, at the same time, significantly improves the segmentation accuracy. Comprehensive experimental results over multi-country, multi-hospital, and multi-machine datasets demonstrate the superior performance of our method over the existing ones and suggest its important application value in combating the disease.

Wave functional materials are artificial materials that can control wave propagation as wish. In this talk, I will give a brief review on the progress of wave functional materials and reveal the secret behind the engineering of these materials to achieve desired properties. In particular, I will focus on our contributions on metamaterials and metasurfaces. I will introduce the development of effective medium, a powerful tool in modeling wave functional materials, followed by some illustrative examples demonstrating the intriguing properties, such as redirection, emission rate enhancement, wave steering and cloaking.

In modern large-scale inference problems, the dimension of the signal to be estimated is comparable or even larger than the number of available observations. Yet the signal of interest lies in some low-dimensional structure, due to sparsity, low-rankness, finite alphabet, ... etc. Non-smooth regularized convex optimization are powerful tools for the recovery of such structured signals from noisy linear measurements. Research has shifted recently to the performance analysis of these optimization tools and optimal turning of their hyper-parameters in high dimensional settings. One powerful performance analysis framework is the Convex Gaussian Min-max Theorem (CGMT). The CGMT is based on Gaussian process methods and is a strong and tight version of the classical Gordon comparison inequality. In this talk, we review the CGMT and illustrate its application to the error analysis of some convex regularized optimization problems.

Small-scale cut and fold patterns imposed on sheet material enable its morphing into three-dimensional shapes. This manufacturing paradigm has received much attention in recent years and poses challenges in both fabrication and computation. It is intimately connected with the interpretation of patterned sheets as mechanical metamaterials, typically of negative Poisson ratio. We discuss a fundamental geometric question, namely the targeted programming of a shape morph from a flat sheet to a curved surface, or even between any two shapes. The solution draws on differential geometry, discrete differential geometry, geometry processing and geometric optimization.