Eigenvalue problems arising from partial differential equations are used to model several applications in science and engineering, ranging from vibrations of structures, industrial microwaves, photonic crystals, and waveguides, to particle accelerators.

Dynamic programming is an efficient technique to solve optimization problems. It is based on decomposing the initial problem into simpler ones and solving these sub-problems beginning from the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects.

Random fields are popular models in statistics and machine learning for spatially dependent data on Euclidian domains. However, in many applications, data is observed on non-Euclidian domains such as street networks. In this case, it is much more difficult to construct valid random field models. In this talk, we discuss some recent approaches to modeling data in this setting, and in particular define a new class of Gaussian processes on compact metric graphs.

In this talk, I will first give an elementary introduction to basic deep learning models and training algorithms from a scientific computing viewpoint. Using image classification as an example, I will try to give mathematical explanations of why and how some popular deep learning models such as convolutional neural network (CNN) work. Most of the talk will be assessable to an audience who have basic knowledge of calculus and matrix. Toward the end of the talk, I will touch upon some advanced topics to demonstrate the potential of new mathematical insights for helping understand and improve the efficiency of deep learning technologies.

No abstract is available.

No abstract is available.

Tile low-rank and hierarchical low-rank matrices can exploit the data sparsity that is discoverable all across computational science. We illustrate in large-scale applications and hybridize with similarly motivated mixed precision representations while featuring ECRC research in progress with many collaborators.

In this section, prof. Gabriel will be introducing the graduate seminar and its requirements.

Federated learning (FL) is an emerging machine learning paradigm involving multiple clients, e.g., mobile phone devices, with an incentive to collaborate in solving a machine learning problem coordinated by a central server. FL was proposed in 2016 by Konecny et al. and McMahan et al. as a viable privacy-preserving alternative to traditional centralized machine learning since, by construction, the training data points are decentralized and never transferred by the clients to a central server. Therefore, to a certain degree, FL mitigates the privacy risks associated with centralized data collection. Unfortunately, optimization for FL faces several specific issues that centralized optimization usually does not need to handle. In this thesis, we identify several of these challenges and propose new methods and algorithms to address them, with the ultimate goal of enabling practical FL solutions supported with mathematically rigorous guarantees.

Bayesian inference is particularly challenging on hierarchical statistical models as computational complexity becomes a significant issue. Sampling-based methods like the popular Markov Chain Monte Carlo (MCMC) can provide accurate solutions, but they likely suffer a high computational burden.

We investigate privacy aspects of tests for symmetry equivalence null hypotheses. Specifically, we consider weighted L2 type tests as well as chi-squared type tests for multivariate symmetry based on the characteristic function, and their privacy properties are specifically quantified within the context of differential privacy. We consider both the case of known centre as well as tests for symmetry about an unknown centre.

During the first part of the talk we present an approach that allows for flexible analysis of multivariate non-stationary time series via dynamic models on the partial autocorrelation domain. We discuss various aspects of these models, including the use of shrinkage priors to deal with overfitting issues, as well as hierarchical extensions.

Geometry plays an important role in the design and fabrication of so-called freeform shapes. This talk will illustrate the fruitful interplay between theory and applications in this area. The focus will be on discrete differential geometry and on applications in architecture and fabrication-aware design.

In the first part of this lecture we present a review dynamic linear models for multivariate time series and hierarchical dynamic linear models for multiple time series. Topics related to model building as well as closed form, approximate and simulation-based methods for Bayesian filtering, smoothing and forecasting within these classes of models will be discussed.

We present a framework for non-Gaussian spatial processes that encompasses large distribution families. Spatial dependence for a set of irregularly scattered locations is described with a mixture of pairwise kernels. Focusing on the nearest neighbors of a given location, within a reference set, we obtain a valid spatial process:

We discuss conditionally Gaussian dynamic linear models for analysis and forecasting of univariate time series and present simulation-based methods for Bayesian filtering and smoothing within this class of models, including Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods.

We will start by presenting the general framework of Bayesian hierarchical dynamic models (BHDM) for space-time data. Within this framework, we will consider in some detail the special case of linear dynamics. We will review MCMC estimation for conditionally linear dynamic models. We will introduce integro-differential models and give a SPDE justification that provides insights into the connections between the dynamics of the process and the properties of the kernel defining the IDE.

In this lecture we present an overview of dynamic linear models for analysis and forecasting of univariate time series. We will discuss principles for model building and methods for Bayesian filtering, smoothing and forecasting. We will illustrate the use of these models in several case studies arising in different applied areas including environmental sciences and neuroscience.

Continuing on with Lecture 1, this short course introduces various cutting-edge methods that handle survival outcome data with ultrahigh dimensional predictors, that is, when the dimension of predictors is much higher than the sample size. We will also discuss several new methods for quantifying the uncertainty of estimates in a high dimensional survival setting, a very active area in machine learning.

Though Gaussian graphical  models have been widely used in many scientific fields, relatively limited progress has been made to link graph structures to external covariates. We propose a Gaussian graphical regression model, which regresses both the mean and the precision matrix of a Gaussian graphical model on covariates. In the context of co-expression quantitative trait locus (QTL) studies, our method can determine how genetic variants and clinical conditions modulate the subject-level network structures, and recover both the population-level and subject-level gene networks.

Mixing is a key process in a wide variety of technological applications. Pharmaceuticals, consumer products, and oil & gas derivatives, among many other products, rely on an energy-efficient, robust and effective mixing process. We will formulate the mixing process as a PDE-constrained optimization problem using special norms that concentrate on the mixedness of a passive scalar transported by nonlinear governing equations.

In the era of biomedical big data, survival outcome data with high-throughput predictors are routinely collected. These high dimensional data defy classical survival regression models, which are either infeasible to fit or likely to incur low predictability because of overfitting. This short course will introduce the basic concepts of survival analysis and various cutting-edge methods that handle survival outcome data with high dimensional predictors. I will cover statistical principles and concepts behind the methods, and will also discuss their applications to the real medical examples.

A personal presentation describing current “data analysis / statistical” challenges in state-of-the art biomedical projects. First, I will provide an overview of the transition between a PhD in Mathematics to a postdoc in Computational Biology: How did it happen? What were the challenges? Secondly, I will briefly present several current case-studies where statistics and machine learning are core to understand novel biological data related to multi-omic data analysis, spatial profiling, gene therapy and more.

Randomized experiments are the gold standard for causal inference. In experiments, usually, one variable is manipulated and its effect is measured on an outcome. However, practitioners may also be interested in the effect of simultaneous interventions on multiple covariates on a fixed target variable.

Two or multiple phases in fluid mixture commonly occur in petroleum industry, where oil, gas and water are often produced and transported together.  Petroleum reservoir engineers spent great efforts in drainage problems arising from the development and production of oil and gas reservoirs so as to obtain a high economic recovery, by developing, conducting, and interpolating the simulation of subsurface flows of reservoir fluids, including water, hydrocarbon, CO2, H2S for example in porous geological formation.