Maths Meets Stats
Abstract
Melanie Weber
Title: Geometric Methods for Machine Learning and Optimization
Abstract: A key challenge in machine learning and optimization is the identification of geometric structure in high-dimensional data. Such structural understanding is of great value for the design of efficient algorithms and for developing fundamental guarantees for their performance. Motivated by the observation that many applications involve non-Euclidean data, such as graphs, strings, or matrices, we discuss how Riemannian geometry can be exploited in Machine Learning and Optimization. First, we consider the task of learning a classifier in hyperbolic space. Such spaces have received a surge of interest for representing large-scale, hierarchical data, since they achieve better representation accuracy with fewer dimensions. Secondly, we consider the problem of optimizing a function on a Riemannian manifold. Specifically, we will consider classes of optimization problems where exploiting Riemannian geometry can deliver algorithms that are computationally superior to standard (Euclidean) approaches.
Francesca Panero
Title: A general overview of the different projects explored during my DPhil in Statistics.
Abstract: In the first half of the talk, I will present my work on statistical models for complex networks. I will propose a model to describe sparse spatial random graph underpinned by the Bayesian nonparametric theory and asymptotic properties of a more general class of these models, regarding sparsity, degree distribution and clustering coefficients.
The second half will be devoted to the statistical quantification of the risk of disclosure, a quantity used to evaluate the level of privacy that can be achieved by publishing a microdata file without modifications. I propose two ways to estimate the risk of disclosure, using both frequentist and Bayes nonparametric statistics.
Mental health and wellbeing
Abstract
*Note the different room location (L2) to usual Fridays@4 sessions*
This week is Mental Health Awareness Week. To mark this, Rebecca Reed from Siendo will deliver a session on mental health and wellbeing. The session will cover the following things:
- The importance of finding a balance with achievement and managing stress and pressure.
- Coping mechanisms work with stresses at work in a positive way (not seeing all stress as bad).
- The difficulties faced in the HE environment, such as the uncertainty felt within jobs and research, combined with the high expectations and workload.
North Meets South
Abstract
Title: Exploring the space of genes in single cell transcriptomics datasets
Abstract: Single cell transcriptomics is a revolutionary technique in biology that allows for the measurement of gene expression levels across the genome for many individual cells simultaneously. Analysis of these vast datasets reveals variations in expression patterns between cells that were previously out of reach. On top of discrete clustering into cell types, continuous patterns of variation become visible, which are associated to differentiation pathways, cell cycle, response to treatment, adaptive heterogeneity or what just whatever the cells are doing at that moment. Current methods for assigning biological meaning to single cell experiments relies on predefining groups of cells and computing what genes are differentially expressed between them. The complexity found in modern single cell transcriptomics datasets calls for more intricate methods to biologically interpret both discrete clusters as well as continuous variations. We propose topologically-inspired data analysis methods that identify coherent gene expression patterns on multiple scales in the dataset. The multiscale methods consider discrete and continuous transcriptional patterns on equal footing based on the mathematics of spectral graph theory. As well as selecting important genes, the methodology allows one to visualise and explore the space of gene expression patterns in the dataset.
CDT in Mathematics of Random Systems April Workshop 2022
Please contact @email for remote viewing details
Abstract
1:30pm Julian Meier, University of Oxford
Interacting-Particle Systems with Elastic Boundaries and Nonlinear SPDEs
We study interacting particle systems on the positive half-line. When we impose an elastic boundary at zero, the particle systems give rise to nonlinear SPDEs with irregular boundaries. We show existence and uniqueness of solutions to these equations. To deal with the nonlinearity we establish a probabilistic representation of solutions and regularity in L2.
2:15pm Dr Omer Karin, Imperial College London
Mathematical Principles of Biological Regulation
Modern research in the life sciences has developed remarkable methods to measure and manipulate biological systems. We now have detailed knowledge of the molecular interactions inside cells and the way cells communicate with each other. Yet many of the most fundamental questions (such as how do cells choose and maintain their identities? how is development coordinated? why do homeostatic processes fail in disease?) remain elusive, as addressing them requires a good understanding of complex dynamical processes. In this talk, I will present a mathematical approach for tackling these questions, which emphasises the role of control and of emergent properties. We will explore the application of this approach to various questions in biology and biomedicine, and highlight important future directions.