Talay M Cheema
I am a first year PhD student supervised by Prof Carl Rasmussen. I completed my undergraduate degree (MEng, BA) here at Cambridge University Engineering Department in 2017, and am affiliated with Churchill college.
My research interests are in Bayesian inference in non-linear time series models.
Publications
Understanding Local Linearisation in Variational Gaussian Process State Space Models
Talay M Cheema, 2021. (In Time Series Workshop at the 38th International Conference on Machine Learning).
Abstract▼ URL
We describe variational inference approaches in Gaussian process state space models in terms of local linearisations of the approximate posterior function. Most previous approaches have either assumed independence between the posterior dynamics and latent states (the mean-field (MF) approximation), or optimised free parameters for both, leading to limited scalability. We use our framework to prove that (i) there is a theoretical imperative to use non-MF approaches, to avoid excessive bias in the process noise hyperparameter estimate, and (ii) we can parameterise only the posterior dynamics without any less of performance. Our approach suggests further approximations, based on the existing rich literature on filtering and smoothing for nonlinear systems, and unifies approaches for discrete and continuous time models.
Contrasting Discrete and Continuous Methods for Bayesian System Identification
Talay M Cheema, 2022. (In Workshop on Continuous Time Machine Learning at the 39th International Conference on Machine Learning).
Abstract▼ URL
In recent years, there has been considerable interest in embedding continuous time methods in machine learning algorithms. In system identification, the task is to learn a dynamical model from incomplete observation data, and when prior knowledge is in continuous time – for example, mechanistic differential equation models – it seems natural to use continuous time models for learning. Yet when learning flexible, nonlinear, probabilistic dynamics models, most previous work has focused on discrete time models to avoid computational, numerical, and mathematical difficulties. In this work we show, with the aid of small-scale examples, that this mismatch between model and data generating process can be consequential under certain circumstances, and we discuss possible modifications to discrete time models which may better suit them to handling data generated by continuous time processes.
Kernel Learning for Explainable Climate Science
Vidhi Lalchand, Kenza Tazi, Talay M Cheema, Richard E Turner, Scott Hosking, 2022. (In 16th Bayesian Modelling Applications Workshop at UAI, 2022).
Abstract▼ URL
The Upper Indus Basin, Himalayas provides water for 270 million people and countless ecosystems. However, precipitation, a key component to hydrological modelling, is poorly understood in this area. A key challenge surrounding this uncertainty comes from the complex spatial-temporal distribution of precipitation across the basin. In this work we propose Gaussian processes with structured non-stationary kernels to model precipitation patterns in the UIB. Previous attempts to quantify or model precipitation in the Hindu Kush Karakoram Himalayan region have often been qualitative or include crude assumptions and simplifications which cannot be resolved at lower resolutions. This body of research also provides little to no error propagation. We account for the spatial variation in precipitation with a non-stationary Gibbs kernel parameterised with an input dependent lengthscale. This allows the posterior function samples to adapt to the varying precipitation patterns inherent in the distinct underlying topography of the Indus region. The input dependent lengthscale is governed by a latent Gaussian process with a stationary squared-exponential kernel to allow the function level hyperparameters to vary smoothly. In ablation experiments we motivate each component of the proposed kernel by demonstrating its ability to model the spatial covariance, temporal structure and joint spatio-temporal reconstruction. We benchmark our model with a stationary Gaussian process and a Deep Gaussian processes.