Gaussian processes (GPs), implemented through multivariate Gaussian distributions for a finite collection of data, are the most popular approach in small-area spatiotemporal statistical modelling.
1 code implementation • 22 Feb 2021 • Iwona Hawryluk, Henrique Hoeltgebaum, Swapnil Mishra, Xenia Miscouridou, Ricardo P Schnekenberg, Charles Whittaker, Michaela Vollmer, Seth Flaxman, Samir Bhatt, Thomas A Mellan
An important example of this problem is the nowcasting of COVID-19 mortality: given a stream of reported counts of daily deaths, can we correct for the delays in reporting to paint an accurate picture of the present, with uncertainty?
The approach is shown to be useful in practice when applied to a real problem - to perform model selection for a semi-mechanistic hierarchical Bayesian model of COVID-19 transmission in South Korea involving the integration of a 200D density.
Structured Illumination Microscopy is a widespread methodology to image live and fixed biological structures smaller than the diffraction limits of conventional optical microscopy.
We find that linear models often outperform machine learning methods and that the quality of our predictions for any of the forecasting horizons of 1, 3 or 7 days are comparable as measured in MAE.
The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, and on a Bayesian survey design problem.
The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non parametric regression and classification.
1 code implementation • 23 Apr 2020 • Seth Flaxman, Swapnil Mishra, Axel Gandy, H Juliette T Unwin, Helen Coupland, Thomas A. Mellan, Harrison Zhu, Tresnia Berah, Jeffrey W Eaton, Pablo N P Guzman, Nora Schmit, Lucia Callizo, Imperial College COVID-19 Response Team, Charles Whittaker, Peter Winskill, Xiaoyue Xi, Azra Ghani, Christl A. Donnelly, Steven Riley, Lucy C Okell, Michaela A. C. Vollmer, Neil M. Ferguson, Samir Bhatt
Our model estimates these changes by calculating backwards from temporal data on observed to estimate the number of infections and rate of transmission that occurred several weeks prior, allowing for a probabilistic time lag between infection and death.
We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process).
While the success of deep neural networks (DNNs) is well-established across a variety of domains, our ability to explain and interpret these methods is limited.
We propose a novel approach to multimodal sentiment analysis using deep neural networks combining visual analysis and natural language processing.
While a typical supervised learning framework assumes that the inputs and the outputs are measured at the same levels of granularity, many applications, including global mapping of disease, only have access to outputs at a much coarser level than that of the inputs.
For inference, we discretize the spatiotemporal point pattern and learn a log-intensity function using the Poisson likelihood and highly efficient gradient-based optimization methods.
The use of covariance kernels is ubiquitous in the field of spatial statistics.
Distribution regression has recently attracted much interest as a generic solution to the problem of supervised learning where labels are available at the group level, rather than at the individual level.
Detecting causal associations in time series datasets is a key challenge for novel insights into complex dynamical systems such as the Earth system or the human brain.
Methodology Atmospheric and Oceanic Physics Applications
We combine fine-grained spatially referenced census data with the vote outcomes from the 2016 US presidential election.
However, we prove that the representer theorem does hold in an appropriately transformed RKHS, guaranteeing that the optimization of the penalized likelihood can be cast as a tractable finite-dimensional problem.
We summarize the potential impact that the European Union's new General Data Protection Regulation will have on the routine use of machine learning algorithms.
We tackle the problem of collaborative filtering (CF) with side information, through the lens of Gaussian Process (GP) regression.
The posterior mean of our model is closely related to recently proposed shrinkage estimators for kernel mean embeddings, while the posterior uncertainty is a new, interesting feature with various possible applications.
We present a scalable Gaussian process model for identifying and characterizing smooth multidimensional changepoints, and automatically learning changes in expressive covariance structure.