Gaussian Approximations of Small Noise Diffusions in Kullback-Leibler Divergence

We study Gaussian approximations to the distribution of a diffusion. The approximations are easy to compute: they are defined by two simple ordinary differential equations for the mean and the covariance. Time correlations can also be computed via solution of a linear stochastic differential equation. We show, using the Kullback-Leibler divergence, that the approximations are accurate in the small noise regime. An analogous discrete time setting is also studied. The results provide both theoretical support for the use of Gaussian processes in the approximation of diffusions, and methodological guidance in the construction of Gaussian approximations in applications

Research Priorities for Robust and Beneficial Artificial Intelligence

Success in the quest for artificial intelligence has the potential to bring unprecedented benefits to humanity, and it is therefore worthwhile to investigate how to maximize these benefits while avoiding potential pitfalls. This article gives numerous examples (which should by no means be construed as an exhaustive list) of such worthwhile research aimed at ensuring that AI remains robust and beneficial.Comment: This article gives examples of the type of research advocated by the open letter for robust & beneficial AI at http://futureoflife.org/ai-open-lette

Inverse Problems and Data Assimilation

These notes are designed with the aim of providing a clear and concise introduction to the subjects of Inverse Problems and Data Assimilation, and their inter-relations, together with citations to some relevant literature in this area. The first half of the notes is dedicated to studying the Bayesian framework for inverse problems. Techniques such as importance sampling and Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the desirable property that in the limit of an infinite number of samples they reproduce the full posterior distribution. Since it is often computationally intensive to implement these methods, especially in high dimensional problems, approximate techniques such as approximating the posterior by a Dirac or a Gaussian distribution are discussed. The second half of the notes cover data assimilation. This refers to a particular class of inverse problems in which the unknown parameter is the initial condition of a dynamical system, and in the stochastic dynamics case the subsequent states of the system, and the data comprises partial and noisy observations of that (possibly stochastic) dynamical system. We will also demonstrate that methods developed in data assimilation may be employed to study generic inverse problems, by introducing an artificial time to generate a sequence of probability measures interpolating from the prior to the posterior

Extraction and Classification of Diving Clips from Continuous Video Footage

Due to recent advances in technology, the recording and analysis of video data has become an increasingly common component of athlete training programmes. Today it is incredibly easy and affordable to set up a fixed camera and record athletes in a wide range of sports, such as diving, gymnastics, golf, tennis, etc. However, the manual analysis of the obtained footage is a time-consuming task which involves isolating actions of interest and categorizing them using domain-specific knowledge. In order to automate this kind of task, three challenging sub-problems are often encountered: 1) temporally cropping events/actions of interest from continuous video; 2) tracking the object of interest; and 3) classifying the events/actions of interest. Most previous work has focused on solving just one of the above sub-problems in isolation. In contrast, this paper provides a complete solution to the overall action monitoring task in the context of a challenging real-world exemplar. Specifically, we address the problem of diving classification. This is a challenging problem since the person (diver) of interest typically occupies fewer than 1% of the pixels in each frame. The model is required to learn the temporal boundaries of a dive, even though other divers and bystanders may be in view. Finally, the model must be sensitive to subtle changes in body pose over a large number of frames to determine the classification code. We provide effective solutions to each of the sub-problems which combine to provide a highly functional solution to the task as a whole. The techniques proposed can be easily generalized to video footage recorded from other sports.Comment: To appear at CVsports 201

Noise considerations when determining phase of large-signal microwave measurements

Advances in microwave instrumentation now make it feasible to accurately measure not only the magnitude spectrum, but also the phase spectrum of wide-bandwidth signals. In a practical measurement, the spectrum is measured over a finite window of time. The phase spectrum is related to the position of this window, causing the spectrum to differ between measurements of an identical waveform. It is difficult to compare multiple measurements with different window positions or to incorporate them into a model. Several methods have been proposed for determining the phase spectrum such that multiple measurements can be effectively compared and utilized in models. The methods are reviewed in terms of the information required to determine the phase and compared in terms of their robustness in the presence of measurement noise

Measuring plume-related exhumation of the British Isles in Early Cenozoic times

Mantle plumes have been proposed to exert a first-order control on the morphology of Earth's surface. However, there is little consensus on the lifespan of the convectively supported topography. Here, we focus on the Cenozoic uplift and exhumation history of the British Isles. While uplift in the absence of major regional tectonic activity has long been documented, the causative mechanism is highly controversial, and direct exhumation estimates are hindered by the near-complete absence of onshore post-Cretaceous sediments (outside Northern Ireland) and the truncated stratigraphic record of many offshore basins. Two main hypotheses have been developed by previous studies: epeirogenic exhumation driven by the proto-Iceland plume, or multiple phases of Cenozoic compression driven by far-field stresses. Here, we present a new thermochronological dataset comprising 43 apatite fission track (AFT) and 102 (U–Th–Sm)/He (AHe) dates from the onshore British Isles. Inverse modelling of vertical sample profiles allows us to define well-constrained regional cooling histories. Crucially, during the Paleocene, the thermal history models show that a rapid exhumation pulse (1–2.5 km) occurred, focused on the Irish Sea. Exhumation is greatest in the north of the Irish Sea region, and decreases in intensity to the south and west. The spatial pattern of Paleocene exhumation is in agreement with the extent of magmatic underplating inferred from geophysical studies, and the timing of uplift and exhumation is synchronous with emplacement of the plume-related British and Irish Paleogene Igneous Province (BIPIP). Prior to the Paleocene exhumation pulse, the Mesozoic onshore exhumation pulse is mainly linked to the uplift and erosion of the hinterland during the complex and long-lived rifting history of the neighbouring offshore basins. The extent of Neogene exhumation is difficult to constrain due to the poor sensitivity of the AHe and AFT systems at low temperatures. We conclude that the Cenozoic topographic evolution of the British Isles is the result of plume-driven uplift and exhumation, with inversion under compressive stress playing a secondary role