15 research outputs found
Bayesian Variational Time-lapse Full-waveform Inversion
Time-lapse seismic full-waveform inversion (FWI) provides estimates of
dynamic changes in the subsurface by performing multiple seismic surveys at
different times. Since FWI problems are highly non-linear and non-unique, it is
important to quantify uncertainties in such estimates to allow robust decision
making. Markov chain Monte Carlo (McMC) methods have been used for this
purpose, but due to their high computational cost, those studies often require
an accurate baseline model and estimates of the locations of potential velocity
changes, and neglect uncertainty in the baseline velocity model. Such detailed
and accurate prior information is not always available in practice.
In this study we use an efficient optimization method called stochastic Stein
variational gradient descent (sSVGD) to solve time-lapse FWI problems without
assuming such prior knowledge, and to estimate uncertainty both in the baseline
velocity model and the velocity change. We test two Bayesian strategies:
separate Bayesian inversions for each seismic survey, and a single join
inversion for baseline and repeat surveys, and compare the methods with the
standard linearised double difference inversion. The results demonstrate that
all three methods can produce accurate velocity change estimates in the case of
having fixed (exactly repeatable) acquisition geometries, but that the two
Bayesian methods generate more accurate results when the acquisition geometry
changes between surveys. Furthermore the joint inversion provides the most
accurate velocity change and uncertainty estimates in all cases. We therefore
conclude that Bayesian time-lapse inversion, especially adopting a joint
inversion strategy, may be useful to image and monitor the subsurface changes,
in particular where uncertainty in the results might lead to significantly
different decisions
3D Bayesian Variational Full Waveform Inversion
Seismic full-waveform inversion (FWI) provides high resolution images of the
subsurface by exploiting information in the recorded seismic waveforms. This is
achieved by solving a highly nonnlinear and nonunique inverse problem. Bayesian
inference is therefore used to quantify uncertainties in the solution.
Variational inference is a method that provides probabilistic, Bayesian
solutions efficiently using optimization. The method has been applied to 2D FWI
problems to produce full Bayesian posterior distributions. However, due to
higher dimensionality and more expensive computational cost, the performance of
the method in 3D FWI problems remains unknown. We apply three variational
inference methods to 3D FWI and analyse their performance. Specifically we
apply automatic differential variational inference (ADVI), Stein variational
gradient descent (SVGD) and stochastic SVGD (sSVGD), to a 3D FWI problem, and
compare their results and computational cost. The results show that ADVI is the
most computationally efficient method but systematically underestimates the
uncertainty. The method can therefore be used to provide relatively rapid but
approximate insights into the subsurface together with a lower bound estimate
of the uncertainty. SVGD demands the highest computational cost, and still
produces biased results. In contrast, by including a randomized term in the
SVGD dynamics, sSVGD becomes a Markov chain Monte Carlo method and provides the
most accurate results at intermediate computational cost. We thus conclude that
3D variational full-waveform inversion is practically applicable, at least in
small problems, and can be used to image the Earth's interior and to provide
reasonable uncertainty estimates on those images
Adversarial Machine Learning: Bayesian Perspectives
Adversarial Machine Learning (AML) is emerging as a major field aimed at
protecting machine learning (ML) systems against security threats: in certain
scenarios there may be adversaries that actively manipulate input data to fool
learning systems. This creates a new class of security vulnerabilities that ML
systems may face, and a new desirable property called adversarial robustness
essential to trust operations based on ML outputs. Most work in AML is built
upon a game-theoretic modelling of the conflict between a learning system and
an adversary, ready to manipulate input data. This assumes that each agent
knows their opponent's interests and uncertainty judgments, facilitating
inferences based on Nash equilibria. However, such common knowledge assumption
is not realistic in the security scenarios typical of AML. After reviewing such
game-theoretic approaches, we discuss the benefits that Bayesian perspectives
provide when defending ML-based systems. We demonstrate how the Bayesian
approach allows us to explicitly model our uncertainty about the opponent's
beliefs and interests, relaxing unrealistic assumptions, and providing more
robust inferences. We illustrate this approach in supervised learning settings,
and identify relevant future research problems
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Stein variational gradient descent: Many-particle and long-time asymptotics
Stein variational gradient descent (SVGD) refers to a class of methods for Bayesian inference based on interacting particle systems. In this paper, we consider the originally proposed deterministic dynamics as well as a stochastic variant, each of which represent one of the two main paradigms in Bayesian computational statistics: emphvariational inference and emphMarkov chain Monte Carlo. As it turns out, these are tightly linked through a correspondence between gradient flow structures and large-deviation principles rooted in statistical physics. To expose this relationship, we develop the cotangent space construction for the Stein geometry, prove its basic properties, and determine the large-deviation functional governing the many-particle limit for the empirical measure. Moreover, we identify the emphStein-Fisher information (or emphkernelised Stein discrepancy) as its leading order contribution in the long-time and many-particle regime in the sense of -convergence, shedding some light on the finite-particle properties of SVGD. Finally, we establish a comparison principle between the Stein-Fisher information and RKHS-norms that might be of independent interest