811 research outputs found
The Optimal Uncertainty Algorithm in the Mystic Framework
We have recently proposed a rigorous framework for Uncertainty Quantification
(UQ) in which UQ objectives and assumption/information set are brought into the
forefront, providing a framework for the communication and comparison of UQ
results. In particular, this framework does not implicitly impose inappropriate
assumptions nor does it repudiate relevant information. This framework, which
we call Optimal Uncertainty Quantification (OUQ), is based on the observation
that given a set of assumptions and information, there exist bounds on
uncertainties obtained as values of optimization problems and that these bounds
are optimal. It provides a uniform environment for the optimal solution of the
problems of validation, certification, experimental design, reduced order
modeling, prediction, extrapolation, all under aleatoric and epistemic
uncertainties. OUQ optimization problems are extremely large, and even though
under general conditions they have finite-dimensional reductions, they must
often be solved numerically. This general algorithmic framework for OUQ has
been implemented in the mystic optimization framework. We describe this
implementation, and demonstrate its use in the context of the Caltech surrogate
model for hypervelocity impact
Optimal Uncertainty Quantification
We propose a rigorous framework for Uncertainty Quantification (UQ) in which
the UQ objectives and the assumptions/information set are brought to the forefront.
This framework, which we call Optimal Uncertainty Quantification (OUQ), is based
on the observation that, given a set of assumptions and information about the problem,
there exist optimal bounds on uncertainties: these are obtained as extreme
values of well-defined optimization problems corresponding to extremizing probabilities
of failure, or of deviations, subject to the constraints imposed by the scenarios
compatible with the assumptions and information. In particular, this framework
does not implicitly impose inappropriate assumptions, nor does it repudiate relevant
information.
Although OUQ optimization problems are extremely large, we show that under
general conditions, they have finite-dimensional reductions. As an application,
we develop Optimal Concentration Inequalities (OCI) of Hoeffding and McDiarmid
type. Surprisingly, contrary to the classical sensitivity analysis paradigm, these results
show that uncertainties in input parameters do not necessarily propagate to
output uncertainties.
In addition, a general algorithmic framework is developed for OUQ and is tested
on the Caltech surrogate model for hypervelocity impact, suggesting the feasibility
of the framework for important complex systems
Optimal Uncertainty Quantification
We propose a rigorous framework for Uncertainty Quantification (UQ) in which
the UQ objectives and the assumptions/information set are brought to the
forefront. This framework, which we call \emph{Optimal Uncertainty
Quantification} (OUQ), is based on the observation that, given a set of
assumptions and information about the problem, there exist optimal bounds on
uncertainties: these are obtained as values of well-defined optimization
problems corresponding to extremizing probabilities of failure, or of
deviations, subject to the constraints imposed by the scenarios compatible with
the assumptions and information. In particular, this framework does not
implicitly impose inappropriate assumptions, nor does it repudiate relevant
information. Although OUQ optimization problems are extremely large, we show
that under general conditions they have finite-dimensional reductions. As an
application, we develop \emph{Optimal Concentration Inequalities} (OCI) of
Hoeffding and McDiarmid type. Surprisingly, these results show that
uncertainties in input parameters, which propagate to output uncertainties in
the classical sensitivity analysis paradigm, may fail to do so if the transfer
functions (or probability distributions) are imperfectly known. We show how,
for hierarchical structures, this phenomenon may lead to the non-propagation of
uncertainties or information across scales. In addition, a general algorithmic
framework is developed for OUQ and is tested on the Caltech surrogate model for
hypervelocity impact and on the seismic safety assessment of truss structures,
suggesting the feasibility of the framework for important complex systems. The
introduction of this paper provides both an overview of the paper and a
self-contained mini-tutorial about basic concepts and issues of UQ.Comment: 90 pages. Accepted for publication in SIAM Review (Expository
Research Papers). See SIAM Review for higher quality figure
Optimal uncertainty quantification for legacy data observations of Lipschitz functions
We consider the problem of providing optimal uncertainty quantification (UQ)
--- and hence rigorous certification --- for partially-observed functions. We
present a UQ framework within which the observations may be small or large in
number, and need not carry information about the probability distribution of
the system in operation. The UQ objectives are posed as optimization problems,
the solutions of which are optimal bounds on the quantities of interest; we
consider two typical settings, namely parameter sensitivities (McDiarmid
diameters) and output deviation (or failure) probabilities. The solutions of
these optimization problems depend non-trivially (even non-monotonically and
discontinuously) upon the specified legacy data. Furthermore, the extreme
values are often determined by only a few members of the data set; in our
principal physically-motivated example, the bounds are determined by just 2 out
of 32 data points, and the remainder carry no information and could be
neglected without changing the final answer. We propose an analogue of the
simplex algorithm from linear programming that uses these observations to offer
efficient and rigorous UQ for high-dimensional systems with high-cardinality
legacy data. These findings suggest natural methods for selecting optimal
(maximally informative) next experiments.Comment: 38 page
Robust Control and Monetary Policy Delegation.
This paper adapts in a simple static context the Rogoff's (1985) analysis of monetary policy delegation to a conservative central banker to the robust control framework. In this framework, uncertainty means that policymakers are unsure about their model, in the sense that there is a group of approximate models that they also consider as possibly true, and their objective is to choose a rule that will work under a range of di¤erent model specifications. We find that robustness reveals the emergence of a precautionary behaviour in the case of unstructured model uncertainty, reducing thus government's willingness to delegate monetary policy to a conservative central banker.Robust control, Monetary policy delegation, Central bank conservativeness.
Efficient Learning of Accurate Surrogates for Simulations of Complex Systems
Machine learning methods are increasingly used to build computationally
inexpensive surrogates for complex physical models. The predictive capability
of these surrogates suffers when data are noisy, sparse, or time-dependent. As
we are interested in finding a surrogate that provides valid predictions of any
potential future model evaluations, we introduce an online learning method
empowered by optimizer-driven sampling. The method has two advantages over
current approaches. First, it ensures that all turning points on the model
response surface are included in the training data. Second, after any new model
evaluations, surrogates are tested and "retrained" (updated) if the "score"
drops below a validity threshold. Tests on benchmark functions reveal that
optimizer-directed sampling generally outperforms traditional sampling methods
in terms of accuracy around local extrema, even when the scoring metric favors
overall accuracy. We apply our method to simulations of nuclear matter to
demonstrate that highly accurate surrogates for the nuclear equation of state
can be reliably auto-generated from expensive calculations using a few model
evaluations.Comment: 13 pages, 6 figures, submitted to Nature Machine Intelligenc
Monetary Policy with Uncertain Central Bank Preferences for Robustness.
In this paper,we consider the transparency of monetary policy in a New Keynesian model with misspecification doubts. Model uncertainty allows us to identify a new source of central bank opacity, which refers to a lack of information about central bank’s preference for model robustness. Thus, taking into account this lack of transparency, we study its impacts on macroeconomic variables. We show that greater transparency can reduce the variability of output gap, inflation as well as that of their expected values.
Does Model Uncertainty Lead to Less Central Bank Transparency?
This paper discusses the problem of monetary policy transparency in a simple static robust control framework. In this framework, we identify two sources of monetary policy uncertainty. First, we identify the uncertainty about the central bank’s inflation stabilization preferences, which affects the private sector’s inflation expectations and therefore the realized inflation and output. On the other hand, uncertainty means that central bank is unsure about its model, in the sense that there is a group of approximate models that it also considers as possibly true and its objective is to choose a rule that will work under a range of different model specifications. We find that robustness reveals the emergence of a precautionary behaviour of the central bank in the case of unstructured model uncertainty, reducing thus central bank’s willingness to choice a high degree of monetary policy transparency.central bank transparency, min-max policies, model uncertainty, robust control.
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