33,625 research outputs found
Simulation-based optimal Bayesian experimental design for nonlinear systems
The optimal selection of experimental conditions is essential to maximizing
the value of data for inference and prediction, particularly in situations
where experiments are time-consuming and expensive to conduct. We propose a
general mathematical framework and an algorithmic approach for optimal
experimental design with nonlinear simulation-based models; in particular, we
focus on finding sets of experiments that provide the most information about
targeted sets of parameters.
Our framework employs a Bayesian statistical setting, which provides a
foundation for inference from noisy, indirect, and incomplete data, and a
natural mechanism for incorporating heterogeneous sources of information. An
objective function is constructed from information theoretic measures,
reflecting expected information gain from proposed combinations of experiments.
Polynomial chaos approximations and a two-stage Monte Carlo sampling method are
used to evaluate the expected information gain. Stochastic approximation
algorithms are then used to make optimization feasible in computationally
intensive and high-dimensional settings. These algorithms are demonstrated on
model problems and on nonlinear parameter estimation problems arising in
detailed combustion kinetics.Comment: Preprint 53 pages, 17 figures (54 small figures). v1 submitted to the
Journal of Computational Physics on August 4, 2011; v2 submitted on August
12, 2012. v2 changes: (a) addition of Appendix B and Figure 17 to address the
bias in the expected utility estimator; (b) minor language edits; v3
submitted on November 30, 2012. v3 changes: minor edit
Unscented Bayesian Optimization for Safe Robot Grasping
We address the robot grasp optimization problem of unknown objects
considering uncertainty in the input space. Grasping unknown objects can be
achieved by using a trial and error exploration strategy. Bayesian optimization
is a sample efficient optimization algorithm that is especially suitable for
this setups as it actively reduces the number of trials for learning about the
function to optimize. In fact, this active object exploration is the same
strategy that infants do to learn optimal grasps. One problem that arises while
learning grasping policies is that some configurations of grasp parameters may
be very sensitive to error in the relative pose between the object and robot
end-effector. We call these configurations unsafe because small errors during
grasp execution may turn good grasps into bad grasps. Therefore, to reduce the
risk of grasp failure, grasps should be planned in safe areas. We propose a new
algorithm, Unscented Bayesian optimization that is able to perform sample
efficient optimization while taking into consideration input noise to find safe
optima. The contribution of Unscented Bayesian optimization is twofold as if
provides a new decision process that drives exploration to safe regions and a
new selection procedure that chooses the optimal in terms of its safety without
extra analysis or computational cost. Both contributions are rooted on the
strong theory behind the unscented transformation, a popular nonlinear
approximation method. We show its advantages with respect to the classical
Bayesian optimization both in synthetic problems and in realistic robot grasp
simulations. The results highlights that our method achieves optimal and robust
grasping policies after few trials while the selected grasps remain in safe
regions.Comment: conference pape
On the Design of LQR Kernels for Efficient Controller Learning
Finding optimal feedback controllers for nonlinear dynamic systems from data
is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful
framework for direct controller tuning from experimental trials. For selecting
the next query point and finding the global optimum, BO relies on a
probabilistic description of the latent objective function, typically a
Gaussian process (GP). As is shown herein, GPs with a common kernel choice can,
however, lead to poor learning outcomes on standard quadratic control problems.
For a first-order system, we construct two kernels that specifically leverage
the structure of the well-known Linear Quadratic Regulator (LQR), yet retain
the flexibility of Bayesian nonparametric learning. Simulations of uncertain
linear and nonlinear systems demonstrate that the LQR kernels yield superior
learning performance.Comment: 8 pages, 5 figures, to appear in 56th IEEE Conference on Decision and
Control (CDC 2017
Optimal experimental design for mathematical models of haematopoiesis.
The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters
Determine measurement set for parameter estimation in biological systems modeling
Parameter estimation is challenging for biological systems modelling since the model is normally of high dimension, the measurement data are sparse and noisy, and the cost of experiments is high. Accurate recovery of parameters depend on the quantity and quality of measurement data. It is therefore important to know what measurements to be taken, when and how through optimal experimental design (OED). In this paper we present a method to determine the most informative measurement set for parameter estimation of dynamic systems, in particular biochemical reaction systems, such that the unknown parameters can be inferred with the best possible statistical quality using the data collected from the designed experiments. System analysis using matrix theory is introduced to examine the number of necessary measurement variables. The priority of each measurement variable is determined by optimal experimental design based on Fisher information matrix (FIM). The applicability and advantages of the proposed method are illustrated through an example of a signal pathway model
Gaussian process surrogates for failure detection: a Bayesian experimental design approach
An important task of uncertainty quantification is to identify {the
probability of} undesired events, in particular, system failures, caused by
various sources of uncertainties. In this work we consider the construction of
Gaussian {process} surrogates for failure detection and failure probability
estimation. In particular, we consider the situation that the underlying
computer models are extremely expensive, and in this setting, determining the
sampling points in the state space is of essential importance. We formulate the
problem as an optimal experimental design for Bayesian inferences of the limit
state (i.e., the failure boundary) and propose an efficient numerical scheme to
solve the resulting optimization problem. In particular, the proposed
limit-state inference method is capable of determining multiple sampling points
at a time, and thus it is well suited for problems where multiple computer
simulations can be performed in parallel. The accuracy and performance of the
proposed method is demonstrated by both academic and practical examples
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