30,237 research outputs found
Bayesian System ID: Optimal management of parameter, model, and measurement uncertainty
We evaluate the robustness of a probabilistic formulation of system
identification (ID) to sparse, noisy, and indirect data. Specifically, we
compare estimators of future system behavior derived from the Bayesian
posterior of a learning problem to several commonly used least squares-based
optimization objectives used in system ID. Our comparisons indicate that the
log posterior has improved geometric properties compared with the objective
function surfaces of traditional methods that include differentially
constrained least squares and least squares reconstructions of discrete time
steppers like dynamic mode decomposition (DMD). These properties allow it to be
both more sensitive to new data and less affected by multiple minima ---
overall yielding a more robust approach. Our theoretical results indicate that
least squares and regularized least squares methods like dynamic mode
decomposition and sparse identification of nonlinear dynamics (SINDy) can be
derived from the probabilistic formulation by assuming noiseless measurements.
We also analyze the computational complexity of a Gaussian filter-based
approximate marginal Markov Chain Monte Carlo scheme that we use to obtain the
Bayesian posterior for both linear and nonlinear problems. We then empirically
demonstrate that obtaining the marginal posterior of the parameter dynamics and
making predictions by extracting optimal estimators (e.g., mean, median, mode)
yields orders of magnitude improvement over the aforementioned approaches. We
attribute this performance to the fact that the Bayesian approach captures
parameter, model, and measurement uncertainties, whereas the other methods
typically neglect at least one type of uncertainty
Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables
Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety
of engineering and scientific fields. Dynamic mode decomposition (DMD), which
is a numerical algorithm for the spectral analysis of Koopman operators, has
been attracting attention as a way of obtaining global modal descriptions of
NLDSs without requiring explicit prior knowledge. However, since existing DMD
algorithms are in principle formulated based on the concatenation of scalar
observables, it is not directly applicable to data with dependent structures
among observables, which take, for example, the form of a sequence of graphs.
In this paper, we formulate Koopman spectral analysis for NLDSs with structures
among observables and propose an estimation algorithm for this problem. This
method can extract and visualize the underlying low-dimensional global dynamics
of NLDSs with structures among observables from data, which can be useful in
understanding the underlying dynamics of such NLDSs. To this end, we first
formulate the problem of estimating spectra of the Koopman operator defined in
vector-valued reproducing kernel Hilbert spaces, and then develop an estimation
procedure for this problem by reformulating tensor-based DMD. As a special case
of our method, we propose the method named as Graph DMD, which is a numerical
algorithm for Koopman spectral analysis of graph dynamical systems, using a
sequence of adjacency matrices. We investigate the empirical performance of our
method by using synthetic and real-world data.Comment: 34 pages with 4 figures, Published in Neural Networks, 201
Using Bayesian Programming for Multisensor Multi-Target Tracking in Automative Applications
A prerequisite to the design of future Advanced Driver Assistance Systems for cars is a sensing system providing all the information required for high-level driving assistance tasks. Carsense is a European project whose purpose is to develop such a new sensing system. It will combine different sensors (laser, radar and video) and will rely on the fusion of the information coming from these sensors in order to achieve better accuracy, robustness and an increase of the information content. This paper demonstrates the interest of using
probabilistic reasoning techniques to address this challenging multi-sensor data fusion problem. The approach used is called Bayesian Programming. It is a general approach based on an implementation of the Bayesian theory. It was introduced rst to design robot control programs but its scope of application is much broader and it can be used whenever one has to deal with problems involving uncertain or incomplete knowledge
- …