25,999 research outputs found
Impact of noise on a dynamical system: prediction and uncertainties from a swarm-optimized neural network
In this study, an artificial neural network (ANN) based on particle swarm
optimization (PSO) was developed for the time series prediction. The hybrid
ANN+PSO algorithm was applied on Mackey--Glass chaotic time series in the
short-term . The performance prediction was evaluated and compared with
another studies available in the literature. Also, we presented properties of
the dynamical system via the study of chaotic behaviour obtained from the
predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with
a Gaussian stochastic procedure (called {\it stochastic} hybrid ANN+PSO) in
order to obtain a new estimator of the predictions, which also allowed us to
compute uncertainties of predictions for noisy Mackey--Glass chaotic time
series. Thus, we studied the impact of noise for several cases with a white
noise level () from 0.01 to 0.1.Comment: 11 pages, 8 figure
Learning to Discover Sparse Graphical Models
We consider structure discovery of undirected graphical models from
observational data. Inferring likely structures from few examples is a complex
task often requiring the formulation of priors and sophisticated inference
procedures. Popular methods rely on estimating a penalized maximum likelihood
of the precision matrix. However, in these approaches structure recovery is an
indirect consequence of the data-fit term, the penalty can be difficult to
adapt for domain-specific knowledge, and the inference is computationally
demanding. By contrast, it may be easier to generate training samples of data
that arise from graphs with the desired structure properties. We propose here
to leverage this latter source of information as training data to learn a
function, parametrized by a neural network that maps empirical covariance
matrices to estimated graph structures. Learning this function brings two
benefits: it implicitly models the desired structure or sparsity properties to
form suitable priors, and it can be tailored to the specific problem of edge
structure discovery, rather than maximizing data likelihood. Applying this
framework, we find our learnable graph-discovery method trained on synthetic
data generalizes well: identifying relevant edges in both synthetic and real
data, completely unknown at training time. We find that on genetics, brain
imaging, and simulation data we obtain performance generally superior to
analytical methods
- …