19,500 research outputs found
Echo State Networks: analysis, training and predictive control
The goal of this paper is to investigate the theoretical properties, the
training algorithm, and the predictive control applications of Echo State
Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a
condition guaranteeing incremetal global asymptotic stability is devised. Then,
a modified training algorithm allowing for dimensionality reduction of ESNs is
presented. Eventually, a model predictive controller is designed to solve the
tracking problem, relying on ESNs as the model of the system. Numerical results
concerning the predictive control of a nonlinear process for pH neutralization
confirm the effectiveness of the proposed algorithms for the identification,
dimensionality reduction, and the control design for ESNs.Comment: 6 pages,5 figures, submitted to European Control Conference (ECC
Efficient Optimization of Echo State Networks for Time Series Datasets
Echo State Networks (ESNs) are recurrent neural networks that only train
their output layer, thereby precluding the need to backpropagate gradients
through time, which leads to significant computational gains. Nevertheless, a
common issue in ESNs is determining its hyperparameters, which are crucial in
instantiating a well performing reservoir, but are often set manually or using
heuristics. In this work we optimize the ESN hyperparameters using Bayesian
optimization which, given a limited budget of function evaluations, outperforms
a grid search strategy. In the context of large volumes of time series data,
such as light curves in the field of astronomy, we can further reduce the
optimization cost of ESNs. In particular, we wish to avoid tuning
hyperparameters per individual time series as this is costly; instead, we want
to find ESNs with hyperparameters that perform well not just on individual time
series but rather on groups of similar time series without sacrificing
predictive performance significantly. This naturally leads to a notion of
clusters, where each cluster is represented by an ESN tuned to model a group of
time series of similar temporal behavior. We demonstrate this approach both on
synthetic datasets and real world light curves from the MACHO survey. We show
that our approach results in a significant reduction in the number of ESN
models required to model a whole dataset, while retaining predictive
performance for the series in each cluster
Hierarchical Temporal Representation in Linear Reservoir Computing
Recently, studies on deep Reservoir Computing (RC) highlighted the role of
layering in deep recurrent neural networks (RNNs). In this paper, the use of
linear recurrent units allows us to bring more evidence on the intrinsic
hierarchical temporal representation in deep RNNs through frequency analysis
applied to the state signals. The potentiality of our approach is assessed on
the class of Multiple Superimposed Oscillator tasks. Furthermore, our
investigation provides useful insights to open a discussion on the main aspects
that characterize the deep learning framework in the temporal domain.Comment: This is a pre-print of the paper submitted to the 27th Italian
Workshop on Neural Networks, WIRN 201
Training Echo State Networks with Regularization through Dimensionality Reduction
In this paper we introduce a new framework to train an Echo State Network to
predict real valued time-series. The method consists in projecting the output
of the internal layer of the network on a space with lower dimensionality,
before training the output layer to learn the target task. Notably, we enforce
a regularization constraint that leads to better generalization capabilities.
We evaluate the performances of our approach on several benchmark tests, using
different techniques to train the readout of the network, achieving superior
predictive performance when using the proposed framework. Finally, we provide
an insight on the effectiveness of the implemented mechanics through a
visualization of the trajectory in the phase space and relying on the
methodologies of nonlinear time-series analysis. By applying our method on well
known chaotic systems, we provide evidence that the lower dimensional embedding
retains the dynamical properties of the underlying system better than the
full-dimensional internal states of the network
The Power of Linear Recurrent Neural Networks
Recurrent neural networks are a powerful means to cope with time series. We
show how a type of linearly activated recurrent neural networks, which we call
predictive neural networks, can approximate any time-dependent function f(t)
given by a number of function values. The approximation can effectively be
learned by simply solving a linear equation system; no backpropagation or
similar methods are needed. Furthermore, the network size can be reduced by
taking only most relevant components. Thus, in contrast to others, our approach
not only learns network weights but also the network architecture. The networks
have interesting properties: They end up in ellipse trajectories in the long
run and allow the prediction of further values and compact representations of
functions. We demonstrate this by several experiments, among them multiple
superimposed oscillators (MSO), robotic soccer, and predicting stock prices.
Predictive neural networks outperform the previous state-of-the-art for the MSO
task with a minimal number of units.Comment: 22 pages, 14 figures and tables, revised implementatio
Recommended from our members
Preliminary prediction of individual response to electroconvulsive therapy using whole-brain functional magnetic resonance imaging data.
Electroconvulsive therapy (ECT) works rapidly and has been widely used to treat depressive disorders (DEP). However, identifying biomarkers predictive of response to ECT remains a priority to individually tailor treatment and understand treatment mechanisms. This study used a connectome-based predictive modeling (CPM) approach in 122 patients with DEP to determine if pre-ECT whole-brain functional connectivity (FC) predicts depressive rating changes and remission status after ECT (47 of 122 total subjects or 38.5% of sample), and whether pre-ECT and longitudinal changes (pre/post-ECT) in regional brain network biomarkers are associated with treatment-related changes in depression ratings. Results show the networks with the best predictive performance of ECT response were negative (anti-correlated) FC networks, which predict the post-ECT depression severity (continuous measure) with a 76.23% accuracy for remission prediction. FC networks with the greatest predictive power were concentrated in the prefrontal and temporal cortices and subcortical nuclei, and include the inferior frontal (IFG), superior frontal (SFG), superior temporal (STG), inferior temporal gyri (ITG), basal ganglia (BG), and thalamus (Tha). Several of these brain regions were also identified as nodes in the FC networks that show significant change pre-/post-ECT, but these networks were not related to treatment response. This study design has limitations regarding the longitudinal design and the absence of a control group that limit the causal inference regarding mechanism of post-treatment status. Though predictive biomarkers remained below the threshold of those recommended for potential translation, the analysis methods and results demonstrate the promise and generalizability of biomarkers for advancing personalized treatment strategies
- …