24,239 research outputs found
A Long Short-Term Memory Recurrent Neural Network Framework for Network Traffic Matrix Prediction
Network Traffic Matrix (TM) prediction is defined as the problem of
estimating future network traffic from the previous and achieved network
traffic data. It is widely used in network planning, resource management and
network security. Long Short-Term Memory (LSTM) is a specific recurrent neural
network (RNN) architecture that is well-suited to learn from experience to
classify, process and predict time series with time lags of unknown size. LSTMs
have been shown to model temporal sequences and their long-range dependencies
more accurately than conventional RNNs. In this paper, we propose a LSTM RNN
framework for predicting short and long term Traffic Matrix (TM) in large
networks. By validating our framework on real-world data from GEANT network, we
show that our LSTM models converge quickly and give state of the art TM
prediction performance for relatively small sized models.Comment: Submitted for peer review. arXiv admin note: text overlap with
arXiv:1402.1128 by other author
Online Natural Gradient as a Kalman Filter
We cast Amari's natural gradient in statistical learning as a specific case
of Kalman filtering. Namely, applying an extended Kalman filter to estimate a
fixed unknown parameter of a probabilistic model from a series of observations,
is rigorously equivalent to estimating this parameter via an online stochastic
natural gradient descent on the log-likelihood of the observations.
In the i.i.d. case, this relation is a consequence of the "information
filter" phrasing of the extended Kalman filter. In the recurrent (state space,
non-i.i.d.) case, we prove that the joint Kalman filter over states and
parameters is a natural gradient on top of real-time recurrent learning (RTRL),
a classical algorithm to train recurrent models.
This exact algebraic correspondence provides relevant interpretations for
natural gradient hyperparameters such as learning rates or initialization and
regularization of the Fisher information matrix.Comment: 3rd version: expanded intr
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