11 research outputs found
Pattern-Based Analysis of Time Series: Estimation
While Internet of Things (IoT) devices and sensors create continuous streams
of information, Big Data infrastructures are deemed to handle the influx of
data in real-time. One type of such a continuous stream of information is time
series data. Due to the richness of information in time series and inadequacy
of summary statistics to encapsulate structures and patterns in such data,
development of new approaches to learn time series is of interest. In this
paper, we propose a novel method, called pattern tree, to learn patterns in the
times-series using a binary-structured tree. While a pattern tree can be used
for many purposes such as lossless compression, prediction and anomaly
detection, in this paper we focus on its application in time series estimation
and forecasting. In comparison to other methods, our proposed pattern tree
method improves the mean squared error of estimation
Cover Tree Bayesian Reinforcement Learning
This paper proposes an online tree-based Bayesian approach for reinforcement
learning. For inference, we employ a generalised context tree model. This
defines a distribution on multivariate Gaussian piecewise-linear models, which
can be updated in closed form. The tree structure itself is constructed using
the cover tree method, which remains efficient in high dimensional spaces. We
combine the model with Thompson sampling and approximate dynamic programming to
obtain effective exploration policies in unknown environments. The flexibility
and computational simplicity of the model render it suitable for many
reinforcement learning problems in continuous state spaces. We demonstrate this
in an experimental comparison with least squares policy iteration
Linear MMSE-Optimal Turbo Equalization Using Context Trees
Formulations of the turbo equalization approach to iterative equalization and
decoding vary greatly when channel knowledge is either partially or completely
unknown. Maximum aposteriori probability (MAP) and minimum mean square error
(MMSE) approaches leverage channel knowledge to make explicit use of soft
information (priors over the transmitted data bits) in a manner that is
distinctly nonlinear, appearing either in a trellis formulation (MAP) or inside
an inverted matrix (MMSE). To date, nearly all adaptive turbo equalization
methods either estimate the channel or use a direct adaptation equalizer in
which estimates of the transmitted data are formed from an expressly linear
function of the received data and soft information, with this latter
formulation being most common. We study a class of direct adaptation turbo
equalizers that are both adaptive and nonlinear functions of the soft
information from the decoder. We introduce piecewise linear models based on
context trees that can adaptively approximate the nonlinear dependence of the
equalizer on the soft information such that it can choose both the partition
regions as well as the locally linear equalizer coefficients in each region
independently, with computational complexity that remains of the order of a
traditional direct adaptive linear equalizer. This approach is guaranteed to
asymptotically achieve the performance of the best piecewise linear equalizer
and we quantify the MSE performance of the resulting algorithm and the
convergence of its MSE to that of the linear minimum MSE estimator as the depth
of the context tree and the data length increase.Comment: Submitted to the IEEE Transactions on Signal Processin
Low-Complexity Nonparametric Bayesian Online Prediction with Universal Guarantees
We propose a novel nonparametric online predictor for discrete labels
conditioned on multivariate continuous features. The predictor is based on a
feature space discretization induced by a full-fledged k-d tree with randomly
picked directions and a recursive Bayesian distribution, which allows to
automatically learn the most relevant feature scales characterizing the
conditional distribution. We prove its pointwise universality, i.e., it
achieves a normalized log loss performance asymptotically as good as the true
conditional entropy of the labels given the features. The time complexity to
process the -th sample point is in probability with respect to
the distribution generating the data points, whereas other exact nonparametric
methods require to process all past observations. Experiments on challenging
datasets show the computational and statistical efficiency of our algorithm in
comparison to standard and state-of-the-art methods.Comment: Camera-ready version published in NeurIPS 201
Universal Noiseless Compression for Noisy Data
We study universal compression for discrete data sequences that were corrupted by noise. We show that while, as expected, there exist many cases in which the entropy of these sequences increases from that of the original data, somewhat surprisingly and counter-intuitively, universal coding redundancy of such sequences cannot increase compared to the original data. We derive conditions that guarantee that this redundancy does not decrease asymptotically (in first order) from the original sequence redundancy in the stationary memoryless case. We then provide bounds on the redundancy for coding finite length (large) noisy blocks generated by stationary memoryless sources and corrupted by some speci??c memoryless channels. Finally, we propose a sequential probability estimation method that can be used to compress binary data corrupted by some noisy channel. While there is much benefit in using this method in compressing short blocks of noise corrupted data, the new method is more general and allows sequential compression of binary sequences for which the probability of a bit is known to be limited within any given interval (not necessarily between 0 and 1). Additionally, this method has many different applications, including, prediction, sequential channel estimation, and others