13,394 research outputs found
Robust spatio-temporal latent variable models
Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are widely-used mathematical models for decomposing multivariate data. They capture spatial relationships between variables, but ignore any temporal relationships that might exist between observations. Probabilistic PCA (PPCA) and Probabilistic CCA (ProbCCA) are versions of these two models that explain the statistical properties of the observed variables as linear mixtures of an alternative, hypothetical set of hidden, or latent, variables and explicitly model noise. Both the noise and the latent variables are assumed to be Gaussian distributed.
This thesis introduces two new models, named PPCA-AR and ProbCCA-AR, that augment PPCA and ProbCCA respectively with autoregressive processes over the latent variables to additionally capture temporal relationships between the observations. To make PPCA-AR and ProbCCA-AR robust to outliers and able to model leptokurtic data, the Gaussian assumptions are replaced with infinite scale mixtures of Gaussians, using the Student-t distribution.
Bayesian inference calculates posterior probability distributions for each of the parameter variables, from which we obtain a measure of confidence in the inference. It avoids the pitfalls associated with the maximum likelihood method: integrating over all possible values of the parameter variables guards against overfitting. For these new models the integrals required for exact Bayesian inference are intractable; instead a method of approximation, the variational Bayesian approach, is used. This enables the use of automatic relevance determination to estimate the model orders.
PPCA-AR and ProbCCA-AR can be viewed as linear dynamical systems, so the forward-backward algorithm, also known as the Baum-Welch algorithm, is used as an efficient method for inferring the posterior distributions of the latent variables. The exact algorithm is tractable because Gaussian assumptions are made regarding the distribution of the latent variables. This thesis introduces a variational Bayesian forward-backward algorithm based on Student-t assumptions.
The new models are demonstrated on synthetic datasets and on real remote sensing and EEG data
3D Human Activity Recognition with Reconfigurable Convolutional Neural Networks
Human activity understanding with 3D/depth sensors has received increasing
attention in multimedia processing and interactions. This work targets on
developing a novel deep model for automatic activity recognition from RGB-D
videos. We represent each human activity as an ensemble of cubic-like video
segments, and learn to discover the temporal structures for a category of
activities, i.e. how the activities to be decomposed in terms of
classification. Our model can be regarded as a structured deep architecture, as
it extends the convolutional neural networks (CNNs) by incorporating structure
alternatives. Specifically, we build the network consisting of 3D convolutions
and max-pooling operators over the video segments, and introduce the latent
variables in each convolutional layer manipulating the activation of neurons.
Our model thus advances existing approaches in two aspects: (i) it acts
directly on the raw inputs (grayscale-depth data) to conduct recognition
instead of relying on hand-crafted features, and (ii) the model structure can
be dynamically adjusted accounting for the temporal variations of human
activities, i.e. the network configuration is allowed to be partially activated
during inference. For model training, we propose an EM-type optimization method
that iteratively (i) discovers the latent structure by determining the
decomposed actions for each training example, and (ii) learns the network
parameters by using the back-propagation algorithm. Our approach is validated
in challenging scenarios, and outperforms state-of-the-art methods. A large
human activity database of RGB-D videos is presented in addition.Comment: This manuscript has 10 pages with 9 figures, and a preliminary
version was published in ACM MM'14 conferenc
Bayesian approach to Spatio-temporally Consistent Simulation of Daily Monsoon Rainfall over India
Simulation of rainfall over a region for long time-sequences can be very
useful for planning and policy-making, especially in India where the economy is
heavily reliant on monsoon rainfall. However, such simulations should be able
to preserve the known spatial and temporal characteristics of rainfall over
India. General Circulation Models (GCMs) are unable to do so, and various
rainfall generators designed by hydrologists using stochastic processes like
Gaussian Processes are also difficult to apply over the vast and highly diverse
landscape of India. In this paper, we explore a series of Bayesian models based
on conditional distributions of latent variables that describe weather
conditions at specific locations and over the whole country. During parameter
estimation from observed data, we use spatio-temporal smoothing using Markov
Random Field so that the parameters learnt are spatially and temporally
coherent. Also, we use a nonparametric spatial clustering based on Chinese
Restaurant Process to identify homogeneous regions, which are utilized by some
of the proposed models to improve spatial correlations of the simulated
rainfall. The models are able to simulate daily rainfall across India for
years, and can also utilize contextual information for conditional simulation.
We use two datasets of different spatial resolutions over India, and focus on
the period 2000-2015. We propose a large number of metrics to study the
spatio-temporal properties of the simulations by the models, and compare them
with the observed data to evaluate the strengths and weaknesses of the models
Benefits of spatio-temporal modelling for short term wind power forecasting at both individual and aggregated levels
The share of wind energy in total installed power capacity has grown rapidly
in recent years around the world. Producing accurate and reliable forecasts of
wind power production, together with a quantification of the uncertainty, is
essential to optimally integrate wind energy into power systems. We build
spatio-temporal models for wind power generation and obtain full probabilistic
forecasts from 15 minutes to 5 hours ahead. Detailed analysis of the forecast
performances on the individual wind farms and aggregated wind power are
provided. We show that it is possible to improve the results of forecasting
aggregated wind power by utilizing spatio-temporal correlations among
individual wind farms. Furthermore, spatio-temporal models have the advantage
of being able to produce spatially out-of-sample forecasts. We evaluate the
predictions on a data set from wind farms in western Denmark and compare the
spatio-temporal model with an autoregressive model containing a common
autoregressive parameter for all wind farms, identifying the specific cases
when it is important to have a spatio-temporal model instead of a temporal one.
This case study demonstrates that it is possible to obtain fast and accurate
forecasts of wind power generation at wind farms where data is available, but
also at a larger portfolio including wind farms at new locations. The results
and the methodologies are relevant for wind power forecasts across the globe as
well as for spatial-temporal modelling in general
Online Predictive Optimization Framework for Stochastic Demand-Responsive Transit Services
This study develops an online predictive optimization framework for
dynamically operating a transit service in an area of crowd movements. The
proposed framework integrates demand prediction and supply optimization to
periodically redesign the service routes based on recently observed demand. To
predict demand for the service, we use Quantile Regression to estimate the
marginal distribution of movement counts between each pair of serviced
locations. The framework then combines these marginals into a joint demand
distribution by constructing a Gaussian copula, which captures the structure of
correlation between the marginals. For supply optimization, we devise a linear
programming model, which simultaneously determines the route structure and the
service frequency according to the predicted demand. Importantly, our framework
both preserves the uncertainty structure of future demand and leverages this
for robust route optimization, while keeping both components decoupled. We
evaluate our framework using a real-world case study of autonomous mobility in
a university campus in Denmark. The results show that our framework often
obtains the ground truth optimal solution, and can outperform conventional
methods for route optimization, which do not leverage full predictive
distributions.Comment: 34 pages, 12 figures, 5 table
- …