Hierarchical Bayesian auto-regressive models for large space time data with applications to ozone concentration modelling

Increasingly large volumes of space-time data are collected everywhere by mobile computing applications, and in many of these cases temporal data are obtained by registering events, for example telecommunication or web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space-time auto-regressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method (Banerjee et al. [1]) is extended to include auto-regressive terms of latent space-time processes. Specifically, a space-time auto-regressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space-time process. The resulting model is specified within a hierarchical Bayesian framework and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8-hour average ground level ozone concentration data from 1997 to 2006 from a large study region in the eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of non-compliance with respect to the standard, are obtained and illustrated

Time series forecasting with the WARIMAX-GARCH method

It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (WARIMAX-GARCH) method, is proposed to improve predictive performance and accuracy but also to address, at least in part, the problem of unavailable EVs. Basically, the WARIMAX-GARCH method obtains Wavelet “EVs” (WEVs) from Auto-Regressive Integrated Moving Average with eXogenous variables and Generalized Auto-Regressive Conditional Heteroscedasticity (ARIMAX-GARCH) models applied to Wavelet Components (WCs) that are initially determined from the underlying time series. The WEVs are, in fact, treated by the WARIMAX-GARCH method as if they were conventional EVs. Similarly to GARCH and ARIMA-GARCH models, the WARIMAX-GARCH method is suitable for time series exhibiting non-linear characteristics such as conditional variance that depends on past values of observed data. However, unlike those, it can explicitly model frequency domain patterns in the series to help improve predictive performance. An application to a daily time series of dam displacement in Brazil shows the WARIMAX-GARCH method to remarkably outperform the ARIMA-GARCH method, as well as the (multi-layer perceptron) Artificial Neural Network (ANN) and its wavelet version referred to as Wavelet Artificial Neural Network (WANN) as in [1], on statistical measures for both in-sample and out-of-sample forecasting

Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro

Hidden conditional random fields for classification of imaginary motor tasks from EEG data

Brain-computer interfaces (BCIs) are systems that allow the control of external devices using information extracted from brain signals. Such systems find application in rehabilitation of patients with limited or no muscular control. One mechanism used in BCIs is the imagination of motor activity, which produces variations on the power of the electroencephalography (EEG) signals recorded over the motor cortex. In this paper, we propose a new approach for classification of imaginary motor tasks based on hidden conditional random fields (HCRFs). HCRFs are discriminative graphical models that are attractive for this problem because they involve learned statistical models matched to the classification problem; they do not suffer from some of the limitations of generative models; and they include latent variables that can be used to model different brain states in the signal. Our approach involves auto-regressive modeling of the EEG signals, followed by the computation of the power spectrum. Frequency band selection is performed on the resulting time-frequency representation through feature selection methods. These selected features constitute the data that are fed to the HCRF, parameters of which are learned from training data. Inference algorithms on the HCRFs are used for classification of motor tasks. We experimentally compare this approach to the best performing methods in BCI competition IV and the results show that our approach overperforms all methods proposed in the competition. In addition, we present a comparison with an HMM-based method, and observe that the proposed method produces better classification accuracy