Analytic Long-Term Forecasting with Periodic Gaussian Processes

Gaussian processes are a state-of-the-art method for learning models from data. Data with an underlying periodic structure appears in many areas, e.g., in climatology or robotics. It is often important to predict the long-term evolution of such a time series, and to take the inherent periodicity explicitly into account. In a Gaussian process, periodicity can be accounted for by an appropriate kernel choice. However, the standard periodic kernel does not allow for analytic long-term forecasting. To address this shortcoming, we re-parametrize the periodic kernel, which, in combination with a double approximation, allows for analytic longterm forecasting of a periodic state evolution with Gaussian processes. Our model allows for probabilistic long-term forecasting of periodic processes, which can be valuable in Bayesian decision making, optimal control, reinforcement learning, and robotics

Wavelet Multiresolution Analysis of High-Frequency Asian FX Rates, Summer 1997

FX pricing processes are nonstationary and their frequency characteristics are time-dependent. Most do not conform to geometric Brownian motion, since they exhibit a scaling law with a Hurst exponent between zero and 0.5 and fractal dimensions between 1.5 and 2. This paper uses wavelet multiresolution analysis, with Haar wavelets, to analyze the nonstationarity (time-dependence) and self-similarity (scale-dependence) of intra-day Asian currency spot exchange rates. These are the ask and bid quotes of the currencies of eight Asian countries (Japan, Hong Kong, Indonesia, Malaysia, Philippines, Singapore, Taiwan, Thailand), and of Germany for comparison, for the crisis period May 1, 1998 - August 31, 1997, provided by Telerate (U.S. dollar is the numeraire). Their time-scale dependent spectra, which are localized in time, are observed in wavelet based scalograms. The FX increments can be characterized by the irregularity of their singularities. This degrees of irregularity are measured by homogeneous Hurst exponents. These critical exponents are used to identify the fractal dimension, relative stability and long term dependence of each Asian FX series. The invariance of each identified Hurst exponent is tested by comparing it at varying time and scale (frequency) resolutions. It appears that almost all FX markets show anti-persistent pricing behavior. The anchor currencies of the D-mark and Japanese Yen are ultra-efficient in the sense of being most anti-persistent. The Taiwanese dollar is the most persistent, and thus unpredictable, most likely due to administrative control. FX markets exhibit these non- linear, non-Gaussian dynamic structures, long term dependence, high kurtosis, and high degrees of non-informational (noise) trading, possibly because of frequent capital flows induced by non-synchronized regional business cycles, rapidly changing political risks, unexpected informational shocks to investment opportunities, and, in particular, investment strategies synthesizing interregional claims using cash swaps with different duration horizons.foreign exchange markets, anti-persistence, long-term dependence, multi-resolution analysis, wavelets, time-scale analysis, scaling laws, irregularity analysis, randomness, Asia

Wavelet Multiresolution Analysis of High-Frequency FX Rates, Summer 1997

FX pricing processes are nonstationary and their frequency characteristics are time-dependent. Most do not conform to geometric Brownian motion, since they exhibit a scaling law with a Hurst exponent between zero and 0.5 and fractal dimensions between 1.5 and 2. This paper uses wavelet multiresolution analysis, with Haar wavelets, to analyze the nonstationarity (time-dependence) and self-similarity (scale-dependence) of intra-day Asian currency spot exchange rates.foreign exchange, anti-persistence, multi-resolution analysis, wavelets, Asia

Parallelizable sparse inverse formulation Gaussian processes (SpInGP)

We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used in the algorithm, the time complexity of the basic SpInGP is linear, and because all the computations are parallelizable, the parallel form of the algorithm is sublinear in the number of data points. We provide example algorithms to implement the sparse matrix routines and experimentally test the method using both simulated and real data.Comment: Presented at Machine Learning in Signal Processing (MLSP2017

Information Agents for Pervasive Sensor Networks

In this paper, we describe an information agent, that resides on a mobile computer or personal digital assistant (PDA), that can autonomously acquire sensor readings from pervasive sensor networks (deciding when and which sensor to acquire readings from at any time). Moreover, it can perform a range of information processing tasks including modelling the accuracy of the sensor readings, predicting the value of missing sensor readings, and predicting how the monitored environmental parameters will evolve into the future. Our motivating scenario is the need to provide situational awareness support to first responders at the scene of a large scale incident, and we describe how we use an iterative formulation of a multi-output Gaussian process to build a probabilistic model of the environmental parameters being measured by local sensors, and the correlations and delays that exist between them. We validate our approach using data collected from a network of weather sensors located on the south coast of England

Real-time information processing of environmental sensor network data using Bayesian Gaussian processes

In this article, we consider the problem faced by a sensor network operator who must infer, in real time, the value of some environmental parameter that is being monitored at discrete points in space and time by a sensor network. We describe a powerful and generic approach built upon an efficient multi-output Gaussian process that facilitates this information acquisition and processing. Our algorithm allows effective inference even with minimal domain knowledge, and we further introduce a formulation of Bayesian Monte Carlo to permit the principled management of the hyperparameters introduced by our flexible models. We demonstrate how our methods can be applied in cases where the data is delayed, intermittently missing, censored, and/or correlated. We validate our approach using data collected from three networks of weather sensors and show that it yields better inference performance than both conventional independent Gaussian processes and the Kalman filter. Finally, we show that our formalism efficiently reuses previous computations by following an online update procedure as new data sequentially arrives, and that this results in a four-fold increase in computational speed in the largest cases considered