Sequential anomaly detection in the presence of noise and limited feedback

This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: (1) {\em filtering}, or assigning a belief or likelihood to each successive measurement based upon our ability to predict it from previous noisy observations, and (2) {\em hedging}, or flagging potential anomalies by comparing the current belief against a time-varying and data-adaptive threshold. The threshold is adjusted based on the available feedback from an end user. Our algorithms, which combine universal prediction with recent work on online convex programming, do not require computing posterior distributions given all current observations and involve simple primal-dual parameter updates. At the heart of the proposed approach lie exponential-family models which can be used in a wide variety of contexts and applications, and which yield methods that achieve sublinear per-round regret against both static and slowly varying product distributions with marginals drawn from the same exponential family. Moreover, the regret against static distributions coincides with the minimax value of the corresponding online strongly convex game. We also prove bounds on the number of mistakes made during the hedging step relative to the best offline choice of the threshold with access to all estimated beliefs and feedback signals. We validate the theory on synthetic data drawn from a time-varying distribution over binary vectors of high dimensionality, as well as on the Enron email dataset.Comment: 19 pages, 12 pdf figures; final version to be published in IEEE Transactions on Information Theor

Sensor based real-time process monitoring for ultra-precision manufacturing processes with non-linearity and non-stationarity

This research investigates methodologies for real-time process monitoring in ultra-precision manufacturing processes, specifically, chemical mechanical planarization (CMP) and ultra-precision machining (UPM), are investigated in this dissertation.The three main components of this research are as follows: (1) developing a predictive modeling approaches for early detection of process anomalies/change points, (2) devising approaches that can capture the non-Gaussian and non-stationary characteristics of CMP and UPM processes, and (3) integrating multiple sensor data to make more reliable process related decisions in real-time.In the first part, we establish a quantitative relationship between CMP process performance, such as material removal rate (MRR) and data acquired from wireless vibration sensors. Subsequently, a non-linear sequential Bayesian analysis is integrated with decision theoretic concepts for detection of CMP process end-point for blanket copper wafers. Using this approach, CMP polishing end-point was detected within a 5% error rate.Next, a non-parametric Bayesian analytical approach is utilized to capture the inherently complex, non-Gaussian, and non-stationary sensor signal patterns observed in CMP process. An evolutionary clustering analysis, called Recurrent Nested Dirichlet Process (RNDP) approach is developed for monitoring CMP process changes using MEMS vibration signals. Using this novel signal analysis approach, process drifts are detected within 20 milliseconds and is assessed to be 3-7 times faster than traditional SPC charts. This is very beneficial to the industry from an application standpoint, because, wafer yield losses will be mitigated to a great extent, if the onset of CMP process drifts can be detected timely and accurately.Lastly, a non-parametric Bayesian modeling approach, termed Dirichlet Process (DP) is combined with a multi-level hierarchical information fusion technique for monitoring of surface finish in UPM process. Using this approach, signal patterns from six different sensors (three axis vibration and force) are integrated based on information fusion theory. It was observed that using experimental UPM sensor data that process decisions based on the multiple sensor information fusion approach were 15%-30% more accurate than the decisions from individual sensors. This will enable more accurate and reliable estimation of process conditions in ultra-precision manufacturing applications

Ecological non-linear state space model selection via adaptive particle Markov chain Monte Carlo (AdPMCMC)

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We apply this novel methodology to five population growth models, including models with strong and weak Allee effects, and test if it can efficiently sample from the complex likelihood surface that is often associated with these models. Utilising real and also synthetically generated data sets we examine the extent to which observation noise and process error may frustrate efforts to choose between these models. Our novel algorithm involves an Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm (AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional spaces efficiently, and is therefore superior to standard Gibbs or Metropolis Hastings algorithms that are known to converge very slowly when applied to the non-linear state space ecological models considered in this paper. Additionally, we show how the AdPMCMC algorithm can be used to recursively estimate the Bayesian Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive expressions for these Cram\'er-Rao Bounds and estimate them for the models considered. Our results demonstrate a number of important features of common population growth models, most notably their multi-modal posterior surfaces and dependence between the static and dynamic parameters. We conclude by sampling from the posterior distribution of each of the models, and use Bayes factors to highlight how observation noise significantly diminishes our ability to select among some of the models, particularly those that are designed to reproduce an Allee effect

Bayesian forecasting and scalable multivariate volatility analysis using simultaneous graphical dynamic models

The recently introduced class of simultaneous graphical dynamic linear models (SGDLMs) defines an ability to scale on-line Bayesian analysis and forecasting to higher-dimensional time series. This paper advances the methodology of SGDLMs, developing and embedding a novel, adaptive method of simultaneous predictor selection in forward filtering for on-line learning and forecasting. The advances include developments in Bayesian computation for scalability, and a case study in exploring the resulting potential for improved short-term forecasting of large-scale volatility matrices. A case study concerns financial forecasting and portfolio optimization with a 400-dimensional series of daily stock prices. Analysis shows that the SGDLM forecasts volatilities and co-volatilities well, making it ideally suited to contributing to quantitative investment strategies to improve portfolio returns. We also identify performance metrics linked to the sequential Bayesian filtering analysis that turn out to define a leading indicator of increased financial market stresses, comparable to but leading the standard St. Louis Fed Financial Stress Index (STLFSI) measure. Parallel computation using GPU implementations substantially advance the ability to fit and use these models.Comment: 28 pages, 9 figures, 7 table

Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View

Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information diffusion rules, regardless of the nature evolutionary characteristic of a distributed network. In this paper, we study the adaptive network from the game theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With the proposed formulation, the nodes in the network are regarded as players and the local combiner of estimation information from different neighbors is regarded as different strategies selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, we further propose two error-aware adaptive filtering algorithms. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of our analysis and proposed methods.Comment: Accepted by IEEE Transactions on Signal Processin