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20:09:00. Jeremy/Neil/Nick. Introductory comments, overview of BRIMS, Measurement Systems Division, Structure of the Workshop, Computing resources, Data Sets.
20:09:30. Gershenfeld, Cluster-Weighted Modeling for Prediction and Characterization. (Musical Instruments Data Sets).
20:10:30. Break
20:11:00. Harvey/West, Computational Mixing in Impeller Stirred Reactors (Dow Chemical)
20:12:00. Lunch.
20:01. Marko, Misfire Data Sets/Problems (Ford), Puskorius Catalyst Data Set (Ford)
20:02. Lab/Discussion. Set up notebook computers.
20:03. Tea Break
20:04. Tufillaro, Discuss access to data set access, organization.
21:09:00. McLaughlin, Nonlinear Dynamics and Speech: Some Results and Some Problems. (Human Speech Data Sets, BT)
21:10:00. Fraser, Chaos and Detection.
21.10:30. Break
21:11:00. Davies, Nonlinear Noise Reduction through Monte Carlo Sampling.
21.12. Lunch.
21:01. Lab/Discussion TBA
21:03. Tea Break
21:04. Pendulum demo and neural net modeling by Bakker and deKorte.
Evening. Dinner at Rajdoot Restaurant. Meet at 7:30 for 8:00 pm dinner. (Tel: 926 8033) The address is 83 Park Street,this is a good walk (1.5 miles) from the Rodney Hotel. Worth the walk if you are planning on eating a big meal. It is roughly South of the University.
22:09:00. Guckenheimer
22:10:00. Lloyd, Honest Automata
22.10:30. Break
22.11:00. Saito, Improved Local Discriminant Bases susing Empirical Probability Density Estimation.
22.11:30. Warner, (Analysis of Ford data set?)
22.12. Lunch.
22:01. Discussion/Lab TBA
22:03. Tea Break
23:09.00. Vanden Bossche, Measurement-based black box modelling of Nonlinear RF and Microwave component and systems.
23:10:00. Smith
23:10:30. Break
23.11:00. Tishby, On the theory of data representation for predication and generalization.
23.11:30. L/D
23.12:00. Lunch
23:01. Lab/Discussin TBA
23:03. Tea Break
Evening: Skittles evening at the George Inn Batheaston, Bath (Tel: 01225-42079). A coach has been organized for ferrying participants to and from Rodney Motel and the skittles evening on Thursday. George Inn, Mill Lane, Bathhampton, Bath. Coach departs from the Rodney at 7:30 PM, return at 10:30 PM.
24:09:00. Chatfield, Do Neural Networks Give Better Time Series Forecasts?
24:09:30. Marko, Neural Net Models of Misfire Data.
24:10:00. Puskorius, Neural Net Models of Catalyst Data.
24:10:30. Break
24.11:00. L/D
24.12:00. Lunch
24:01. Lab/Discussion TBA
24:02. Jeremy/Neil/Nick, Concluding remarks. Opening for discussion of "where do we go from here?"
24:03. Tea Break
24:04. Discussion
24.05. Discussion
Chris Chatfield, Do Neural Networks Give Better Time Series Forecasts?
Two case studies (joint work with Julian Faraway) compared neural network (NN)forecasts with Box-Jenkins and Holt-Winters. The results were disappointing and the modeling process was fraught with danger. Methods of examining the responsesurface implied by a NN model are examined as well as alternative procedures using Generalized Additive Models and Projection Pursuit Regression. (schedule)
Mike Davies, Nonlinear Noise Reduction through Monte Carlo Sampling
We consider the problem of nonlinear noise reduction within the framework of Bayesian Theory. This enables us to place appropriate weights on the measurement and dynamic errors and thereby avoid over cleaning the data. Using a Metropolis-Hastings sampler we are able to achieve robust noise reduction without the introduction of ad hoc parameters but at the expense of higher computational complexity. Such an algorithm also allows us to numerically explore the potential and limitations other noise reduction methods. (schedule)
Andrew Fraser, Chaos and Detection
I report on numerical experiments in which a detector reliably found chaotic signals at signal to noise ratios as low as -15dB. The detector was based on a variant of the hidden Markov models used in speech research. The task was particularly difficult because the Fourier power spectrum of the noise was constructed to match the spectrum of the signal. I review likelihood ratio detectors, limitations on the performance of linear models implied by the broad Fourier power spectra of chaotic signals, and the upper limit that the {\em KS entropy} of a chaotic system places on the expected log likelihood attainable by any model. I find that KS entropy estimates indicate that even better detection performance is possible. (schedule)
Neil Gershenfeld, Cluster-Weighted Modeling for Prediction and Characterization
Cluster Weighted Modeling is a framework for nonlinear inference based on factoring an unknown joint density into a cluster expansion, a domain of influence, a local model, and an output error. Using local instead of globa priors enables this technique to handle nonlinear, non-Gaussion, discontinuous, high-dimensional, non-stationary data, and introduces just a single adjustable algorithm parameter to control under- versus over-fitting. Having access to the unconditional density permits an efficient Expectation-Maximization technique to be derived for determining the cluster parameters, and a range of quantities of interest can be derived from the clusters, including conditional forecasts, errors, and dimensions. This algorithm provides many of the attributes required for nonlinear instrumentation that can be used without experienced operator intervention. (schedule).
Bert Harvey, Computational Mixing in Impeller Stirred Reactors
Stirred tank reactors are commonly used in the chemical industry for mixing and blending of constituents for reaction to commercial chemicals. Due to high fluid viscosities and or mechanical limitations these mixing devices quite often are operated in a laminar flow regime. For laminar flows in the absence of enhanced turbulent diffusion, efficient mixing can be difficult and relies primarily on large scale transport (macromixing) in the vessel. Computational (Navier-Stokes) techniques are used to determine the flow field in the vessel and then Lagrangian particle trajectories are computed. These trajectories are evaluated using a variety of techniques from dynamical systems theory. Some computational and experimental results are included in the Dow datasets. (schedule).
This talk explores the problems of learning and adaptive control in the context of probabilistic automata. An `honest' learning process is one that results in automata that ascribe no more features to the data than it actually possesses at a statistically significant level. The resulting models are used to investigate adaptive control, in which there is a trade-off between learning for learning's sake, and learning to attain a practical goal. (schedule)
Stephen McLaughlin, Nonlinear Dynamics and Speech: Some Results and Some Problems!
The ability to speak is a gift which we take for granted. Few of us can recall our early formative years during which we gurgled, cried and tried in vain to copy the sounds adults make as a matter of course. Consequently it is of no surprise that when it comes to the synthesis of speech that we assume that computers can reproduce these sounds with ease. Unfortunately, most modern speech synthesizers while intelligible lack something; in general they are easily identifiable as machines. Recently there has been a growing interest in analyzing speech using the new paradigm which is nonlinear dynamical systems, in particular chaos theory. This talk will present some results on the analysis of a variety of speech sounds, in particular voiced sounds, using a range of invariant measure from chaos theory. These results will then be used a highlight the difficulties that analyzing a real world signal like speech presents to these techniques. Some suggestions/questions will then be raised on how to deal with these difficulties. (schedule)
Naoki Saito, Improved Local Discriminant Bases susing Empirical Probability Density Estimation
We developed the so-called Local Discriminant Bases (LDB) method for signal and image classification problems a few years back. The original LDB method relies on the difference in time-frequency energy distributions of the signal classes: it selects a basis (coordinate system) from a time-frequency dictionary (e.g., a hierarchical set of redundant wavelet packet bases or local trigonometric bases) so that these energy distributions in that coordinate system are well separated by some distance measure. Through our experience and experiments on various datasets, however, we realized that the time-frequency energy distribution is not always the best quantity to analyze for classification. In this presentation, we propose to use empirical probability densities of coordinates for discrimination instead of the time-frequency energy distributions. That is, we estimate the probability density of each class in each coordinate in the time-frequency dictionary. Then, evaluate a power of discrimination of each basis by selecting the K most discriminant coordinates in terms of the "distance" among the corresponding densities (e.g., by the Kullback-Leibler divergence or the Hellinger distance). We use this information to select a basis from the dictionary for classification. (This is a joint work with R.R.Coifman.) (schedule).
Naftali Tisby, On the theory of data representation for predication and generalization
I discuss the problem of nonlinear prediction in the framework of computational learning theory. I show how the notion of uniform convergence in the model-hypotheses space can provide a general solution to the fundamental problem of good representation of data and hypothesis for learning and prediction. We characterize the quality of representations by introducing the notions "balanced" and "faithful" binary representations, and prove that balanced-faithful representations exist whenever the hypothesis space is (PAC) learnable. The main result is that by combining balanced - faithful representations of both input and hypotheses spaces, any learnable problem becomes linearly-separable with high probability when embedded in an Eucleadian space. In other words, any "learnable" boolean prediction problem can be faithfully represented as learning of a "single layer-perceptron". (schedule)
Nicholas B. Tufillaro, A dynamical systems approach to behavioral modeling
A test and measurement methodology is described for nonlinear components (eg. microwave, mechanical) based on differentiable dynamical systems and statistical inference theories. (schedule)
Marc Vanden Bossche, Measurement - based black box modelling of Nonlinear RF and Microwave component and systems
The talk provides inside in the measurement technology and its problems to provide good time domain - frequency domain measurements of RF and microwave components.Afterwards, the black box modeling technology from NMDG is discussed in detail and some focus is given on the relationship signals and models and the different level of models, going from physical device models, circuit level models and system models. I also will discuss the dataset and example circuit. (schedule)