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Register a new userA Nonparametric Adaptive Nonlinear Statistical Filter
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Added by
Michael Busch Jr
Publication date
2014
fields
Mathematical Statistics
and research's language is
English
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We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the systems process and measurement uncertainty. We propose that these uncertainties can be estimated from (conditioned on) past observed data, and without making any assumptions of the systems prior distribution. The systems prior distribution at each time step is constructed from an ensemble of least-squares estimates on sub-sampled sets of the data via jackknife sampling. As new data is acquired, the state estimates, process uncertainty, and measurement uncertainty are updated accordingly, as described in this manuscript.
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We develop a data driven approach to perform clustering and end-to-end feature learning simultaneously for streaming data that can adaptively detect novel clusters in emerging data. Our approach, Adaptive Nonparametric Variational Autoencoder (AdapVAE), learns the cluster membership through a Bayesian Nonparametric (BNP) modeling framework with Deep Neural Networks (DNNs) for feature learning. We develop a joint online variational inference algorithm to learn feature representations and clustering assignments simultaneously via iteratively optimizing the Evidence Lower Bound (ELBO). We resolve the catastrophic forgetting citep{kirkpatrick2017overcoming} challenges with streaming data by adopting generative samples from the trained AdapVAE using previous data, which avoids the need of storing and reusing past data. We demonstrate the advantages of our model including adaptive novel cluster detection without discarding useful information learned from past data, high quality sample generation and comparable clustering performance as end-to-end batch mode clustering methods on both image and text corpora benchmark datasets.
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