13,337 research outputs found
Bayesian Conditional Density Filtering
We propose a Conditional Density Filtering (C-DF) algorithm for efficient
online Bayesian inference. C-DF adapts MCMC sampling to the online setting,
sampling from approximations to conditional posterior distributions obtained by
propagating surrogate conditional sufficient statistics (a function of data and
parameter estimates) as new data arrive. These quantities eliminate the need to
store or process the entire dataset simultaneously and offer a number of
desirable features. Often, these include a reduction in memory requirements and
runtime and improved mixing, along with state-of-the-art parameter inference
and prediction. These improvements are demonstrated through several
illustrative examples including an application to high dimensional compressed
regression. Finally, we show that C-DF samples converge to the target posterior
distribution asymptotically as sampling proceeds and more data arrives.Comment: 41 pages, 7 figures, 12 table
The Hitchhiker's Guide to Nonlinear Filtering
Nonlinear filtering is the problem of online estimation of a dynamic hidden
variable from incoming data and has vast applications in different fields,
ranging from engineering, machine learning, economic science and natural
sciences. We start our review of the theory on nonlinear filtering from the
simplest `filtering' task we can think of, namely static Bayesian inference.
From there we continue our journey through discrete-time models, which is
usually encountered in machine learning, and generalize to and further
emphasize continuous-time filtering theory. The idea of changing the
probability measure connects and elucidates several aspects of the theory, such
as the parallels between the discrete- and continuous-time problems and between
different observation models. Furthermore, it gives insight into the
construction of particle filtering algorithms. This tutorial is targeted at
scientists and engineers and should serve as an introduction to the main ideas
of nonlinear filtering, and as a segway to more advanced and specialized
literature.Comment: 64 page
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