41,379 research outputs found
Robust phase retrieval with the swept approximate message passing (prSAMP) algorithm
In phase retrieval, the goal is to recover a complex signal from the
magnitude of its linear measurements. While many well-known algorithms
guarantee deterministic recovery of the unknown signal using i.i.d. random
measurement matrices, they suffer serious convergence issues some
ill-conditioned matrices. As an example, this happens in optical imagers using
binary intensity-only spatial light modulators to shape the input wavefront.
The problem of ill-conditioned measurement matrices has also been a topic of
interest for compressed sensing researchers during the past decade. In this
paper, using recent advances in generic compressed sensing, we propose a new
phase retrieval algorithm that well-adopts for both Gaussian i.i.d. and binary
matrices using both sparse and dense input signals. This algorithm is also
robust to the strong noise levels found in some imaging applications
The Extended Parameter Filter
The parameters of temporal models, such as dynamic Bayesian networks, may be
modelled in a Bayesian context as static or atemporal variables that influence
transition probabilities at every time step. Particle filters fail for models
that include such variables, while methods that use Gibbs sampling of parameter
variables may incur a per-sample cost that grows linearly with the length of
the observation sequence. Storvik devised a method for incremental computation
of exact sufficient statistics that, for some cases, reduces the per-sample
cost to a constant. In this paper, we demonstrate a connection between
Storvik's filter and a Kalman filter in parameter space and establish more
general conditions under which Storvik's filter works. Drawing on an analogy to
the extended Kalman filter, we develop and analyze, both theoretically and
experimentally, a Taylor approximation to the parameter posterior that allows
Storvik's method to be applied to a broader class of models. Our experiments on
both synthetic examples and real applications show improvement over existing
methods
Structural Drift: The Population Dynamics of Sequential Learning
We introduce a theory of sequential causal inference in which learners in a
chain estimate a structural model from their upstream teacher and then pass
samples from the model to their downstream student. It extends the population
dynamics of genetic drift, recasting Kimura's selectively neutral theory as a
special case of a generalized drift process using structured populations with
memory. We examine the diffusion and fixation properties of several drift
processes and propose applications to learning, inference, and evolution. We
also demonstrate how the organization of drift process space controls fidelity,
facilitates innovations, and leads to information loss in sequential learning
with and without memory.Comment: 15 pages, 9 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/sdrift.ht
Inference via low-dimensional couplings
We investigate the low-dimensional structure of deterministic transformations
between random variables, i.e., transport maps between probability measures. In
the context of statistics and machine learning, these transformations can be
used to couple a tractable "reference" measure (e.g., a standard Gaussian) with
a target measure of interest. Direct simulation from the desired measure can
then be achieved by pushing forward reference samples through the map. Yet
characterizing such a map---e.g., representing and evaluating it---grows
challenging in high dimensions. The central contribution of this paper is to
establish a link between the Markov properties of the target measure and the
existence of low-dimensional couplings, induced by transport maps that are
sparse and/or decomposable. Our analysis not only facilitates the construction
of transformations in high-dimensional settings, but also suggests new
inference methodologies for continuous non-Gaussian graphical models. For
instance, in the context of nonlinear state-space models, we describe new
variational algorithms for filtering, smoothing, and sequential parameter
inference. These algorithms can be understood as the natural
generalization---to the non-Gaussian case---of the square-root
Rauch-Tung-Striebel Gaussian smoother.Comment: 78 pages, 25 figure
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