7,820 research outputs found
Variable Splitting Methods for Constrained State Estimation in Partially Observed Markov Processes
In this paper, we propose a class of efficient, accurate, and general methods
for solving state-estimation problems with equality and inequality constraints.
The methods are based on recent developments in variable splitting and
partially observed Markov processes. We first present the generalized framework
based on variable splitting, then develop efficient methods to solve the
state-estimation subproblems arising in the framework. The solutions to these
subproblems can be made efficient by leveraging the Markovian structure of the
model as is classically done in so-called Bayesian filtering and smoothing
methods. The numerical experiments demonstrate that our methods outperform
conventional optimization methods in computation cost as well as the estimation
performance.Comment: 3 figure
Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization
Multiplicative noise (also known as speckle noise) models are central to the
study of coherent imaging systems, such as synthetic aperture radar and sonar,
and ultrasound and laser imaging. These models introduce two additional layers
of difficulties with respect to the standard Gaussian additive noise scenario:
(1) the noise is multiplied by (rather than added to) the original image; (2)
the noise is not Gaussian, with Rayleigh and Gamma being commonly used
densities. These two features of multiplicative noise models preclude the
direct application of most state-of-the-art algorithms, which are designed for
solving unconstrained optimization problems where the objective has two terms:
a quadratic data term (log-likelihood), reflecting the additive and Gaussian
nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a
total variation or wavelet-based regularizer/prior). In this paper, we address
these difficulties by: (1) converting the multiplicative model into an additive
one by taking logarithms, as proposed by some other authors; (2) using variable
splitting to obtain an equivalent constrained problem; and (3) dealing with
this optimization problem using the augmented Lagrangian framework. A set of
experiments shows that the proposed method, which we name MIDAL (multiplicative
image denoising by augmented Lagrangian), yields state-of-the-art results both
in terms of speed and denoising performance.Comment: 11 pages, 7 figures, 2 tables. To appear in the IEEE Transactions on
Image Processing
Robot introspection through learned hidden Markov models
In this paper we describe a machine learning approach for acquiring a model of a robot behaviour from raw sensor data. We are interested in automating the acquisition of behavioural models to provide a robot with an introspective capability. We assume that the behaviour of a robot in achieving a task can be modelled as a finite stochastic state transition system. Beginning with data recorded by a robot in the execution of a task, we use unsupervised learning techniques to estimate a hidden Markov model (HMM) that can be used both for predicting and explaining the behaviour of the robot in subsequent executions of the task. We demonstrate that it is feasible to automate the entire process of learning a high quality HMM from the data recorded by the robot during execution of its task.The learned HMM can be used both for monitoring and controlling the behaviour of the robot. The ultimate purpose of our work is to learn models for the full set of tasks associated with a given problem domain, and to integrate these models with a generative task planner. We want to show that these models can be used successfully in controlling the execution of a plan. However, this paper does not develop the planning and control aspects of our work, focussing instead on the learning methodology and the evaluation of a learned model. The essential property of the models we seek to construct is that the most probable trajectory through a model, given the observations made by the robot, accurately diagnoses, or explains, the behaviour that the robot actually performed when making these observations. In the work reported here we consider a navigation task. We explain the learning process, the experimental setup and the structure of the resulting learned behavioural models. We then evaluate the extent to which explanations proposed by the learned models accord with a human observer's interpretation of the behaviour exhibited by the robot in its execution of the task
The Computational Structure of Spike Trains
Neurons perform computations, and convey the results of those computations
through the statistical structure of their output spike trains. Here we present
a practical method, grounded in the information-theoretic analysis of
prediction, for inferring a minimal representation of that structure and for
characterizing its complexity. Starting from spike trains, our approach finds
their causal state models (CSMs), the minimal hidden Markov models or
stochastic automata capable of generating statistically identical time series.
We then use these CSMs to objectively quantify both the generalizable structure
and the idiosyncratic randomness of the spike train. Specifically, we show that
the expected algorithmic information content (the information needed to
describe the spike train exactly) can be split into three parts describing (1)
the time-invariant structure (complexity) of the minimal spike-generating
process, which describes the spike train statistically; (2) the randomness
(internal entropy rate) of the minimal spike-generating process; and (3) a
residual pure noise term not described by the minimal spike-generating process.
We use CSMs to approximate each of these quantities. The CSMs are inferred
nonparametrically from the data, making only mild regularity assumptions, via
the causal state splitting reconstruction algorithm. The methods presented here
complement more traditional spike train analyses by describing not only spiking
probability and spike train entropy, but also the complexity of a spike train's
structure. We demonstrate our approach using both simulated spike trains and
experimental data recorded in rat barrel cortex during vibrissa stimulation.Comment: Somewhat different format from journal version but same conten
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