11,312 research outputs found
Online Natural Gradient as a Kalman Filter
We cast Amari's natural gradient in statistical learning as a specific case
of Kalman filtering. Namely, applying an extended Kalman filter to estimate a
fixed unknown parameter of a probabilistic model from a series of observations,
is rigorously equivalent to estimating this parameter via an online stochastic
natural gradient descent on the log-likelihood of the observations.
In the i.i.d. case, this relation is a consequence of the "information
filter" phrasing of the extended Kalman filter. In the recurrent (state space,
non-i.i.d.) case, we prove that the joint Kalman filter over states and
parameters is a natural gradient on top of real-time recurrent learning (RTRL),
a classical algorithm to train recurrent models.
This exact algebraic correspondence provides relevant interpretations for
natural gradient hyperparameters such as learning rates or initialization and
regularization of the Fisher information matrix.Comment: 3rd version: expanded intr
Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models
This tutorial provides a gentle introduction to the particle
Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear
state-space models together with a software implementation in the statistical
programming language R. We employ a step-by-step approach to develop an
implementation of the PMH algorithm (and the particle filter within) together
with the reader. This final implementation is also available as the package
pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some
intuition as to how the algorithm operates and discuss some solutions to
problems that might occur in practice. To illustrate the use of PMH, we
consider parameter inference in a linear Gaussian state-space model with
synthetic data and a nonlinear stochastic volatility model with real-world
data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software.
Source code for R, Python and MATLAB available at:
https://github.com/compops/pmh-tutoria
Unscented Bayesian Optimization for Safe Robot Grasping
We address the robot grasp optimization problem of unknown objects
considering uncertainty in the input space. Grasping unknown objects can be
achieved by using a trial and error exploration strategy. Bayesian optimization
is a sample efficient optimization algorithm that is especially suitable for
this setups as it actively reduces the number of trials for learning about the
function to optimize. In fact, this active object exploration is the same
strategy that infants do to learn optimal grasps. One problem that arises while
learning grasping policies is that some configurations of grasp parameters may
be very sensitive to error in the relative pose between the object and robot
end-effector. We call these configurations unsafe because small errors during
grasp execution may turn good grasps into bad grasps. Therefore, to reduce the
risk of grasp failure, grasps should be planned in safe areas. We propose a new
algorithm, Unscented Bayesian optimization that is able to perform sample
efficient optimization while taking into consideration input noise to find safe
optima. The contribution of Unscented Bayesian optimization is twofold as if
provides a new decision process that drives exploration to safe regions and a
new selection procedure that chooses the optimal in terms of its safety without
extra analysis or computational cost. Both contributions are rooted on the
strong theory behind the unscented transformation, a popular nonlinear
approximation method. We show its advantages with respect to the classical
Bayesian optimization both in synthetic problems and in realistic robot grasp
simulations. The results highlights that our method achieves optimal and robust
grasping policies after few trials while the selected grasps remain in safe
regions.Comment: conference pape
Inverse Problems and Data Assimilation
These notes are designed with the aim of providing a clear and concise
introduction to the subjects of Inverse Problems and Data Assimilation, and
their inter-relations, together with citations to some relevant literature in
this area. The first half of the notes is dedicated to studying the Bayesian
framework for inverse problems. Techniques such as importance sampling and
Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the
desirable property that in the limit of an infinite number of samples they
reproduce the full posterior distribution. Since it is often computationally
intensive to implement these methods, especially in high dimensional problems,
approximate techniques such as approximating the posterior by a Dirac or a
Gaussian distribution are discussed. The second half of the notes cover data
assimilation. This refers to a particular class of inverse problems in which
the unknown parameter is the initial condition of a dynamical system, and in
the stochastic dynamics case the subsequent states of the system, and the data
comprises partial and noisy observations of that (possibly stochastic)
dynamical system. We will also demonstrate that methods developed in data
assimilation may be employed to study generic inverse problems, by introducing
an artificial time to generate a sequence of probability measures interpolating
from the prior to the posterior
Recent Progress in Image Deblurring
This paper comprehensively reviews the recent development of image
deblurring, including non-blind/blind, spatially invariant/variant deblurring
techniques. Indeed, these techniques share the same objective of inferring a
latent sharp image from one or several corresponding blurry images, while the
blind deblurring techniques are also required to derive an accurate blur
kernel. Considering the critical role of image restoration in modern imaging
systems to provide high-quality images under complex environments such as
motion, undesirable lighting conditions, and imperfect system components, image
deblurring has attracted growing attention in recent years. From the viewpoint
of how to handle the ill-posedness which is a crucial issue in deblurring
tasks, existing methods can be grouped into five categories: Bayesian inference
framework, variational methods, sparse representation-based methods,
homography-based modeling, and region-based methods. In spite of achieving a
certain level of development, image deblurring, especially the blind case, is
limited in its success by complex application conditions which make the blur
kernel hard to obtain and be spatially variant. We provide a holistic
understanding and deep insight into image deblurring in this review. An
analysis of the empirical evidence for representative methods, practical
issues, as well as a discussion of promising future directions are also
presented.Comment: 53 pages, 17 figure
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