19,644 research outputs found
Partition MCMC for inference on acyclic digraphs
Acyclic digraphs are the underlying representation of Bayesian networks, a
widely used class of probabilistic graphical models. Learning the underlying
graph from data is a way of gaining insights about the structural properties of
a domain. Structure learning forms one of the inference challenges of
statistical graphical models.
MCMC methods, notably structure MCMC, to sample graphs from the posterior
distribution given the data are probably the only viable option for Bayesian
model averaging. Score modularity and restrictions on the number of parents of
each node allow the graphs to be grouped into larger collections, which can be
scored as a whole to improve the chain's convergence. Current examples of
algorithms taking advantage of grouping are the biased order MCMC, which acts
on the alternative space of permuted triangular matrices, and non ergodic edge
reversal moves.
Here we propose a novel algorithm, which employs the underlying combinatorial
structure of DAGs to define a new grouping. As a result convergence is improved
compared to structure MCMC, while still retaining the property of producing an
unbiased sample. Finally the method can be combined with edge reversal moves to
improve the sampler further.Comment: Revised version. 34 pages, 16 figures. R code available at
https://github.com/annlia/partitionMCM
The semiclassical relation between open trajectories and periodic orbits for the Wigner time delay
The Wigner time delay of a classically chaotic quantum system can be
expressed semiclassically either in terms of pairs of scattering trajectories
that enter and leave the system or in terms of the periodic orbits trapped
inside the system. We show how these two pictures are related on the
semiclassical level. We start from the semiclassical formula with the
scattering trajectories and derive from it all terms in the periodic orbit
formula for the time delay. The main ingredient in this calculation is a new
type of correlation between scattering trajectories which is due to
trajectories that approach the trapped periodic orbits closely. The equivalence
between the two pictures is also demonstrated by considering correlation
functions of the time delay. A corresponding calculation for the conductance
gives no periodic orbit contributions in leading order.Comment: 21 pages, 5 figure
Learning and Acting in Peripersonal Space: Moving, Reaching, and Grasping
The young infant explores its body, its sensorimotor system, and the
immediately accessible parts of its environment, over the course of a few
months creating a model of peripersonal space useful for reaching and grasping
objects around it. Drawing on constraints from the empirical literature on
infant behavior, we present a preliminary computational model of this learning
process, implemented and evaluated on a physical robot. The learning agent
explores the relationship between the configuration space of the arm, sensing
joint angles through proprioception, and its visual perceptions of the hand and
grippers. The resulting knowledge is represented as the peripersonal space
(PPS) graph, where nodes represent states of the arm, edges represent safe
movements, and paths represent safe trajectories from one pose to another. In
our model, the learning process is driven by intrinsic motivation. When
repeatedly performing an action, the agent learns the typical result, but also
detects unusual outcomes, and is motivated to learn how to make those unusual
results reliable. Arm motions typically leave the static background unchanged,
but occasionally bump an object, changing its static position. The reach action
is learned as a reliable way to bump and move an object in the environment.
Similarly, once a reliable reach action is learned, it typically makes a
quasi-static change in the environment, moving an object from one static
position to another. The unusual outcome is that the object is accidentally
grasped (thanks to the innate Palmar reflex), and thereafter moves dynamically
with the hand. Learning to make grasps reliable is more complex than for
reaches, but we demonstrate significant progress. Our current results are steps
toward autonomous sensorimotor learning of motion, reaching, and grasping in
peripersonal space, based on unguided exploration and intrinsic motivation.Comment: 35 pages, 13 figure
Sequential Monte Carlo EM for multivariate probit models
Multivariate probit models (MPM) have the appealing feature of capturing some
of the dependence structure between the components of multidimensional binary
responses. The key for the dependence modelling is the covariance matrix of an
underlying latent multivariate Gaussian. Most approaches to MLE in multivariate
probit regression rely on MCEM algorithms to avoid computationally intensive
evaluations of multivariate normal orthant probabilities. As an alternative to
the much used Gibbs sampler a new SMC sampler for truncated multivariate
normals is proposed. The algorithm proceeds in two stages where samples are
first drawn from truncated multivariate Student distributions and then
further evolved towards a Gaussian. The sampler is then embedded in a MCEM
algorithm. The sequential nature of SMC methods can be exploited to design a
fully sequential version of the EM, where the samples are simply updated from
one iteration to the next rather than resampled from scratch. Recycling the
samples in this manner significantly reduces the computational cost. An
alternative view of the standard conditional maximisation step provides the
basis for an iterative procedure to fully perform the maximisation needed in
the EM algorithm. The identifiability of MPM is also thoroughly discussed. In
particular, the likelihood invariance can be embedded in the EM algorithm to
ensure that constrained and unconstrained maximisation are equivalent. A simple
iterative procedure is then derived for either maximisation which takes
effectively no computational time. The method is validated by applying it to
the widely analysed Six Cities dataset and on a higher dimensional simulated
example. Previous approaches to the Six Cities overly restrict the parameter
space but, by considering the correct invariance, the maximum likelihood is
quite naturally improved when treating the full unrestricted model.Comment: 26 pages, 2 figures. In press, Computational Statistics & Data
Analysi
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