76,042 research outputs found
Differentiating the multipoint Expected Improvement for optimal batch design
This work deals with parallel optimization of expensive objective functions
which are modeled as sample realizations of Gaussian processes. The study is
formalized as a Bayesian optimization problem, or continuous multi-armed bandit
problem, where a batch of q > 0 arms is pulled in parallel at each iteration.
Several algorithms have been developed for choosing batches by trading off
exploitation and exploration. As of today, the maximum Expected Improvement
(EI) and Upper Confidence Bound (UCB) selection rules appear as the most
prominent approaches for batch selection. Here, we build upon recent work on
the multipoint Expected Improvement criterion, for which an analytic expansion
relying on Tallis' formula was recently established. The computational burden
of this selection rule being still an issue in application, we derive a
closed-form expression for the gradient of the multipoint Expected Improvement,
which aims at facilitating its maximization using gradient-based ascent
algorithms. Substantial computational savings are shown in application. In
addition, our algorithms are tested numerically and compared to
state-of-the-art UCB-based batch-sequential algorithms. Combining starting
designs relying on UCB with gradient-based EI local optimization finally
appears as a sound option for batch design in distributed Gaussian Process
optimization
Polynomial-Chaos-based Kriging
Computer simulation has become the standard tool in many engineering fields
for designing and optimizing systems, as well as for assessing their
reliability. To cope with demanding analysis such as optimization and
reliability, surrogate models (a.k.a meta-models) have been increasingly
investigated in the last decade. Polynomial Chaos Expansions (PCE) and Kriging
are two popular non-intrusive meta-modelling techniques. PCE surrogates the
computational model with a series of orthonormal polynomials in the input
variables where polynomials are chosen in coherency with the probability
distributions of those input variables. On the other hand, Kriging assumes that
the computer model behaves as a realization of a Gaussian random process whose
parameters are estimated from the available computer runs, i.e. input vectors
and response values. These two techniques have been developed more or less in
parallel so far with little interaction between the researchers in the two
fields. In this paper, PC-Kriging is derived as a new non-intrusive
meta-modeling approach combining PCE and Kriging. A sparse set of orthonormal
polynomials (PCE) approximates the global behavior of the computational model
whereas Kriging manages the local variability of the model output. An adaptive
algorithm similar to the least angle regression algorithm determines the
optimal sparse set of polynomials. PC-Kriging is validated on various benchmark
analytical functions which are easy to sample for reference results. From the
numerical investigations it is concluded that PC-Kriging performs better than
or at least as good as the two distinct meta-modeling techniques. A larger gain
in accuracy is obtained when the experimental design has a limited size, which
is an asset when dealing with demanding computational models
Tree models for difference and change detection in a complex environment
A new family of tree models is proposed, which we call "differential trees."
A differential tree model is constructed from multiple data sets and aims to
detect distributional differences between them. The new methodology differs
from the existing difference and change detection techniques in its
nonparametric nature, model construction from multiple data sets, and
applicability to high-dimensional data. Through a detailed study of an arson
case in New Zealand, where an individual is known to have been laying
vegetation fires within a certain time period, we illustrate how these models
can help detect changes in the frequencies of event occurrences and uncover
unusual clusters of events in a complex environment.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS548 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
fMRI Investigation of Cortical and Subcortical Networks in the Learning of Abstract and Effector-Specific Representations of Motor Sequences
A visuomotor sequence can be learned as a series of visuo-spatial cues or as a sequence of effector movements. Earlier imaging studies have revealed that a network of brain areas is activated in the course of motor sequence learning. However these studies do not address the question of the type of representation being established at various stages of visuomotor sequence learning. In an earlier behavioral study, we demonstrated that acquisition of visuo-spatial sequence representation enables rapid learning in the early stage and progressive establishment of somato-motor representation helps speedier execution by the late stage. We conducted functional magnetic resonance imaging (fMRI) experiments wherein subjects learned and practiced the same sequence alternately in normal and rotated settings. In one rotated setting (visual), subjects learned a new motor sequence in response to an identical sequence of visual cues as in normal. In another rotated setting (motor), the display sequence was altered as compared to normal, but the same sequence of effector movements were used to perform the sequence. Comparison of different rotated settings revealed analogous transitions both in the cortical and subcortical sites during visuomotor sequence learning a transition of activity from parietal to parietal-premotor and then to premotor cortex and a concomitant shift was observed from anterior putamen to a combined activity in both anterior and posterior putamen and finally to posterior putamen. These results suggest a putative role for engagement of different cortical and subcortical networks at various stages of learning in supporting distinct sequence representations
Learning and Production of Movement Sequences: Behavioral, Neurophysiological, and Modeling Perspectives
A growing wave of behavioral studies, using a wide variety of paradigms that were introduced or greatly refined in recent years, has generated a new wealth of parametric observations about serial order behavior. What was a mere trickle of neurophysiological studies has grown to a more steady stream of probes of neural sites and mechanisms underlying sequential behavior. Moreover, simulation models of serial behavior generation have begun to open a channel to link cellular dynamics with cognitive and behavioral dynamics. Here we summarize the major results from prominent sequence learning and performance tasks, namely immediate serial recall, typing, 2XN, discrete sequence production, and serial reaction time. These populate a continuum from higher to lower degrees of internal control of sequential organization. The main movement classes covered are speech and keypressing, both involving small amplitude movements that are very amenable to parametric study. A brief synopsis of classes of serial order models, vis-à-vis the detailing of major effects found in the behavioral data, leads to a focus on competitive queuing (CQ) models. Recently, the many behavioral predictive successes of CQ models have been joined by successful prediction of distinctively patterend electrophysiological recordings in prefrontal cortex, wherein parallel activation dynamics of multiple neural ensembles strikingly matches the parallel dynamics predicted by CQ theory. An extended CQ simulation model-the N-STREAMS neural network model-is then examined to highlight issues in ongoing attemptes to accomodate a broader range of behavioral and neurophysiological data within a CQ-consistent theory. Important contemporary issues such as the nature of working memory representations for sequential behavior, and the development and role of chunks in hierarchial control are prominent throughout.Defense Advanced Research Projects Agency/Office of Naval Research (N00014-95-1-0409); National Institute of Mental Health (R01 DC02852
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