248 research outputs found
Genetic Transfer or Population Diversification? Deciphering the Secret Ingredients of Evolutionary Multitask Optimization
Evolutionary multitasking has recently emerged as a novel paradigm that
enables the similarities and/or latent complementarities (if present) between
distinct optimization tasks to be exploited in an autonomous manner simply by
solving them together with a unified solution representation scheme. An
important matter underpinning future algorithmic advancements is to develop a
better understanding of the driving force behind successful multitask
problem-solving. In this regard, two (seemingly disparate) ideas have been put
forward, namely, (a) implicit genetic transfer as the key ingredient
facilitating the exchange of high-quality genetic material across tasks, and
(b) population diversification resulting in effective global search of the
unified search space encompassing all tasks. In this paper, we present some
empirical results that provide a clearer picture of the relationship between
the two aforementioned propositions. For the numerical experiments we make use
of Sudoku puzzles as case studies, mainly because of their feature that
outwardly unlike puzzle statements can often have nearly identical final
solutions. The experiments reveal that while on many occasions genetic transfer
and population diversity may be viewed as two sides of the same coin, the wider
implication of genetic transfer, as shall be shown herein, captures the true
essence of evolutionary multitasking to the fullest.Comment: 7 pages, 6 figure
Large-scale Heteroscedastic Regression via Gaussian Process
Heteroscedastic regression considering the varying noises among observations
has many applications in the fields like machine learning and statistics. Here
we focus on the heteroscedastic Gaussian process (HGP) regression which
integrates the latent function and the noise function together in a unified
non-parametric Bayesian framework. Though showing remarkable performance, HGP
suffers from the cubic time complexity, which strictly limits its application
to big data. To improve the scalability, we first develop a variational sparse
inference algorithm, named VSHGP, to handle large-scale datasets. Furthermore,
two variants are developed to improve the scalability and capability of VSHGP.
The first is stochastic VSHGP (SVSHGP) which derives a factorized evidence
lower bound, thus enhancing efficient stochastic variational inference. The
second is distributed VSHGP (DVSHGP) which (i) follows the Bayesian committee
machine formalism to distribute computations over multiple local VSHGP experts
with many inducing points; and (ii) adopts hybrid parameters for experts to
guard against over-fitting and capture local variety. The superiority of DVSHGP
and SVSHGP as compared to existing scalable heteroscedastic/homoscedastic GPs
is then extensively verified on various datasets.Comment: 14 pages, 15 figure
Understanding and Comparing Scalable Gaussian Process Regression for Big Data
As a non-parametric Bayesian model which produces informative predictive
distribution, Gaussian process (GP) has been widely used in various fields,
like regression, classification and optimization. The cubic complexity of
standard GP however leads to poor scalability, which poses challenges in the
era of big data. Hence, various scalable GPs have been developed in the
literature in order to improve the scalability while retaining desirable
prediction accuracy. This paper devotes to investigating the methodological
characteristics and performance of representative global and local scalable GPs
including sparse approximations and local aggregations from four main
perspectives: scalability, capability, controllability and robustness. The
numerical experiments on two toy examples and five real-world datasets with up
to 250K points offer the following findings. In terms of scalability, most of
the scalable GPs own a time complexity that is linear to the training size. In
terms of capability, the sparse approximations capture the long-term spatial
correlations, the local aggregations capture the local patterns but suffer from
over-fitting in some scenarios. In terms of controllability, we could improve
the performance of sparse approximations by simply increasing the inducing
size. But this is not the case for local aggregations. In terms of robustness,
local aggregations are robust to various initializations of hyperparameters due
to the local attention mechanism. Finally, we highlight that the proper hybrid
of global and local scalable GPs may be a promising way to improve both the
model capability and scalability for big data.Comment: 25 pages, 15 figures, preprint submitted to KB
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