1,372 research outputs found
A dimensionality reduction technique for unconstrained global optimization of functions with low effective dimensionality
We investigate the unconstrained global optimization of functions with low
effective dimensionality, that are constant along certain (unknown) linear
subspaces. Extending the technique of random subspace embeddings in [Wang et
al., Bayesian optimization in a billion dimensions via random embeddings. JAIR,
55(1): 361--387, 2016], we study a generic Random Embeddings for Global
Optimization (REGO) framework that is compatible with any global minimization
algorithm. Instead of the original, potentially large-scale optimization
problem, within REGO, a Gaussian random, low-dimensional problem with bound
constraints is formulated and solved in a reduced space. We provide novel
probabilistic bounds for the success of REGO in solving the original, low
effective-dimensionality problem, which show its independence of the
(potentially large) ambient dimension and its precise dependence on the
dimensions of the effective and randomly embedding subspaces. These results
significantly improve existing theoretical analyses by providing the exact
distribution of a reduced minimizer and its Euclidean norm and by the general
assumptions required on the problem. We validate our theoretical findings by
extensive numerical testing of REGO with three types of global optimization
solvers, illustrating the improved scalability of REGO compared to the
full-dimensional application of the respective solvers.Comment: 32 pages, 10 figures, submitted to Information and Inference: a
journal of the IMA, also submitted to optimization-online repositor
ZOOpt: Toolbox for Derivative-Free Optimization
Recent advances of derivative-free optimization allow efficient approximating
the global optimal solutions of sophisticated functions, such as functions with
many local optima, non-differentiable and non-continuous functions. This
article describes the ZOOpt (https://github.com/eyounx/ZOOpt) toolbox that
provides efficient derivative-free solvers and are designed easy to use. ZOOpt
provides a Python package for single-thread optimization, and a light-weighted
distributed version with the help of the Julia language for Python described
functions. ZOOpt toolbox particularly focuses on optimization problems in
machine learning, addressing high-dimensional, noisy, and large-scale problems.
The toolbox is being maintained toward ready-to-use tool in real-world machine
learning tasks
Optimal Hyperparameters for Deep LSTM-Networks for Sequence Labeling Tasks
Selecting optimal parameters for a neural network architecture can often make
the difference between mediocre and state-of-the-art performance. However,
little is published which parameters and design choices should be evaluated or
selected making the correct hyperparameter optimization often a "black art that
requires expert experiences" (Snoek et al., 2012). In this paper, we evaluate
the importance of different network design choices and hyperparameters for five
common linguistic sequence tagging tasks (POS, Chunking, NER, Entity
Recognition, and Event Detection). We evaluated over 50.000 different setups
and found, that some parameters, like the pre-trained word embeddings or the
last layer of the network, have a large impact on the performance, while other
parameters, for example the number of LSTM layers or the number of recurrent
units, are of minor importance. We give a recommendation on a configuration
that performs well among different tasks.Comment: 34 pages. 9 page version of this paper published at EMNLP 201
Search Efficient Binary Network Embedding
Traditional network embedding primarily focuses on learning a dense vector
representation for each node, which encodes network structure and/or node
content information, such that off-the-shelf machine learning algorithms can be
easily applied to the vector-format node representations for network analysis.
However, the learned dense vector representations are inefficient for
large-scale similarity search, which requires to find the nearest neighbor
measured by Euclidean distance in a continuous vector space. In this paper, we
propose a search efficient binary network embedding algorithm called BinaryNE
to learn a sparse binary code for each node, by simultaneously modeling node
context relations and node attribute relations through a three-layer neural
network. BinaryNE learns binary node representations efficiently through a
stochastic gradient descent based online learning algorithm. The learned binary
encoding not only reduces memory usage to represent each node, but also allows
fast bit-wise comparisons to support much quicker network node search compared
to Euclidean distance or other distance measures. Our experiments and
comparisons show that BinaryNE not only delivers more than 23 times faster
search speed, but also provides comparable or better search quality than
traditional continuous vector based network embedding methods
BOCK : Bayesian Optimization with Cylindrical Kernels
A major challenge in Bayesian Optimization is the boundary issue (Swersky,
2017) where an algorithm spends too many evaluations near the boundary of its
search space. In this paper, we propose BOCK, Bayesian Optimization with
Cylindrical Kernels, whose basic idea is to transform the ball geometry of the
search space using a cylindrical transformation. Because of the transformed
geometry, the Gaussian Process-based surrogate model spends less budget
searching near the boundary, while concentrating its efforts relatively more
near the center of the search region, where we expect the solution to be
located. We evaluate BOCK extensively, showing that it is not only more
accurate and efficient, but it also scales successfully to problems with a
dimensionality as high as 500. We show that the better accuracy and scalability
of BOCK even allows optimizing modestly sized neural network layers, as well as
neural network hyperparameters.Comment: 10 pages, 5 figures, 5 tables, 1 algorith
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