72,731 research outputs found
A Bi-level Nonlinear Eigenvector Algorithm for Wasserstein Discriminant Analysis
Much like the classical Fisher linear discriminant analysis, Wasserstein
discriminant analysis (WDA) is a supervised linear dimensionality reduction
method that seeks a projection matrix to maximize the dispersion of different
data classes and minimize the dispersion of same data classes. However, in
contrast, WDA can account for both global and local inter-connections between
data classes using a regularized Wasserstein distance. WDA is formulated as a
bi-level nonlinear trace ratio optimization. In this paper, we present a
bi-level nonlinear eigenvector (NEPv) algorithm, called WDA-nepv. The inner
kernel of WDA-nepv for computing the optimal transport matrix of the
regularized Wasserstein distance is formulated as an NEPv, and meanwhile the
outer kernel for the trace ratio optimization is also formulated as another
NEPv. Consequently, both kernels can be computed efficiently via
self-consistent-field iterations and modern solvers for linear eigenvalue
problems. Comparing with the existing algorithms for WDA, WDA-nepv is
derivative-free and surrogate-model-free. The computational efficiency and
applications in classification accuracy of WDA-nepv are demonstrated using
synthetic and real-life datasets
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
Open-Category Classification by Adversarial Sample Generation
In real-world classification tasks, it is difficult to collect training
samples from all possible categories of the environment. Therefore, when an
instance of an unseen class appears in the prediction stage, a robust
classifier should be able to tell that it is from an unseen class, instead of
classifying it to be any known category. In this paper, adopting the idea of
adversarial learning, we propose the ASG framework for open-category
classification. ASG generates positive and negative samples of seen categories
in the unsupervised manner via an adversarial learning strategy. With the
generated samples, ASG then learns to tell seen from unseen in the supervised
manner. Experiments performed on several datasets show the effectiveness of
ASG.Comment: Published in IJCAI 201
Riemann-Theta Boltzmann Machine
A general Boltzmann machine with continuous visible and discrete integer
valued hidden states is introduced. Under mild assumptions about the connection
matrices, the probability density function of the visible units can be solved
for analytically, yielding a novel parametric density function involving a
ratio of Riemann-Theta functions. The conditional expectation of a hidden state
for given visible states can also be calculated analytically, yielding a
derivative of the logarithmic Riemann-Theta function. The conditional
expectation can be used as activation function in a feedforward neural network,
thereby increasing the modelling capacity of the network. Both the Boltzmann
machine and the derived feedforward neural network can be successfully trained
via standard gradient- and non-gradient-based optimization techniques.Comment: 29 pages, 11 figures, final version published in Neurocomputin
A multi-objective DIRECT algorithm for ship hull optimization
The paper is concerned with black-box nonlinear constrained multi-objective optimization problems. Our interest is the definition of a multi-objective deterministic partition-based algorithm. The main target of the proposed algorithm is the solution of a real ship hull optimization problem. To this purpose and in pursuit of an efficient method, we develop an hybrid algorithm by coupling a multi-objective DIRECT-type algorithm with an efficient derivative-free local algorithm. The results obtained on a set of “hard” nonlinear constrained multi-objective test problems show viability of the proposed approach. Results on a hull-form optimization of a high-speed catamaran (sailing in head waves in the North Pacific Ocean) are also presented. In order to consider a real ocean environment, stochastic sea state and speed are taken into account. The problem is formulated as a multi-objective optimization aimed at (i) the reduction of the expected value of the mean total resistance in irregular head waves, at variable speed and (ii) the increase of the ship operability, with respect to a set of motion-related constraints. We show that the hybrid method performs well also on this industrial problem
Noise Tolerance under Risk Minimization
In this paper we explore noise tolerant learning of classifiers. We formulate
the problem as follows. We assume that there is an
training set which is noise-free. The actual training set given to the learning
algorithm is obtained from this ideal data set by corrupting the class label of
each example. The probability that the class label of an example is corrupted
is a function of the feature vector of the example. This would account for most
kinds of noisy data one encounters in practice. We say that a learning method
is noise tolerant if the classifiers learnt with the ideal noise-free data and
with noisy data, both have the same classification accuracy on the noise-free
data. In this paper we analyze the noise tolerance properties of risk
minimization (under different loss functions), which is a generic method for
learning classifiers. We show that risk minimization under 0-1 loss function
has impressive noise tolerance properties and that under squared error loss is
tolerant only to uniform noise; risk minimization under other loss functions is
not noise tolerant. We conclude the paper with some discussion on implications
of these theoretical results
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