72,731 research outputs found

    A Bi-level Nonlinear Eigenvector Algorithm for Wasserstein Discriminant Analysis

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Full text link
    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

    Get PDF
    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

    Full text link
    In this paper we explore noise tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an unobservable{\bf unobservable} 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
    corecore