Statistical learning theory

About: Statistical learning theory is a research topic. Over the lifetime, 1618 publications have been published within this topic receiving 158033 citations.

Fault diagnosis model of DGA for power transformer based on FCM and SVM

Abstract: Support vector machine (SVM) is a novel machine learning based on statistical learning theory, SVM is powerful for the problem with small sample, nonlinear and high dimension. A model of transformer diagnosis based on SVM is present in this paper in which it uses the grid search method based on cross-validation to determine model parameters. Taking into account the compactness characteristics of DGA data, the fuzzy C-means (FCM) clustering method is adopted to pre-select samples achieved. It solves the problem of long time expended on model parameters determined, and enhances a certain promotion of the model extension ability. Practical analysis shows that this model has a good classification results and extension ability.

Generalisation in fully-connected neural networks for time series forecasting.

Abstract: In this paper we study the generalization capabilities of fully-connected neural networks trained in the context of time series forecasting. Time series do not satisfy the typical assumption in statistical learning theory of the data being i.i.d. samples from some data-generating distribution. We use the input and weight Hessians, that is the smoothness of the learned function with respect to the input and the width of the minimum in weight space, to quantify a network's ability to generalize to unseen data. While such generalization metrics have been studied extensively in the i.i.d. setting of for example image recognition, here we empirically validate their use in the task of time series forecasting. Furthermore we discuss how one can control the generalization capability of the network by means of the training process using the learning rate, batch size and the number of training iterations as controls. Using these hyperparameters one can efficiently control the complexity of the output function without imposing explicit constraints.

SVM Applied to Modeling of Cancer Date

Abstract: As a novel kind of general learning machine based on statistical learning theory(SLT),Support Vector Machine is received much attentions in recent years,and successfully used in some topics of pattern recognition region.SVM classification algorithms were applied to the cancer data compared with KNN and ANN,the prediction accuracy reached 98%,the results showed that SVM is a better prediction method than ANN and KNN in this problem,the model might be referred as an aiding means of the diagnosis for the cancer.

A nonasymptotic law of iterated logarithm for general M-estimators

Abstract: M-estimators are ubiquitous in machine learning and statistical learning theory They are used both for defining prediction strategies and for evaluating their precision In this paper, we propose the first non-asymptotic "any-time" deviation bounds for general M-estimators, where "any-time" means that the bound holds with a prescribed probability for every sample size These bounds are nonasymptotic versions of the law of iterated logarithm They are established under general assumptions such as Lipschitz continuity of the loss function and (local) curvature of the population risk These conditions are satisfied for most examples used in machine learning, including those ensuring robustness to outliers and to heavy tailed distributions As an example of application, we consider the problem of best arm identification in a parametric stochastic multi-arm bandit setting We show that the established bound can be converted into a new algorithm, with provably optimal theoretical guarantees Numerical experiments illustrating the validity of the algorithm are reported

SVM-based supervised and unsupervised classification schemes

Abstract: The aim of the research reported is to propose a training algorithm for support vector machine based on kernel functions and to test its performance in case of non-linearly separable data. The training is based on the Sequential Minimal Optimization introduced by J.C. Platt in 1999. Several classifications schemes resulted by combining the SVM and the 2-means methods are proposed in the fifth section of the paper. A series of conclusions derived experimentally concerning the comparative analysis of the performances proved by the proposed methods are summarized in the final part of the paper. The tests were performed on samples randomly generated from Gaussian two-dimensional distributions, and on data available in Wisconsin Diagnostic Breast Cancer Database.