Robust chance-constrained support vector machines with second-order moment information
Support vector machines (SVM) is one of the well known supervised classes of learning algorithms. Basic SVM models are dealing with the situation where the exact values of the data points are known. This paper studies SVM when the data points are uncertain. With some properties known for the distributions, chance-constrained SVM is used to ensure the small probability of misclassification for the uncertain data. As infinite number of distributions could have the known properties, the robust chance-constrained SVM requires efficient transformations of the chance constraints to make the problem solvable. In this paper, robust chance-constrained SVM with second-order moment information is studied and we obtain equivalent semidefinite programming and second order cone programming reformulations. The geometric interpretation is presented and numerical experiments are conducted. Three types of estimation errors for mean and covariance information are studied in this paper and the corresponding formulations and techniques to handle these types of errors are presented.
Interactive image segmentation is an important computer vision problem that has numerous real world applications. Models for image segmentation are generally trained to minimize the Hamming error in pixel labeling. The Hamming loss does not ensure that the topology/structure of the object being segmented is preserved and therefore is not a strong indicator of the quality of the segmentation as perceived by users. However, it is still ubiquitously used for training models because it decomposes over pixels and thus enables efficient learning. In this paper, we propose the use of a novel family of higher-order loss functions that encourage segmentations whose layout is similar to the ground-truth segmentation. Unlike the Hamming loss, these loss functions do not decompose over pixels and therefore cannot be directly used for loss-augmented inference. We show how our loss functions can be transformed to allow efficient learning and demonstrate the effectiveness of our method on a challenging segmentation dataset and validate the results using a user study. Our experimental results reveal that training with our layout-aware loss functions results in better segmentations that are preferred by users over segmentations obtained using conventional loss functions.
The paper considers the phoneme recognition by facial expressions of a speaker in voice-activated control systems. We have developed a neural network recognition algorithm by using the phonetic words decoding method and the requirement for isolated syllable pronunciation of voice commands. The paper presents the experimental results of viseme (facial and lip position corresponding to a particular phoneme) classification of Russian vowels. We show the dependence of the classification accuracy on the used classifier (multilayer feed-forward network, support vector machine, k-nearest neighbor method), image features (histogram of oriented gradients, eigenvectors, SURF local descriptors) and the type of camera (built-in or Kinect one). The best accuracy of speaker-dependent recognition is shown to be 85% for a built-in camera and 96% for Kinect depth maps when the classification is performed with the histogram of oriented gradients and the support vector machine.
This book constitutes the refereed proceedings of the 10th International Conference on Machine Learning and Data Mining in Pattern Recognition, MLDM 2014, held in St. Petersburg, Russia in July 2014. The 40 full papers presented were carefully reviewed and selected from 128 submissions. The topics range from theoretical topics for classification, clustering, association rule and pattern mining to specific data mining methods for the different multimedia data types such as image mining, text mining, video mining and Web mining.
This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Learning and Optimization, LION 8, which was held in Gainesville, FL, USA, in February 2014. The 33 contributions presented were carefully reviewed and selected for inclusion in this book. A large variety of topics are covered, such as algorithm configuration; multiobjective optimization; metaheuristics; graphs and networks; logistics and transportation; and biomedical applications.
Varying coefficient models are useful generalizations of parametric linear models. They allow for parameters that depend on a covariate or that develop in time. They have a wide range of applications in time series analysis and regression. In time series analysis they have turned out to be a powerful approach to infer on behavioral and structural changes over time. In this paper, we are concerned with high dimensional varying coefficient models including the time varying coefficient model. Most studies in high dimensional nonparametric models treat penalization of series estimators. On the other side, kernel smoothing is a well established, well understood and successful approach in nonparametric estimation, in particular in the time varying coefficient model. But not much has been done for kernel smoothing in high-dimensional models. In this paper we will close this gap and we develop a penalized kernel smoothing approach for sparse high-dimensional models. The proposed estimators make use of a novel penalization scheme working with kernel smoothing. We establish a general and systematic theoretical analysis in high dimensions. This complements recent alternative approaches that are based on basis approximations and that allow more direct arguments to carry over insights from high-dimensional linear models. Furthermore, we develop theory not only for regression with independent observations but also for local stationary time series in high-dimensional sparse varying coefficient models. The development of theory for local stationary processes in a high-dimensional setting creates technical challenges. We also address issues of numerical implementation and of data adaptive selection of tuning parameters for penalization.The finite sample performance of the proposed methods is studied by simulations and it is illustrated by an empirical analysis of NASDAQ composite index data.
Support Vector Machines (SVM) is one of the well known supervised classes of learning algorithms. SVM have wide applications to many fields in recent years and also many algorithmic and modeling variations. Basic SVM models are dealing with the situation where the exact values of the data points are known. This paper presents a survey of SVM when the data points are uncertain. When a direct model cannot guarantee a generally good performance on the uncertainty set, robust optimization is introduced to deal with the worst case scenario and still guarantee an optimal performance. The data uncertainty could be an additive noise which is bounded by norm, where some efficient linear programming models are presented under certain conditions; or could be intervals with support and extremum values; or a more general case of polyhedral uncertainties with formulations presented. Another field of the uncertainty analysis is chance constrained SVM which is used to ensure the small probability of misclassification for the uncertain data. The multivariate Chebyshev inequality and Bernstein bounding schemes have been used to transform the chance constraints through robust optimization. The Chebyshev based model employs moment information of the uncertain training points. The Bernstein bounds can be less conservative than the Chebyshev bounds since it employs both support and moment information, but it also makes a strong assumption that all the elements in the data set are independent.
In this paper, we use robust optimization models to formulate the support vector machines (SVMs) with polyhedral uncertainties of the input data points. The formulations in our models are nonlinear and we use Lagrange multipliers to give the first-order optimality conditions and reformulation methods to solve these problems. In addition, we have proposed the models for transductive SVMs with input uncertainties.
Summarizes the latest applications of robust optimization in data mining.
An essential accompaniment for theoreticians and data miners Data uncertainty is a concept closely related with most real life applications that involve data collection and interpretation. Examples can be found in data acquired with biomedical instruments or other experimental techniques. Integration of robust optimization in the existing data mining techniques aims to create new algorithms resilient to error and noise.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.