Topic
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.
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TL;DR: In this paper, support vector machines (SVM) are applied to global prediction of nuclear properties as functions of proton and neutron numbers across the nuclidic chart, and results indicate that SVM models can match or even surpass the predictive performance of the best conventional ''theory-thick'' global models based on nuclear phenomenology.
Abstract: Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the application of Support Vector Machines (SVMs) to global prediction of nuclear properties as functions of proton and neutron numbers $Z$ and $N$ across the nuclidic chart. Based on the principle of structural-risk minimization, SVMs learn from examples in the existing database of a given property $Y$, automatically and optimally identify a set of ``support vectors'' corresponding to representative nuclei in the training set, and approximate the mapping $(Z,N) \to Y$ in terms of these nuclei. Results are reported for nuclear masses, beta-decay lifetimes, and spins/parities of nuclear ground states. These results indicate that SVM models can match or even surpass the predictive performance of the best conventional ``theory-thick'' global models based on nuclear phenomenology.
5 citations
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TL;DR: The definitions of the empirical risk functional, the expected risk function and empirical risk minimization principle about gλ samples corrupted by noise are proposed and proved.
Abstract: The key theorem plays an important role in the statistical learning theory.However,the researches about it at present mainly focus on real random variable and the samples which are supposed to be noise-free.In this paper,the definitions of com- plex gλ variable and primary norm are introduced.Then,the definitions of the empirical risk functional,the expected risk function- al and empirical risk minimization principle about gλ samples corrupted by noise are proposed.Finally,the key theorem of learn- ing theory about complex gλ samples corrupted by noise is proposed and proved.The investigations help lay essential theoretical foundations for the systematic and comprehensive development of the statistical learning theory of complex gλ samples.
5 citations
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TL;DR: In this paper, the authors present a survey of the recent advances of learning in repeated auctions, starting from the traditional economical study of optimal one-shot auctions with a Bayesian prior and then focusing on the question of learning these mechanism from a dataset of the past values of bidders.
Abstract: Auction theory historically focused on the question of designing the best way to sell a single item to potential buyers, with the concurrent objectives of maximizing the revenue generated or the welfare created. Those results relied on some prior Bayesian knowledge agents have on each-other and/or on infinite computational power. All those assumptions are no longer satisfied in new markets such as online advertisement: similar items are sold repeatedly, agents are agnostic and try to manipulate each-other. On the other hand, statistical learning theory now provides tools to supplement those missing assumptions in the long run, as agents are able to learn from their environment to improve their strategies. This survey covers the recent advances of learning in repeated auctions, starting from the traditional economical study of optimal one-shot auctions with a Bayesian prior. We will then focus on the question of learning these mechanism from a dataset of the past values of bidders. The sample complexity as well as the computational efficiency of different methods will be studied. We will also investigate online variants where gathering those data has a cost to be integrated ("earning while learning"). In a second step, we will further assume that bidders are also adaptive to the mechanism as they interact repeatedly with the same seller. We will show how strategic agents can actually manipulate repeated auctions, at their own advantage. At the end of this stand-alone survey (reminders of the different techniques used are provided), we will describe new interesting direction of research on repeated auctions.
5 citations
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TL;DR: A survey of the recent new development on the research and application of the support vector machines is made.
Abstract: A support vector machine is a new machine learning technique developed on the basis of statistical learning theory, and it is the most successful realization of statistical learning theory. For machine learning tasks involving pattern classification, regression estimation, and function approximation, the support vector machine has increasingly become a popular tool. In this paper a survey of the recent new development on the research and application of the support vector machines is made. Some important issues to be investigated in application and the direction of research of the support vector machine have been pointed out simultaneously.
5 citations
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TL;DR: This approach fully tailored to Markovian data permits to interpret the rate bound results obtained in frequentist terms, in contrast to alternative coupling techniques based on mixing conditions: the larger the expected number of cycles over a trajectory of finite length, the more accurate the MV-set estimates.
Abstract: In statistical learning theory, numerous works established non-asymptotic bounds assessing the generalization capacity of empirical risk minimizers under a large variety of complexity assumptions for the class of decision rules over which optimization is performed, by means of sharp control of uniform deviation of i.i.d. averages from their expectation, while fully ignoring the possible dependence across training data in general. It is the purpose of this paper to show that similar results can be obtained when statistical learning is based on a data sequence drawn from a (Harris positive) Markov chain X, through the running example of estimation of minimum volume sets (MV-sets) related to X’s stationary distribution, an unsupervised statistical learning approach to anomaly/novelty detection. Based on novel maximal deviation inequalities we establish, using the regenerative method, learning rate bounds that depend not only on the complexity of the class of candidate sets but also on the ergodicity rate of the chain X, expressed in terms of tail conditions for the length of the regenerative cycles. In particular, this approach fully tailored to Markovian data permits to interpret the rate bound results obtained in frequentist terms, in contrast to alternative coupling techniques based on mixing conditions: the larger the expected number of cycles over a trajectory of finite length, the more accurate the MV-set estimates. Beyond the theoretical analysis, this phenomenon is supported by illustrative numerical experiments.
5 citations