314,479 research outputs found

    Approximate Inference in Continuous Determinantal Point Processes

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    Determinantal point processes (DPPs) are random point processes well-suited for modeling repulsion. In machine learning, the focus of DPP-based models has been on diverse subset selection from a discrete and finite base set. This discrete setting admits an efficient sampling algorithm based on the eigendecomposition of the defining kernel matrix. Recently, there has been growing interest in using DPPs defined on continuous spaces. While the discrete-DPP sampler extends formally to the continuous case, computationally, the steps required are not tractable in general. In this paper, we present two efficient DPP sampling schemes that apply to a wide range of kernel functions: one based on low rank approximations via Nystrom and random Fourier feature techniques and another based on Gibbs sampling. We demonstrate the utility of continuous DPPs in repulsive mixture modeling and synthesizing human poses spanning activity spaces

    Continuous Modeling of Foreign Exchange Rate of USD versus TRY

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    This study aims to construct continuous-time autoregressive (CAR) model and continuous-time GARCH (COGARCH) model from discrete time data of foreign exchange rate of United States Dollar (USD) versus Turkish Lira (TRY). These processes are solutions to stochastic differential equation LĂ©vy-driven processes. We have shown that CAR(1) and COGARCH(1,1) processes are proper models to represent foreign exchange rate of USD and TRY for different periods of time February 2002- June 2010Continuous modeling; Continuous AR; COGARCH; USD/TRY

    Modeling, analyzing and controlling hybrid systems by Guarded Flexible Nets

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    A number of artificial and natural systems can be modeled as hybrid models in which continuous and discrete variables interact. Such hybrid models are usually challenging to analyze and control due to the computational complexity associated with existing methods. In this paper, the novel modeling formalism of Guarded Flexible Nets (GFNs) is proposed for the modeling, analysis and control of hybrid system. A GFN consists of an event net that determines how the state changes as processes execute, and an intensity net that determines the speeds of the processes. In a GFN, the continuous state is given by the value of its state variables, and the discrete state is given by the region within which such variables lie. GFNs are shown to possess a high modeling power while offering appealing analysis and control possibilities
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