Browsing by Subject "Nonstationary source"
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Item Open Access Estimating distributions varying in time in a universal manner(IEEE, 2017) Gökçesu, Kaan; Manış, Eren; Kurt, Ali Emirhan; Yar, ErsinWe investigate the estimation of distributions with time-varying parameters. We introduce an algorithm that achieves the optimal negative likelihood performance against the true probability distribution. We achieve this optimum regret performance without any knowledge about the total change of the parameters of true distribution. Our results are guaranteed to hold in an individual sequence manner such that we have no assumptions on the underlying sequences. Apart from the regret bounds, through synthetic and real life experiments, we demonstrate substantial performance gains with respect to the state-of-the-art probability density estimation algorithms in the literature.Item Open Access Online density estimation of nonstationary sources using exponential family of distributions(Institute of Electrical and Electronics Engineers Inc., 2018) Gokcesu, K.; Kozat, Süleyman SerdarWe investigate online probability density estimation (or learning) of nonstationary (and memoryless) sources using exponential family of distributions. To this end, we introduce a truly sequential algorithm that achieves Hannan-consistent log-loss regret performance against true probability distribution without requiring any information about the observation sequence (e.g., the time horizon T and the drift of the underlying distribution C) to optimize its parameters. Our results are guaranteed to hold in an individual sequence manner. Our log-loss performance with respect to the true probability density has regret bounds of O((CT)1/2), where C is the total change (drift) in the natural parameters of the underlying distribution. To achieve this, we design a variety of probability density estimators with exponentially quantized learning rates and merge them with a mixture-of-experts notion. Hence, we achieve this square-root regret with computational complexity only logarithmic in the time horizon. Thus, our algorithm can be efficiently used in big data applications. Apart from the regret bounds, through synthetic and real-life experiments, we demonstrate substantial performance gains with respect to the state-of-the-art probability density estimation algorithms in the literature. IEEE