Online Learning for Time Series Prediction

Anava, Oren; Hazan, Elad; Mannor, Shie; Shamir, Ohad

doi:10.48550/arxiv.1302.6927

Cited by 3 publications

(5 citation statements)

References 7 publications

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“…For simplicity, our exposition was limited to the case of noise-free observations (translating to noise-free loss observations). Fortunately however, there exist a variety of online convex programming algorithms that address noisy losses [12,5,4,2] the offer expected regret bounds that can be converted into high-probability bounds. If we applied those, all our results presented in this paper would hold with arbitrarily high probability.…”

Section: Discussionmentioning

confidence: 99%

“…No-regret bounds and algorithms have been studied and deployed in a great many online learning scenarios, including, among others, time-series prediction in ARMA models [2], multi-agent coordination [9], game-theory [14,6,21]. For a classic text book, the reader is referred to [11], whereas a recent survey can be found in [18].…”

Section: Contractive Dynamical Systems With Increasingly Permanently ...mentioning

confidence: 99%

“…No-regret algorithms and more generally, online programming algorithms can be utilised for fast online learning and prediction of time series (e.g. [11,2]). If a no-external regret bound is achieved then, provided the prediction loss is convex in the parameters, (sub-) optimality guarantees can be given to bound the average prediction errors and the degree of sub-optimality of the parametric predictor whose parameter is the average of all choices of the adapted online predictors' parameters.…”

Section: Introductionmentioning

confidence: 99%

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Online Optimisation for Online Learning and Control -- From No-Regret to Generalised Error Convergence

Calliess¹

2019

Preprint

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This paper presents early work aiming at the development of a new framework for the design and analysis of algorithms for online learning based prediction and control. Firstly, we consider the task of predicting values of a function or time series based on incrementally arriving sequences of inputs by utilising online programming. Introducing a generalisation of standard notions of convergence, we derive theoretical guarantees on the asymptotic behaviour of the prediction accuracies when prediction models are updated by a no-external-regret algorithm. We prove generalised learning guarantees for online regression and provide an example of how this can be applied to online learning-based control. We devise a model-reference adaptive controller with novel online performance guarantees on tracking success in the presence of a priori dynamic uncertainty. Our theoretical results are accompanied by illustrations on simple regression and control problems.

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Section: Discussionmentioning

confidence: 99%

Section: Contractive Dynamical Systems With Increasingly Permanently ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Online Optimisation for Online Learning and Control -- From No-Regret to Generalised Error Convergence

Calliess¹

2019

Preprint

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“…A wide range of time series prediction methods [Anava et al, 2013] are in effect realizations of Gaussian processes that correspond to specific choices of a covariance function [Rasmussen et al, 2007]. Classic methods, including autoregressive and moving average methods and their various combinations and extensions, e.g., the well-known Box-Jenkins methods, are such in-effect realizations, as are various spline methods, e.g., smoothing and B-splines [Brockwell, et al 2009]. However, spaghetti prediction is not a realization of a Gaussian process.…”

Section: Discussionmentioning

confidence: 99%

Spaghetti prediction: A robust method for forecasting short time series

Gustafson¹,

Pedrotti²

2014

Preprint

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A novel method for predicting time series is described and demonstrated. This method inputs time series data points and outputs multiple "spaghetti" functions from which predictions can be made. Spaghetti prediction has desirable properties that are not realized by classic autoregression, moving average, spline, Gaussian process, and other methods. It is particularly appropriate for short time series because it allows asymmetric prediction distributions and produces prediction functions which are robust in that they use multiple independent models.

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“…Exponential weighting has also been investigated in the case of weakly dependent stationary data in Alquier and Wintenberger (2012). More recently, an approach inspired from individual sequences prediction has been studied in Anava et al (2013) for bounded ARMA processes under some specific conditions on the (constant) ARMA coefficients.…”

mentioning

confidence: 99%

Aggregation of predictors for nonstationary sub-linear processes and online adaptive forecasting of time varying autoregressive processes

Giraud¹,

Roueff²,

Sanchez-Perez³

2015

Ann. Statist.

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In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the ℓ 1 norm of the time varying sub-linear coefficients, (2) a Lipschitz assumption on the predictors and (3) moment conditions on the noise appearing in the linear representation. Two kinds of aggregations are considered giving rise to different moment conditions on the noise and more or less sharp oracle inequalities. We apply this approach for deriving an adaptive predictor for locally stationary time varying autoregressive (TVAR) processes. It is obtained by aggregating a finite number of well chosen predictors, each of them enjoying an optimal minimax convergence rate under specific smoothness conditions on the TVAR coefficients. We show that the obtained aggregated predictor achieves a minimax rate while adapting to the unknown smoothness. To prove this result, a lower bound is established for the minimax rate of the prediction risk for the TVAR process. Numerical experiments complete this study. An important feature of this approach is that the aggregated predictor can be computed recursively and is thus applicable in an online prediction context.

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Online Learning for Time Series Prediction

Cited by 3 publications

References 7 publications

Online Optimisation for Online Learning and Control -- From No-Regret to Generalised Error Convergence

Online Optimisation for Online Learning and Control -- From No-Regret to Generalised Error Convergence

Spaghetti prediction: A robust method for forecasting short time series

Aggregation of predictors for nonstationary sub-linear processes and online adaptive forecasting of time varying autoregressive processes

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