2023
Moreno-Pino, Fernando; Olmos, Pablo M; Artés-Rodríguez, Antonio
Deep Autoregressive Models with Spectral Attention Artículo de revista
En: Pattern Recognition, pp. 109014, 2023, ISSN: 0031-3203.
Resumen | Enlaces | BibTeX | Etiquetas: Attention models, Deep learning, Filtering, global-local contexts, Signal processing, spectral domain attention, time series forecasting
@article{MORENOPINO2022109014,
title = {Deep Autoregressive Models with Spectral Attention},
author = {Fernando Moreno-Pino and Pablo M Olmos and Antonio Art\'{e}s-Rodr\'{i}guez},
url = {https://www.sciencedirect.com/science/article/pii/S0031320322004940},
doi = {https://doi.org/10.1016/j.patcog.2022.109014},
issn = {0031-3203},
year = {2023},
date = {2023-01-01},
urldate = {2022-01-01},
journal = {Pattern Recognition},
pages = {109014},
abstract = {Time series forecasting is an important problem across many domains, playing a crucial role in multiple real-world applications. In this paper, we propose a forecasting architecture that combines deep autoregressive models with a Spectral Attention (SA) module, which merges global and local frequency domain information in the model’s embedded space. By characterizing in the spectral domain the embedding of the time series as occurrences of a random process, our method can identify global trends and seasonality patterns. Two spectral attention models, global and local to the time series, integrate this information within the forecast and perform spectral filtering to remove time series’s noise. The proposed architecture has a number of useful properties: it can be effectively incorporated into well-known forecast architectures, requiring a low number of parameters and producing explainable results that improve forecasting accuracy. We test the Spectral Attention Autoregressive Model (SAAM) on several well-known forecast datasets, consistently demonstrating that our model compares favorably to state-of-the-art approaches.},
keywords = {Attention models, Deep learning, Filtering, global-local contexts, Signal processing, spectral domain attention, time series forecasting},
pubstate = {published},
tppubtype = {article}
}
Time series forecasting is an important problem across many domains, playing a crucial role in multiple real-world applications. In this paper, we propose a forecasting architecture that combines deep autoregressive models with a Spectral Attention (SA) module, which merges global and local frequency domain information in the model’s embedded space. By characterizing in the spectral domain the embedding of the time series as occurrences of a random process, our method can identify global trends and seasonality patterns. Two spectral attention models, global and local to the time series, integrate this information within the forecast and perform spectral filtering to remove time series’s noise. The proposed architecture has a number of useful properties: it can be effectively incorporated into well-known forecast architectures, requiring a low number of parameters and producing explainable results that improve forecasting accuracy. We test the Spectral Attention Autoregressive Model (SAAM) on several well-known forecast datasets, consistently demonstrating that our model compares favorably to state-of-the-art approaches.
2021
Pérez-Vieites, Sara; Míguez, Joaquín
Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models Artículo de revista
En: Signal Processing, vol. 189, pp. 108295, 2021, ISSN: 0165-1684.
Resumen | Enlaces | BibTeX | Etiquetas: Bayesian inference, Filtering, Kalman, Monte Carlo, Parameter estimation
@article{PEREZVIEITES2021108295,
title = {Nested Gaussian filters for recursive Bayesian inference and nonlinear tracking in state space models},
author = {Sara P\'{e}rez-Vieites and Joaqu\'{i}n M\'{i}guez},
url = {https://www.sciencedirect.com/science/article/pii/S0165168421003327},
doi = {https://doi.org/10.1016/j.sigpro.2021.108295},
issn = {0165-1684},
year = {2021},
date = {2021-01-01},
urldate = {2021-01-01},
journal = {Signal Processing},
volume = {189},
pages = {108295},
abstract = {We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that combines two layers of filters, one inside the other, to compute the joint posterior probability distribution of the static parameters and the state variables. In particular, we explore the use of deterministic sampling techniques for Gaussian approximation in the first layer of the algorithm, instead of the Monte Carlo methods employed in the original procedure. The resulting scheme reduces the computational cost and so makes the algorithms potentially better-suited for high-dimensional state and parameter spaces. We describe a specific instance of the new method and then study its performance and efficiency of the resulting algorithms for a stochastic Lorenz 63 model and for a stochastic volatility model with real data.},
keywords = {Bayesian inference, Filtering, Kalman, Monte Carlo, Parameter estimation},
pubstate = {published},
tppubtype = {article}
}
We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that combines two layers of filters, one inside the other, to compute the joint posterior probability distribution of the static parameters and the state variables. In particular, we explore the use of deterministic sampling techniques for Gaussian approximation in the first layer of the algorithm, instead of the Monte Carlo methods employed in the original procedure. The resulting scheme reduces the computational cost and so makes the algorithms potentially better-suited for high-dimensional state and parameter spaces. We describe a specific instance of the new method and then study its performance and efficiency of the resulting algorithms for a stochastic Lorenz 63 model and for a stochastic volatility model with real data.
2010
Djuric, Petar M; Miguez, Joaquin
Assessment of Nonlinear Dynamic Models by Kolmogorov–Smirnov Statistics Artículo de revista
En: IEEE Transactions on Signal Processing, vol. 58, no 10, pp. 5069–5079, 2010, ISSN: 1053-587X.
Resumen | Enlaces | BibTeX | Etiquetas: Cumulative distributions, discrete random variables, dynamic nonlinear models, Electrical capacitance tomography, Filtering, filtering theory, Iron, Kolmogorov-Smirnov statistics, Kolomogorov–Smirnov statistics, model assessment, nonlinear dynamic models, nonlinear dynamical systems, Permission, predictive cumulative distributions, predictive distributions, Predictive models, Random variables, Robots, statistical analysis, statistical distributions, statistics, Telecommunication control
@article{Djuric2010a,
title = {Assessment of Nonlinear Dynamic Models by Kolmogorov\textendashSmirnov Statistics},
author = {Petar M Djuric and Joaquin Miguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5491124},
issn = {1053-587X},
year = {2010},
date = {2010-01-01},
journal = {IEEE Transactions on Signal Processing},
volume = {58},
number = {10},
pages = {5069--5079},
abstract = {Model assessment is a fundamental problem in science and engineering and it addresses the question of the validity of a model in the light of empirical evidence. In this paper, we propose a method for the assessment of dynamic nonlinear models based on empirical and predictive cumulative distributions of data and the Kolmogorov-Smirnov statistics. The technique is based on the generation of discrete random variables that come from a known discrete distribution if the entertained model is correct. We provide simulation examples that demonstrate the performance of the proposed method.},
keywords = {Cumulative distributions, discrete random variables, dynamic nonlinear models, Electrical capacitance tomography, Filtering, filtering theory, Iron, Kolmogorov-Smirnov statistics, Kolomogorov\textendashSmirnov statistics, model assessment, nonlinear dynamic models, nonlinear dynamical systems, Permission, predictive cumulative distributions, predictive distributions, Predictive models, Random variables, Robots, statistical analysis, statistical distributions, statistics, Telecommunication control},
pubstate = {published},
tppubtype = {article}
}
Model assessment is a fundamental problem in science and engineering and it addresses the question of the validity of a model in the light of empirical evidence. In this paper, we propose a method for the assessment of dynamic nonlinear models based on empirical and predictive cumulative distributions of data and the Kolmogorov-Smirnov statistics. The technique is based on the generation of discrete random variables that come from a known discrete distribution if the entertained model is correct. We provide simulation examples that demonstrate the performance of the proposed method.