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; Closas, Pau; Bugallo, Monica F; Miguez, Joaquin
Evaluation of a Method's Robustness Proceedings Article
En: 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3598–3601, IEEE, Dallas, 2010, ISSN: 1520-6149.
Resumen | Enlaces | BibTeX | Etiquetas: Electronic mail, Extraterrestrial measurements, Filtering, Gaussian processes, method's robustness, Random variables, robustness, sequential methods, Signal processing, statistical distributions, Telecommunications, uniform distribution, Wireless communication
@inproceedings{Djuric2010,
title = {Evaluation of a Method's Robustness},
author = {Petar M Djuric and Pau Closas and Monica F Bugallo and Joaquin Miguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5495921},
issn = {1520-6149},
year = {2010},
date = {2010-01-01},
booktitle = {2010 IEEE International Conference on Acoustics, Speech and Signal Processing},
pages = {3598--3601},
publisher = {IEEE},
address = {Dallas},
abstract = {In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is to model deviations. To that end, it is useful to have a metric that can quantify the robustness of the method. In this paper we propose a procedure for developing a variety of metrics for measuring robustness. They are based on a discrete random variable that is generated from observed data and data generated according to past data and the adopted model. This random variable is uniform if the model is correct. When the model deviates from the true one, the distribution of the random variable deviates from the uniform distribution. One can then employ measures for differences between distributions in order to quantify robustness. In this paper we describe the proposed methodology and demonstrate it with simulated data.},
keywords = {Electronic mail, Extraterrestrial measurements, Filtering, Gaussian processes, method's robustness, Random variables, robustness, sequential methods, Signal processing, statistical distributions, Telecommunications, uniform distribution, Wireless communication},
pubstate = {published},
tppubtype = {inproceedings}
}
In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is to model deviations. To that end, it is useful to have a metric that can quantify the robustness of the method. In this paper we propose a procedure for developing a variety of metrics for measuring robustness. They are based on a discrete random variable that is generated from observed data and data generated according to past data and the adopted model. This random variable is uniform if the model is correct. When the model deviates from the true one, the distribution of the random variable deviates from the uniform distribution. One can then employ measures for differences between distributions in order to quantify robustness. In this paper we describe the proposed methodology and demonstrate it with simulated data.
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.
2009
Djuric, Petar M; Miguez, Joaquin
Model Assessment with Kolmogorov-Smirnov Statistics Proceedings Article
En: 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 2973–2976, IEEE, Taipei, 2009, ISSN: 1520-6149.
Resumen | Enlaces | BibTeX | Etiquetas: Bayesian methods, Computer Simulation, Context modeling, Electronic mail, Filtering, ill-conditioned problem, Kolmogorov-Smirnov statistics, model assessment, modelling, Predictive models, Probability, statistical analysis, statistics, Testing
@inproceedings{Djuric2009,
title = {Model Assessment with Kolmogorov-Smirnov Statistics},
author = {Petar M Djuric and Joaquin Miguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4960248},
issn = {1520-6149},
year = {2009},
date = {2009-01-01},
booktitle = {2009 IEEE International Conference on Acoustics, Speech and Signal Processing},
pages = {2973--2976},
publisher = {IEEE},
address = {Taipei},
abstract = {One of the most basic problems in science and engineering is the assessment of a considered model. The model should describe a set of observed data and the objective is to find ways of deciding if the model should be rejected. It seems that this is an ill-conditioned problem because we have to test the model against all the possible alternative models. In this paper we use the Kolmogorov-Smirnov statistic to develop a test that shows if the model should be kept or it should be rejected. We explain how this testing can be implemented in the context of particle filtering. We demonstrate the performance of the proposed method by computer simulations.},
keywords = {Bayesian methods, Computer Simulation, Context modeling, Electronic mail, Filtering, ill-conditioned problem, Kolmogorov-Smirnov statistics, model assessment, modelling, Predictive models, Probability, statistical analysis, statistics, Testing},
pubstate = {published},
tppubtype = {inproceedings}
}
One of the most basic problems in science and engineering is the assessment of a considered model. The model should describe a set of observed data and the objective is to find ways of deciding if the model should be rejected. It seems that this is an ill-conditioned problem because we have to test the model against all the possible alternative models. In this paper we use the Kolmogorov-Smirnov statistic to develop a test that shows if the model should be kept or it should be rejected. We explain how this testing can be implemented in the context of particle filtering. We demonstrate the performance of the proposed method by computer simulations.
Maiz, Cristina S; Miguez, Joaquin; Djuric, Petar M
Particle Filtering in the Presence of Outliers Proceedings Article
En: 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, pp. 33–36, IEEE, Cardiff, 2009, ISBN: 978-1-4244-2709-3.
Resumen | Enlaces | BibTeX | Etiquetas: computer simulations, Degradation, Filtering, multidimensional random variates, Multidimensional signal processing, Multidimensional systems, Nonlinear tracking, Outlier detection, predictive distributions, Signal processing, signal processing tools, signal-power observations, spatial depth, statistical analysis, statistical distributions, statistics, Target tracking, Testing
@inproceedings{Maiz2009,
title = {Particle Filtering in the Presence of Outliers},
author = {Cristina S Maiz and Joaquin Miguez and Petar M Djuric},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5278645},
isbn = {978-1-4244-2709-3},
year = {2009},
date = {2009-01-01},
booktitle = {2009 IEEE/SP 15th Workshop on Statistical Signal Processing},
pages = {33--36},
publisher = {IEEE},
address = {Cardiff},
abstract = {Particle filters have become very popular signal processing tools for problems that involve nonlinear tracking of an unobserved signal of interest given a series of related observations. In this paper we propose a new scheme for particle filtering when the observed data are possibly contaminated with outliers. An outlier is an observation that has been generated by some (unknown) mechanism different from the assumed model of the data. Therefore, when handled in the same way as regular observations, outliers may drastically degrade the performance of the particle filter. To address this problem, we introduce an auxiliary particle filtering scheme that incorporates an outlier detection step. We propose to implement it by means of a test involving statistics of the predictive distributions of the observations. Specifically, we investigate the use of a proposed statistic called spatial depth that can easily be applied to multidimensional random variates. The performance of the resulting algorithm is assessed by computer simulations of target tracking based on signal-power observations.},
keywords = {computer simulations, Degradation, Filtering, multidimensional random variates, Multidimensional signal processing, Multidimensional systems, Nonlinear tracking, Outlier detection, predictive distributions, Signal processing, signal processing tools, signal-power observations, spatial depth, statistical analysis, statistical distributions, statistics, Target tracking, Testing},
pubstate = {published},
tppubtype = {inproceedings}
}
Particle filters have become very popular signal processing tools for problems that involve nonlinear tracking of an unobserved signal of interest given a series of related observations. In this paper we propose a new scheme for particle filtering when the observed data are possibly contaminated with outliers. An outlier is an observation that has been generated by some (unknown) mechanism different from the assumed model of the data. Therefore, when handled in the same way as regular observations, outliers may drastically degrade the performance of the particle filter. To address this problem, we introduce an auxiliary particle filtering scheme that incorporates an outlier detection step. We propose to implement it by means of a test involving statistics of the predictive distributions of the observations. Specifically, we investigate the use of a proposed statistic called spatial depth that can easily be applied to multidimensional random variates. The performance of the resulting algorithm is assessed by computer simulations of target tracking based on signal-power observations.
Djuric, Petar M; Bugallo, Monica F; Closas, Pau; Miguez, Joaquin
Measuring the Robustness of Sequential Methods Proceedings Article
En: 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop, pp. 29–32, IEEE, Aruba, Dutch Antilles, 2009, ISBN: 978-1-4244-5179-1.
Resumen | Enlaces | BibTeX | Etiquetas: Additive noise, cumulative distribution functions, data processing method, extended Kalman filtering, Extraterrestrial measurements, Filtering, Gaussian distribution, Gaussian noise, Kalman filters, Kolmogorov-Smirnov distance, Least squares approximation, Noise robustness, nonlinear filters, robustness, sequential methods, statistical distributions, telecommunication computing
@inproceedings{Djuric2009a,
title = {Measuring the Robustness of Sequential Methods},
author = {Petar M Djuric and Monica F Bugallo and Pau Closas and Joaquin Miguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5413275},
isbn = {978-1-4244-5179-1},
year = {2009},
date = {2009-01-01},
booktitle = {2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop},
pages = {29--32},
publisher = {IEEE},
address = {Aruba, Dutch Antilles},
abstract = {Whenever we apply methods for processing data, we make a number of model assumptions. In reality, these assumptions are not always correct. Robust methods can withstand model inaccuracies, that is, despite some incorrect assumptions they can still produce good results. We often want to know how robust employed methods are. To that end we need to have a yardstick for measuring robustness. In this paper, we propose an approach for constructing such metrics for sequential methods. These metrics are derived from the Kolmogorov-Smirnov distance between the cumulative distribution functions of the actual observations and the ones based on the assumed model. The use of the proposed metrics is demonstrated with simulation examples.},
keywords = {Additive noise, cumulative distribution functions, data processing method, extended Kalman filtering, Extraterrestrial measurements, Filtering, Gaussian distribution, Gaussian noise, Kalman filters, Kolmogorov-Smirnov distance, Least squares approximation, Noise robustness, nonlinear filters, robustness, sequential methods, statistical distributions, telecommunication computing},
pubstate = {published},
tppubtype = {inproceedings}
}
Whenever we apply methods for processing data, we make a number of model assumptions. In reality, these assumptions are not always correct. Robust methods can withstand model inaccuracies, that is, despite some incorrect assumptions they can still produce good results. We often want to know how robust employed methods are. To that end we need to have a yardstick for measuring robustness. In this paper, we propose an approach for constructing such metrics for sequential methods. These metrics are derived from the Kolmogorov-Smirnov distance between the cumulative distribution functions of the actual observations and the ones based on the assumed model. The use of the proposed metrics is demonstrated with simulation examples.
Martino, Luca; Miguez, Joaquin
An Adaptive Accept/Reject Sampling Algorithm for Posterior Probability Distributions Proceedings Article
En: 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, pp. 45–48, IEEE, Cardiff, 2009, ISBN: 978-1-4244-2709-3.
Resumen | Enlaces | BibTeX | Etiquetas: adaptive accept/reject sampling, Adaptive rejection sampling, arbitrary target probability distributions, Computer Simulation, Filtering, Monte Carlo integration, Monte Carlo methods, posterior probability distributions, Probability, Probability density function, Probability distribution, Proposals, Rejection sampling, Sampling methods, sensor networks, Signal processing algorithms, signal sampling, Testing
@inproceedings{Martino2009b,
title = {An Adaptive Accept/Reject Sampling Algorithm for Posterior Probability Distributions},
author = {Luca Martino and Joaquin Miguez},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5278644},
isbn = {978-1-4244-2709-3},
year = {2009},
date = {2009-01-01},
booktitle = {2009 IEEE/SP 15th Workshop on Statistical Signal Processing},
pages = {45--48},
publisher = {IEEE},
address = {Cardiff},
abstract = {Accept/reject sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. In this paper we introduce an adaptive method to build a sequence of proposal pdf's that approximate the target density and hence can ensure a high acceptance rate. In order to illustrate the application of the method we design an accept/reject particle filter and then assess its performance and sampling efficiency numerically, by means of computer simulations.},
keywords = {adaptive accept/reject sampling, Adaptive rejection sampling, arbitrary target probability distributions, Computer Simulation, Filtering, Monte Carlo integration, Monte Carlo methods, posterior probability distributions, Probability, Probability density function, Probability distribution, Proposals, Rejection sampling, Sampling methods, sensor networks, Signal processing algorithms, signal sampling, Testing},
pubstate = {published},
tppubtype = {inproceedings}
}
Accept/reject sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. In this paper we introduce an adaptive method to build a sequence of proposal pdf's that approximate the target density and hence can ensure a high acceptance rate. In order to illustrate the application of the method we design an accept/reject particle filter and then assess its performance and sampling efficiency numerically, by means of computer simulations.