1,983 research outputs found
Experiments on the Application of IOHMMs to Model Financial Returns Series
Input/Output Hidden Markov Models (IOHMMs) are conditional hidden Markov models in which the emission (and possibly the transition) probabilities can be conditioned on an input sequence. For example, these conditional distributions can be linear, logistic, or non-linear (using for example multi-layer neural networks). We compare the generalization performance of several models which are special cases of Input/Output Hidden Markov Models on financial time-series prediction tasks: an unconditional Gaussian, a conditional linear Gaussian, a mixture of Gaussians, a mixture of conditional linear Gaussians, a hidden Markov model, and various IOHMMs. The experiments compare these models on predicting the conditional density of returns of market and sector indices. Note that the unconditional Gaussian estimates the first moment with the historical average. The results show that, although for the first moment the historical average gives the best results, for the higher moments, the IOHMMs yielded significantly better performance, as estimated by the out-of-sample likelihood. "Input/Output Hidden Markov Models" (IOHMMs) sont des modèles de Markov cachés pour lesquels les probabilités d'émission (et possiblement de transition) peuvent dépendre d'une séquence d'entrée. Par exemple, ces distributions conditionnelles peuvent être linéaires, logistique, ou non-linéaire (utilisant, par exemple, une réseau de neurones multi-couches). Nous comparons les performances de généralisation de plusieurs modèles qui sont des cas particuliers de IOHMMs pour des problèmes de prédictions de séries financières : une gaussienne inconditionnelle, une gaussienne linéaire conditionnelle, une mixture de gaussienne, une mixture de gaussiennes linéaires conditionnelles, un modèle de Markov caché, et divers IOHMMs. Les expériences comparent ces modèles sur leur prédictions de la densité conditionnelle des rendements des indices sectoriels et du marché. Notons qu'une gaussienne inconditionnelle estime le premier moment avec une moyenne historique. Les résultats montrent que, même si la moyenne historique donne les meilleurs résultats pour le premier moment, pour les moments d'ordres supérieurs les IOHMMs performent significativement mieux, comme estimé par la vraisemblance hors-échantillon.Input/Output Hidden Markov Model (IOHMM), financial series, volatility, Modèles de Markov cachés, IOHMM, séries financières, volatilité
Bayesian Interpolation and Parameter Estimation in a Dynamic Sinusoidal Model
In this paper, we propose a method for restoring the missing or corrupted observations of nonstationary sinusoidal signals which are often encountered in music and speech applications. To model nonstationary signals, we use a time-varying sinusoidal model which is obtained by extending the static sinusoidal model into a dynamic sinusoidal model. In this model, the in-phase and quadrature components of the sinusoids are modeled as first-order Gauss–Markov processes. The inference scheme for the model parameters and missing observations is formulated in a Bayesian framework and is based on a Markov chain Monte Carlo method known as Gibbs sampler. We focus on the parameter estimation in the dynamic sinusoidal model since this constitutes the core of model-based interpolation. In the simulations, we first investigate the applicability of the model and then demonstrate the inference scheme by applying it to the restoration of lost audio packets on a packet-based network. The results show that the proposed method is a reasonable inference scheme for estimating unknown signal parameters and interpolating gaps consisting of missing/corrupted signal segments
Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields
The aim of this paper is to propose diffusion strategies for distributed
estimation over adaptive networks, assuming the presence of spatially
correlated measurements distributed according to a Gaussian Markov random field
(GMRF) model. The proposed methods incorporate prior information about the
statistical dependency among observations, while at the same time processing
data in real-time and in a fully decentralized manner. A detailed mean-square
analysis is carried out in order to prove stability and evaluate the
steady-state performance of the proposed strategies. Finally, we also
illustrate how the proposed techniques can be easily extended in order to
incorporate thresholding operators for sparsity recovery applications.
Numerical results show the potential advantages of using such techniques for
distributed learning in adaptive networks deployed over GMRF.Comment: Submitted to IEEE Transactions on Signal Processing. arXiv admin
note: text overlap with arXiv:1206.309
Graph Signal Processing: Overview, Challenges and Applications
Research in Graph Signal Processing (GSP) aims to develop tools for
processing data defined on irregular graph domains. In this paper we first
provide an overview of core ideas in GSP and their connection to conventional
digital signal processing. We then summarize recent developments in developing
basic GSP tools, including methods for sampling, filtering or graph learning.
Next, we review progress in several application areas using GSP, including
processing and analysis of sensor network data, biological data, and
applications to image processing and machine learning. We finish by providing a
brief historical perspective to highlight how concepts recently developed in
GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE
Dynamic Compressive Sensing of Time-Varying Signals via Approximate Message Passing
In this work the dynamic compressive sensing (CS) problem of recovering
sparse, correlated, time-varying signals from sub-Nyquist, non-adaptive, linear
measurements is explored from a Bayesian perspective. While there has been a
handful of previously proposed Bayesian dynamic CS algorithms in the
literature, the ability to perform inference on high-dimensional problems in a
computationally efficient manner remains elusive. In response, we propose a
probabilistic dynamic CS signal model that captures both amplitude and support
correlation structure, and describe an approximate message passing algorithm
that performs soft signal estimation and support detection with a computational
complexity that is linear in all problem dimensions. The algorithm, DCS-AMP,
can perform either causal filtering or non-causal smoothing, and is capable of
learning model parameters adaptively from the data through an
expectation-maximization learning procedure. We provide numerical evidence that
DCS-AMP performs within 3 dB of oracle bounds on synthetic data under a variety
of operating conditions. We further describe the result of applying DCS-AMP to
two real dynamic CS datasets, as well as a frequency estimation task, to
bolster our claim that DCS-AMP is capable of offering state-of-the-art
performance and speed on real-world high-dimensional problems.Comment: 32 pages, 7 figure
Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond
Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity
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