Related papers: Statistical Inference for Oscillation Processes
Time series are used in many domains including finance, engineering, economics and bioinformatics generally to represent the change of a measurement over time. Modeling techniques may then be used to give a synthetic representation of such…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…
Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spectral algorithm to…
We propose a methodology to analyze data arising from a curve that, over its domain, switches among J states. We consider a sequence of response variables, where each response y depends on a covariate x according to an unobserved state z.…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
This paper presents a fast algorithm for estimating hidden states of Bayesian state space models. The algorithm is a variation of amortized simulation-based inference algorithms, where a large number of artificial datasets are generated at…
We develop Bayesian state space methods for modelling changes to the mean level or temporal correlation structure of an observed time series due to intermittent coupling with an unobserved process. Novel intervention methods are proposed to…
We develop and apply an approach for analyzing multi-curve data where each curve is driven by a latent state process. The state at any particular point determines a smooth function, forcing the individual curve to switch from one function…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference \emph{and learning} (i.e. state estimation and system…
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…
We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian…
A new approach for signal parametrization, which consists of a specific regression model incorporating a discrete hidden logistic process, is proposed. The model parameters are estimated by the maximum likelihood method performed by a…
Time series subject to change in regime have attracted much interest in domains such as econometry, finance or meteorology. For discrete-valued regimes, some models such as the popular Hidden Markov Chain (HMC) describe time series whose…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
We consider the problem of inference in a linear regression model in which the relative ordering of the input features and output labels is not known. Such datasets naturally arise from experiments in which the samples are shuffled or…
Inferring dynamics from time series is an important objective in data analysis. In particular, it is challenging to infer stochastic dynamics given incomplete data. We propose an expectation maximization (EM) algorithm that iterates between…