777 research outputs found
Probabilistic sequential matrix factorization
We introduce the probabilistic sequential matrix factorization (PSMF) method
for factorizing time-varying and non-stationary datasets consisting of
high-dimensional time-series. In particular, we consider nonlinear Gaussian
state-space models where sequential approximate inference results in the
factorization of a data matrix into a dictionary and time-varying coefficients
with potentially nonlinear Markovian dependencies. The assumed Markovian
structure on the coefficients enables us to encode temporal dependencies into a
low-dimensional feature space. The proposed inference method is solely based on
an approximate extended Kalman filtering scheme, which makes the resulting
method particularly efficient. PSMF can account for temporal nonlinearities
and, more importantly, can be used to calibrate and estimate generic
differentiable nonlinear subspace models. We also introduce a robust version of
PSMF, called rPSMF, which uses Student-t filters to handle model
misspecification. We show that PSMF can be used in multiple contexts: modeling
time series with a periodic subspace, robustifying changepoint detection
methods, and imputing missing data in several high-dimensional time-series,
such as measurements of pollutants across London.Comment: Accepted for publication at AISTATS 202
Probabilistic sequential matrix factorization
We introduce the probabilistic sequential matrix factorization (PSMF) method for factorizing time-varying and non-stationary datasets consisting of high-dimensional time-series. In particular, we consider nonlinear Gaussian state-space models where sequential approximate inference results in the factorization of a data matrix into a dictionary and time-varying coefficients with potentially nonlinear Markovian dependencies. The assumed Markovian structure on the coefficients enables us to encode temporal dependencies into a low-dimensional feature space. The proposed inference method is solely based on an approximate extended Kalman filtering scheme, which makes the resulting method particularly efficient. PSMF can account for temporal nonlinearities and, more importantly, can be used to calibrate and estimate generic differentiable nonlinear subspace models. We also introduce a robust version of PSMF, called rPSMF, which uses Student-t filters to handle model misspecification. We show that PSMF can be used in multiple contexts: modeling time series with a periodic subspace, robustifying changepoint detection methods, and imputing missing data in several high-dimensional time-series, such as measurements of pollutants across London
Bayesian Detection of Changepoints in Finite-State Markov Chains for Multiple Sequences
We consider the analysis of sets of categorical sequences consisting of
piecewise homogeneous Markov segments. The sequences are assumed to be governed
by a common underlying process with segments occurring in the same order for
each sequence. Segments are defined by a set of unobserved changepoints where
the positions and number of changepoints can vary from sequence to sequence. We
propose a Bayesian framework for analyzing such data, placing priors on the
locations of the changepoints and on the transition matrices and using Markov
chain Monte Carlo (MCMC) techniques to obtain posterior samples given the data.
Experimental results using simulated data illustrates how the methodology can
be used for inference of posterior distributions for parameters and
changepoints, as well as the ability to handle considerable variability in the
locations of the changepoints across different sequences. We also investigate
the application of the approach to sequential data from two applications
involving monsoonal rainfall patterns and branching patterns in trees
- …