1,523 research outputs found
Interpretable Vector AutoRegressions with Exogenous Time Series
The Vector AutoRegressive (VAR) model is fundamental to the study of
multivariate time series. Although VAR models are intensively investigated by
many researchers, practitioners often show more interest in analyzing VARX
models that incorporate the impact of unmodeled exogenous variables (X) into
the VAR. However, since the parameter space grows quadratically with the number
of time series, estimation quickly becomes challenging. While several proposals
have been made to sparsely estimate large VAR models, the estimation of large
VARX models is under-explored. Moreover, typically these sparse proposals
involve a lasso-type penalty and do not incorporate lag selection into the
estimation procedure. As a consequence, the resulting models may be difficult
to interpret. In this paper, we propose a lag-based hierarchically sparse
estimator, called "HVARX", for large VARX models. We illustrate the usefulness
of HVARX on a cross-category management marketing application. Our results show
how it provides a highly interpretable model, and improves out-of-sample
forecast accuracy compared to a lasso-type approach.Comment: Presented at NIPS 2017 Symposium on Interpretable Machine Learnin
Regularized estimation of linear functionals of precision matrices for high-dimensional time series
This paper studies a Dantzig-selector type regularized estimator for linear
functionals of high-dimensional linear processes. Explicit rates of convergence
of the proposed estimator are obtained and they cover the broad regime from
i.i.d. samples to long-range dependent time series and from sub-Gaussian
innovations to those with mild polynomial moments. It is shown that the
convergence rates depend on the degree of temporal dependence and the moment
conditions of the underlying linear processes. The Dantzig-selector estimator
is applied to the sparse Markowitz portfolio allocation and the optimal linear
prediction for time series, in which the ratio consistency when compared with
an oracle estimator is established. The effect of dependence and innovation
moment conditions is further illustrated in the simulation study. Finally, the
regularized estimator is applied to classify the cognitive states on a real
fMRI dataset and to portfolio optimization on a financial dataset.Comment: 44 pages, 4 figure
Transposable regularized covariance models with an application to missing data imputation
Missing data estimation is an important challenge with high-dimensional data
arranged in the form of a matrix. Typically this data matrix is transposable,
meaning that either the rows, columns or both can be treated as features. To
model transposable data, we present a modification of the matrix-variate
normal, the mean-restricted matrix-variate normal, in which the rows and
columns each have a separate mean vector and covariance matrix. By placing
additive penalties on the inverse covariance matrices of the rows and columns,
these so-called transposable regularized covariance models allow for maximum
likelihood estimation of the mean and nonsingular covariance matrices. Using
these models, we formulate EM-type algorithms for missing data imputation in
both the multivariate and transposable frameworks. We present theoretical
results exploiting the structure of our transposable models that allow these
models and imputation methods to be applied to high-dimensional data.
Simulations and results on microarray data and the Netflix data show that these
imputation techniques often outperform existing methods and offer a greater
degree of flexibility.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS314 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Estimating Time-Varying Effective Connectivity in High-Dimensional fMRI Data Using Regime-Switching Factor Models
Recent studies on analyzing dynamic brain connectivity rely on sliding-window
analysis or time-varying coefficient models which are unable to capture both
smooth and abrupt changes simultaneously. Emerging evidence suggests
state-related changes in brain connectivity where dependence structure
alternates between a finite number of latent states or regimes. Another
challenge is inference of full-brain networks with large number of nodes. We
employ a Markov-switching dynamic factor model in which the state-driven
time-varying connectivity regimes of high-dimensional fMRI data are
characterized by lower-dimensional common latent factors, following a
regime-switching process. It enables a reliable, data-adaptive estimation of
change-points of connectivity regimes and the massive dependencies associated
with each regime. We consider the switching VAR to quantity the dynamic
effective connectivity. We propose a three-step estimation procedure: (1)
extracting the factors using principal component analysis (PCA) and (2)
identifying dynamic connectivity states using the factor-based switching vector
autoregressive (VAR) models in a state-space formulation using Kalman filter
and expectation-maximization (EM) algorithm, and (3) constructing the
high-dimensional connectivity metrics for each state based on subspace
estimates. Simulation results show that our proposed estimator outperforms the
K-means clustering of time-windowed coefficients, providing more accurate
estimation of regime dynamics and connectivity metrics in high-dimensional
settings. Applications to analyzing resting-state fMRI data identify dynamic
changes in brain states during rest, and reveal distinct directed connectivity
patterns and modular organization in resting-state networks across different
states.Comment: 21 page
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