545 research outputs found
Towards Efficient Maximum Likelihood Estimation of LPV-SS Models
How to efficiently identify multiple-input multiple-output (MIMO) linear
parameter-varying (LPV) discrete-time state-space (SS) models with affine
dependence on the scheduling variable still remains an open question, as
identification methods proposed in the literature suffer heavily from the curse
of dimensionality and/or depend on over-restrictive approximations of the
measured signal behaviors. However, obtaining an SS model of the targeted
system is crucial for many LPV control synthesis methods, as these synthesis
tools are almost exclusively formulated for the aforementioned representation
of the system dynamics. Therefore, in this paper, we tackle the problem by
combining state-of-the-art LPV input-output (IO) identification methods with an
LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step.
The resulting modular LPV-SS identification approach achieves statical
efficiency with a relatively low computational load. The method contains the
following three steps: 1) estimation of the Markov coefficient sequence of the
underlying system using correlation analysis or Bayesian impulse response
estimation, then 2) LPV-SS realization of the estimated coefficients by using a
basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate
from a maximum-likelihood point of view by a gradient-based or an
expectation-maximization optimization methodology. The effectiveness of the
full identification scheme is demonstrated by a Monte Carlo study where our
proposed method is compared to existing schemes for identifying a MIMO LPV
system
DAMM: Directionality-Aware Mixture Model Parallel Sampling for Efficient Dynamical System Learning
The Linear Parameter Varying Dynamical System (LPV-DS) is a promising
framework for learning stable time-invariant motion policies in robot control.
By employing statistical modeling and semi-definite optimization, LPV-DS
encodes complex motions via non-linear DS, ensuring the robustness and
stability of the system. However, the current LPV-DS scheme faces challenges in
accurately interpreting trajectory data while maintaining model efficiency and
computational efficiency. To address these limitations, we propose the
Directionality-aware Mixture Model (DAMM), a new statistical model that
leverages Riemannian metric on -dimensional sphere , and
efficiently incorporates non-Euclidean directional information with position.
Additionally, we introduce a hybrid Markov chain Monte Carlo method that
combines the Gibbs Sampling and the Split/Merge Proposal, facilitating parallel
computation and enabling faster inference for near real-time learning
performance. Through extensive empirical validation, we demonstrate that the
improved LPV-DS framework with DAMM is capable of producing
physically-meaningful representations of the trajectory data and improved
performance of the generated DS while showcasing significantly enhanced
learning speed compared to its previous iterations
Black Box Variational Inference
Variational inference has become a widely used method to approximate
posteriors in complex latent variables models. However, deriving a variational
inference algorithm generally requires significant model-specific analysis, and
these efforts can hinder and deter us from quickly developing and exploring a
variety of models for a problem at hand. In this paper, we present a "black
box" variational inference algorithm, one that can be quickly applied to many
models with little additional derivation. Our method is based on a stochastic
optimization of the variational objective where the noisy gradient is computed
from Monte Carlo samples from the variational distribution. We develop a number
of methods to reduce the variance of the gradient, always maintaining the
criterion that we want to avoid difficult model-based derivations. We evaluate
our method against the corresponding black box sampling based methods. We find
that our method reaches better predictive likelihoods much faster than sampling
methods. Finally, we demonstrate that Black Box Variational Inference lets us
easily explore a wide space of models by quickly constructing and evaluating
several models of longitudinal healthcare data
To what extent airborne particulate matters are influenced by ammonia and nitrogen oxides?
Intensive farming is known to significantly impact air quality, particularly
fine particulate matter (PM). Understanding in detial their relation is
important for scientific reasons and policy making. Ammonia emissions convey
the impact of farming, but are not directly observed. They are computed through
emission inventories based on administrative data and provided on a regular
spatial grid at daily resolution. In this paper, we aim to validate
\textit{lato sensu} the approach mentioned above by considering ammonia
concentrations instead of emissions in the Lombardy Region, Italy. While the
former are available only in few monitoring stations around the region, they
are direct observations. Hence, we build a model explaining PM2.5 based on
precursors, ammonia (NH3) and nitrogen oxides (NOX), and meteorological
variables. To do this, we use a seasonal interaction regression model allowing
for temporal autocorrelation, correlation between stations, and
heteroskedasticity. It is found that the sensitivity of PM2.5 to NH3 and NOX
depends on season, area, and NOX level. It is recommended that an emission
reduction policy should focus on the entire manure cycle and not only on spread
practices
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