545 research outputs found

    Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

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    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

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    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 dd-dimensional sphere Sd\mathbb{S}^d, 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

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    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?

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    Intensive farming is known to significantly impact air quality, particularly fine particulate matter (PM2.5_{2.5}). 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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