Classical vs. Bayesian methods for linear system identification: point estimators and confidence sets

This paper compares classical parametric methods with recently developed Bayesian methods for system identification. A Full Bayes solution is considered together with one of the standard approximations based on the Empirical Bayes paradigm. Results regarding point estimators for the impulse response as well as for confidence regions are reported.Comment: number of pages = 8, number of figures =

Nonparametric Bayesian Mixed-effect Model: a Sparse Gaussian Process Approach

Multi-task learning models using Gaussian processes (GP) have been developed and successfully applied in various applications. The main difficulty with this approach is the computational cost of inference using the union of examples from all tasks. Therefore sparse solutions, that avoid using the entire data directly and instead use a set of informative "representatives" are desirable. The paper investigates this problem for the grouped mixed-effect GP model where each individual response is given by a fixed-effect, taken from one of a set of unknown groups, plus a random individual effect function that captures variations among individuals. Such models have been widely used in previous work but no sparse solutions have been developed. The paper presents the first sparse solution for such problems, showing how the sparse approximation can be obtained by maximizing a variational lower bound on the marginal likelihood, generalizing ideas from single-task Gaussian processes to handle the mixed-effect model as well as grouping. Experiments using artificial and real data validate the approach showing that it can recover the performance of inference with the full sample, that it outperforms baseline methods, and that it outperforms state of the art sparse solutions for other multi-task GP formulations.Comment: Preliminary version appeared in ECML201

A new kernel-based approach to system identification with quantized output data

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation–maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.</p

Bayesian identification of LPV-BJ models : a multidimensional kernel approach

poster, no abstract available

Forecasting and Granger Modelling with Non-linear Dynamical Dependencies

Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the reproducing kernel Hilbert space and develop a method for learning prediction functions that accommodate such non-linearities. The method not only learns the predictive function but also the matrix-valued kernel underlying the function search space directly from the data. Our approach is based on learning multiple matrix-valued kernels, each of those composed of a set of input kernels and a set of output kernels learned in the cone of positive semi-definite matrices. In addition to superior predictive performance in the presence of strong non-linearities, our method also recovers the hidden dynamic relationships between the series and thus is a new alternative to existing graphical Granger techniques.Comment: Accepted for ECML-PKDD 201

Advantages of the single delay model for the assessment of insulin sensitivity from the intravenous glucose tolerance test

The Minimal Model, (MM), used to assess insulin sensitivity (IS) from Intra-Venous Glucose-Tolerance Test (IVGTT) data, suffers from frequent lack of identifiability (parameter estimates with Coefficients of Variation (CV) less than 52%). The recently proposed Single Delay Model (SDM) is evaluated as a practical alternative

Dimensional analysis of MINMOD leads to definition of the disposition index of glucose regulation and improved simulation algorithm

BACKGROUND: Frequently Sampled Intravenous Glucose Tolerance Test (FSIVGTT) together with its mathematical model, the minimal model (MINMOD), have become important clinical tools to evaluate the metabolic control of glucose in humans. Dimensional analysis of the model is up to now not available. METHODS: A formal dimensional analysis of MINMOD was carried out and the degree of freedom of MINMOD was examined. Through re-expressing all state variable and parameters in terms of their reference scales, MINMOD was transformed into a dimensionless format. Previously defined physiological indices including insulin sensitivity, glucose effectiveness, and first and second phase insulin responses were re-examined in this new formulation. Further, the parameter estimation from FSIVGTT was implemented using both the dimensional and the dimensionless formulations of MINMOD, and the performances were compared utilizing Monte Carlo simulation as well as real human FSIVGTT data. RESULTS: The degree of freedom (DOF) of MINMOD was found to be 7. The model was maximally simplified in the dimensionless formulation that normalizes the variation in glucose and insulin during FSIVGTT. In the new formulation, the disposition index (Dl), a composite parameter known to be important in diabetes pathology, was naturally defined as one of the dimensionless parameters in the system. The numerical simulation using the dimensionless formulation led to a 1.5–5 fold gain in speed, and significantly improved accuracy and robustness in parameter estimation compared to the dimensional implementation. CONCLUSION: Dimensional analysis of MINMOD led to simplification of the model, direct identification of the important composite factors in the dynamics of glucose metabolic control, and better simulations algorithms