119 research outputs found
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
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
Multi-task learning for subthalamic nucleus identification in deep brain stimulation
Deep brain stimulation (DBS) of Subthalamic nucleus (STN) is the most successful treatment for advanced Parkinson’s disease. Localization of the STN through Microelectrode recordings (MER) is a key step during the surgery. However, it is a complex task even for a skilled neurosurgeon. Different researchers have developed methodologies for processing and classification of MER signals to locate the STN. Previous works employ the classical paradigm of supervised classification, assuming independence between patients. The aim of this paper is to introduce a patient-dependent learning scenario, where the predictive ability for STN identification at the level of a particular patient, can be used to improve the accuracy for STN identification in other patients. Our inspiration is the multi-task learning framework, that has been receiving increasing interest within the machine learning community in the last few years. To this end, we employ the multi-task Gaussian processes framework that exhibits state of the art performance in multi-task learning problems. In our context, we assume that each patient undergoing DBS is a different task, and we refer to the method as multi-patient learning. We show that the multi-patient learning framework improves the accuracy in the identification of STN in a range from 4.1 to 7.7%, compared to the usual patient-independent setup, for two different datasets. Given that MER are non stationary and noisy signals. Traditional approaches in machine learning fail to recognize accurately the STN during DBS. By contrast in our proposed method, we properly exploit correlations between patients with similar diseases, obtaining an additional information. This information allows to improve the accuracy not only for locating STN for DBS but also for other biomedical signal classification problems
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