749 research outputs found
Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography
This work addresses the inverse problem of electrocardiography from a new
perspective, by combining electrical and mechanical measurements. Our strategy
relies on the defini-tion of a model of the electromechanical contraction which
is registered on ECG data but also on measured mechanical displacements of the
heart tissue typically extracted from medical images. In this respect, we
establish in this work the convergence of a sequential estimator which combines
for such coupled problems various state of the art sequential data assimilation
methods in a unified consistent and efficient framework. Indeed we ag-gregate a
Luenberger observer for the mechanical state and a Reduced Order Unscented
Kalman Filter applied on the parameters to be identified and a POD projection
of the electrical state. Then using synthetic data we show the benefits of our
approach for the estimation of the electrical state of the ventricles along the
heart beat compared with more classical strategies which only consider an
electrophysiological model with ECG measurements. Our numerical results
actually show that the mechanical measurements improve the identifiability of
the electrical problem allowing to reconstruct the electrical state of the
coupled system more precisely. Therefore, this work is intended to be a first
proof of concept, with theoretical justifications and numerical investigations,
of the ad-vantage of using available multi-modal observations for the
estimation and identification of an electromechanical model of the heart
Least squares volatility change point estimation for partially observed diffusion processes
A one dimensional diffusion process , with drift
and diffusion coefficient
known up to , is supposed to switch volatility regime at some point
. On the basis of discrete time observations from , the
problem is the one of estimating the instant of change in the volatility
structure as well as the two values of , say and
, before and after the change point. It is assumed that the sampling
occurs at regularly spaced times intervals of length with
. To work out our statistical problem we use a least squares
approach. Consistency, rates of convergence and distributional results of the
estimators are presented under an high frequency scheme. We also study the case
of a diffusion process with unknown drift and unknown volatility but constant
Learning with Limited Labeled Data in Biomedical Domain by Disentanglement and Semi-Supervised Learning
In this dissertation, we are interested in improving the generalization of deep neural networks for biomedical data (e.g., electrocardiogram signal, x-ray images, etc). Although deep neural networks have attained state-of-the-art performance and, thus, deployment across a variety of domains, similar performance in the clinical setting remains challenging due to its ineptness to generalize across unseen data (e.g., new patient cohort).
We address this challenge of generalization in the deep neural network from two perspectives: 1) learning disentangled representations from the deep network, and 2) developing efficient semi-supervised learning (SSL) algorithms using the deep network.
In the former, we are interested in designing specific architectures and objective functions to learn representations, where variations in the data are well separated, i.e., disentangled. In the latter, we are interested in designing regularizers that encourage the underlying neural function\u27s behavior toward a common inductive bias to avoid over-fitting the function to small labeled data.
Our end goal is to improve the generalization of the deep network for the diagnostic model in both of these approaches. In disentangled representations, this translates to appropriately learning latent representations from the data, capturing the observed input\u27s underlying explanatory factors in an independent and interpretable way. With data\u27s expository factors well separated, such disentangled latent space can then be useful for a large variety of tasks and domains within data distribution even with a small amount of labeled data, thus improving generalization. In developing efficient semi-supervised algorithms, this translates to utilizing a large volume of the unlabelled dataset to assist the learning from the limited labeled dataset, commonly encountered situation in the biomedical domain.
By drawing ideas from different areas within deep learning like representation learning (e.g., autoencoder), variational inference (e.g., variational autoencoder), Bayesian nonparametric (e.g., beta-Bernoulli process), learning theory (e.g., analytical learning theory), function smoothing (Lipschitz Smoothness), etc., we propose several leaning algorithms to improve generalization in the associated task. We test our algorithms on real-world clinical data and show that our approach yields significant improvement over existing methods. Moreover, we demonstrate the efficacy of the proposed models in the benchmark data and simulated data to understand different aspects of the proposed learning methods.
We conclude by identifying some of the limitations of the proposed methods, areas of further improvement, and broader future directions for the successful adoption of AI models in the clinical environment
Analysis, estimation and control for perturbed and singular systems and for systems subject to discrete events.
Annual technical report for grant AFOSR-88-0032.Investigators: Alan S. Willsky, George C. Verghese.Includes bibliographical references (p. [10]-[15]).Research supported by the AFOSR. AFOSR-88-003
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
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