scholarly journals Bayesian inversion of a diffusion model with application to biology

2021 ◽  
Vol 83 (2) ◽  
Author(s):  
Jean-Charles Croix ◽  
Nicolas Durrande ◽  
Mauricio A. Alvarez
Keyword(s):  
State Of The Art ◽  
Self Regulation ◽  
Natural Phenomenon ◽  
Linear Parabolic Equation ◽  
Mcmc Algorithm ◽  
Infinite Dimensional ◽  
Common Task ◽  
Ill Posed ◽  
Non Gaussian ◽  
Protein Transcription

AbstractA common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modelling). When complex dynamical systems are considered, such as partial differential equations, this task may become challenging or ill-posed. In this work, a linear parabolic equation is considered as a model for protein transcription from MRNA. The objective is to estimate jointly the differential operator coefficients, namely the rates of diffusion and self-regulation, as well as a functional source. The recent Bayesian methodology for infinite dimensional inverse problems is applied, providing a unique posterior distribution on the parameter space continuous in the data. This posterior is then summarized using a Maximum a Posteriori estimator. Finally, the theoretical solution is illustrated using a state-of-the-art MCMC algorithm adapted to this non-Gaussian setting.

Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime

1996 ◽  
Vol 54 (1) ◽  
pp. 706-716 ◽  
Author(s):  
S. Ciuchi ◽  
F. de Pasquale ◽  
B. Spagnolo
Keyword(s):  
Self Regulation ◽  
Regulation Mechanism ◽  
Non Gaussian

scholarly journals Gradient Profile Estimation Using Exponential Cubic Spline Smoothing in a Bayesian Framework

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 674
Author(s):  
Kushani De De Silva ◽  
Carlo Cafaro ◽  
Adom Giffin
Keyword(s):  
State Of The Art ◽  
Estimation Method ◽  
Synthetic Data ◽  
Noisy Data ◽  
Bayesian Framework ◽  
Physical Systems ◽  
Gradient Profile ◽  
Ill Posed ◽  
Profile Estimation ◽  
Different Levels

Attaining reliable gradient profiles is of utmost relevance for many physical systems. In many situations, the estimation of the gradient is inaccurate due to noise. It is common practice to first estimate the underlying system and then compute the gradient profile by taking the subsequent analytic derivative of the estimated system. The underlying system is often estimated by fitting or smoothing the data using other techniques. Taking the subsequent analytic derivative of an estimated function can be ill-posed. This becomes worse as the noise in the system increases. As a result, the uncertainty generated in the gradient estimate increases. In this paper, a theoretical framework for a method to estimate the gradient profile of discrete noisy data is presented. The method was developed within a Bayesian framework. Comprehensive numerical experiments were conducted on synthetic data at different levels of noise. The accuracy of the proposed method was quantified. Our findings suggest that the proposed gradient profile estimation method outperforms the state-of-the-art methods.

scholarly journals The Regularized Weak Functional Matching Pursuit for linear inverse problems

2019 ◽  
Vol 27 (3) ◽  
pp. 317-340 ◽  
Author(s):  
Max Kontak ◽  
Volker Michel
Keyword(s):  
Inverse Problems ◽  
Matching Pursuit ◽  
A Priori ◽  
Computation Time ◽  
Point Of View ◽  
Computational Point ◽  
Linear Inverse Problems ◽  
Infinite Dimensional ◽  
Frame Condition ◽  
Ill Posed

Abstract In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the “weak” approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90  of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.

scholarly journals Optimization Learning: Perspective, Method, and Applications

2020 ◽  
Author(s):  
Risheng Liu
Keyword(s):  
Inverse Problems ◽  
Theoretical Analysis ◽  
Iterative Methods ◽  
State Of The Art ◽  
Learning Paradigm ◽  
Rigorous Analysis ◽  
The Core ◽  
Globally Convergent ◽  
Ill Posed ◽  
Art Performance

Numerous tasks at the core of statistics, learning, and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems. Nevertheless, integrating learnable structures into iterations is still a laborious process, which can only be guided by intuitions or empirical insights. Moreover, there is a lack of rigorous analysis of the convergence behaviors of these reimplemented iterations, and thus the significance of such methods is a little bit vague. We move beyond these limits and propose a theoretically guaranteed optimization learning paradigm, a generic and provable paradigm for nonconvex inverse problems, and develop a series of convergent deep models. Our theoretical analysis reveals that the proposed optimization learning paradigm allows us to generate globally convergent trajectories for learning-based iterative methods. Thanks to the superiority of our framework, we achieve state-of-the-art performance on different real applications.

scholarly journals An O(log2N) Fully-Balanced Resampling Algorithm for Particle Filters on Distributed Memory Architectures

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 342
Author(s):  
Alessandro Varsi ◽  
Simon Maskell ◽  
Paul G. Spirakis
Keyword(s):  
Parallel Computing ◽  
Shared Memory ◽  
Time Complexity ◽  
Distributed Memory ◽  
Particle Filters ◽  
Dynamic Models ◽  
State Of The Art ◽  
Novel Approach ◽  
Non Gaussian ◽  
Memory Architectures

Resampling is a well-known statistical algorithm that is commonly applied in the context of Particle Filters (PFs) in order to perform state estimation for non-linear non-Gaussian dynamic models. As the models become more complex and accurate, the run-time of PF applications becomes increasingly slow. Parallel computing can help to address this. However, resampling (and, hence, PFs as well) necessarily involves a bottleneck, the redistribution step, which is notoriously challenging to parallelize if using textbook parallel computing techniques. A state-of-the-art redistribution takes O((log2N)2) computations on Distributed Memory (DM) architectures, which most supercomputers adopt, whereas redistribution can be performed in O(log2N) on Shared Memory (SM) architectures, such as GPU or mainstream CPUs. In this paper, we propose a novel parallel redistribution for DM that achieves an O(log2N) time complexity. We also present empirical results that indicate that our novel approach outperforms the O((log2N)2) approach.

scholarly journals Deep Learning-Based Monocular Depth Estimation Methods—A State-of-the-Art Review

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2272 ◽  
Author(s):  
Faisal Khan ◽  
Saqib Salahuddin ◽  
Hossein Javidnia
Keyword(s):  
Deep Learning ◽  
State Of The Art ◽  
Research Work ◽  
Depth Estimation ◽  
Autonomous Driving ◽  
Estimation Methods ◽  
Future Research ◽  
Comprehensive Overview ◽  
Ill Posed ◽  
Monocular Depth

Monocular depth estimation from Red-Green-Blue (RGB) images is a well-studied ill-posed problem in computer vision which has been investigated intensively over the past decade using Deep Learning (DL) approaches. The recent approaches for monocular depth estimation mostly rely on Convolutional Neural Networks (CNN). Estimating depth from two-dimensional images plays an important role in various applications including scene reconstruction, 3D object-detection, robotics and autonomous driving. This survey provides a comprehensive overview of this research topic including the problem representation and a short description of traditional methods for depth estimation. Relevant datasets and 13 state-of-the-art deep learning-based approaches for monocular depth estimation are reviewed, evaluated and discussed. We conclude this paper with a perspective towards future research work requiring further investigation in monocular depth estimation challenges.

scholarly journals Hyperspectral Nonlinear Unmixing by Using Plug-and-Play Prior for Abundance Maps

2020 ◽  
Vol 12 (24) ◽  
pp. 4117
Author(s):  
Zhicheng Wang ◽  
Lina Zhuang ◽  
Lianru Gao ◽  
Andrea Marinoni ◽  
Bing Zhang ◽  
...  
Keyword(s):  
State Of The Art ◽  
Solution Space ◽  
Simulated Data ◽  
Spectral Unmixing ◽  
Group Sparsity ◽  
Plug And Play ◽  
Mixed Pixel ◽  
Method Base ◽  
Ill Posed ◽  
Nonlinear Mixing

Spectral unmixing (SU) aims at decomposing the mixed pixel into basic components, called endmembers with corresponding abundance fractions. Linear mixing model (LMM) and nonlinear mixing models (NLMMs) are two main classes to solve the SU. This paper proposes a new nonlinear unmixing method base on general bilinear model, which is one of the NLMMs. Since retrieving the endmembers’ abundances represents an ill-posed inverse problem, prior knowledge of abundances has been investigated by conceiving regularizations techniques (e.g., sparsity, total variation, group sparsity, and low rankness), so to enhance the ability to restrict the solution space and thus to achieve reliable estimates. All the regularizations mentioned above can be interpreted as denoising of abundance maps. In this paper, instead of investing effort in designing more powerful regularizations of abundances, we use plug-and-play prior technique, that is to use directly a state-of-the-art denoiser, which is conceived to exploit the spatial correlation of abundance maps and nonlinear interaction maps. The numerical results in simulated data and real hyperspectral dataset show that the proposed method can improve the estimation of abundances dramatically compared with state-of-the-art nonlinear unmixing methods.

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