scholarly journals Asymptotic Expansion as Prior Knowledge in Deep Learning Method for High Dimensional BSDEs

2017 ◽  
Author(s):  
Masaaki Fujii ◽  
Akihiko Takahashi ◽  
Masayuki Takahashi
Keyword(s):  
Asymptotic Expansion ◽  
Deep Learning ◽  
Prior Knowledge ◽  
High Dimensional ◽  
Learning Method

An acceleration scheme for deep learning-based BSDE solver using weak expansions

2020 ◽  
Vol 07 (02) ◽  
pp. 2050012
Author(s):  
Riu Naito ◽  
Toshihiro Yamada
Keyword(s):  
Deep Learning ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Backward Stochastic Differential Equation ◽  
Nonlinear Partial Differential Equations ◽  
High Dimensional ◽  
Parabolic Partial Differential Equations ◽  
Weak Approximation ◽  
Learning Method ◽  
Partial Differential

This paper gives an acceleration scheme for deep backward stochastic differential equation (BSDE) solver, a deep learning method for solving BSDEs introduced in Weinan et al. [Weinan, E, J Han and A Jentzen (2017). Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations, Communications in Mathematics and Statistics, 5(4), 349–380]. The solutions of nonlinear partial differential equations are quickly estimated using technique of weak approximation even if the dimension is high. In particular, the loss function and the relative error for the target solution become sufficiently small through a smaller number of iteration steps in the new deep BSDE solver.

scholarly journals A New Interpolation Approach and Corresponding Instance-Based Learning

2021 ◽  
Author(s):  
Shiyou Lian
Keyword(s):  
Deep Learning ◽  
High Efficiency ◽  
Inductive Learning ◽  
Simple Calculation ◽  
High Dimensional ◽  
Learning Method ◽  
Mathematical Basis ◽  
Instance Based Learning ◽  
Difference Formula ◽  
Wide Range

Starting from finding approximate value of a function, introduces the measure of approximation-degree between two numerical values, proposes the concepts of “strict approximation” and “strict approximation region”, then, derives the corresponding one-dimensional interpolation methods and formulas, and then presents a calculation model called “sum-times-difference formula” for high-dimensional interpolation, thus develops a new interpolation approach, that is, ADB interpolation. ADB interpolation is applied to the interpolation of actual functions with satisfactory results. Viewed from principle and effect, the interpolation approach is of novel idea, and has the advantages of simple calculation, stable accuracy, facilitating parallel processing, very suiting for high-dimensional interpolation, and easy to be extended to the interpolation of vector valued functions. Applying the approach to instance-based learning, a new instance-based learning method, learning using ADB interpolation, is obtained. The learning method is of unique technique, which has also the advantages of definite mathematical basis, implicit distance weights, avoiding misclassification, high efficiency, and wide range of applications, as well as being interpretable, etc. In principle, this method is a kind of learning by analogy, which and the deep learning that belongs to inductive learning can complement each other, and for some problems, the two can even have an effect of “different approaches but equal results” in big data and cloud computing environment. Thus, the learning using ADB interpolation can also be regarded as a kind of “wide learning” that is dual to deep learning.

scholarly journals A New Interpolation Approach and Corresponding Instance-Based Learning

2021 ◽  
Author(s):  
Shiyou Lian
Keyword(s):  
Deep Learning ◽  
High Efficiency ◽  
Inductive Learning ◽  
Simple Calculation ◽  
High Dimensional ◽  
Learning Method ◽  
Mathematical Basis ◽  
Instance Based Learning ◽  
Difference Formula ◽  
Wide Range

Starting from finding approximate value of a function, introduces the measure of approximation-degree between two numerical values, proposes the concepts of “strict approximation” and “strict approximation region”, then, derives the corresponding one-dimensional interpolation methods and formulas, and then presents a calculation model called “sum-times-difference formula” for high-dimensional interpolation, thus develops a new interpolation approach, that is, ADB interpolation. ADB interpolation is applied to the interpolation of actual functions with satisfactory results. Viewed from principle and effect, the interpolation approach is of novel idea, and has the advantages of simple calculation, stable accuracy, facilitating parallel processing, very suiting for high-dimensional interpolation, and easy to be extended to the interpolation of vector valued functions. Applying the approach to instance-based learning, a new instance-based learning method, learning using ADB interpolation, is obtained. The learning method is of unique technique, which has also the advantages of definite mathematical basis, implicit distance weights, avoiding misclassification, high efficiency, and wide range of applications, as well as being interpretable, etc. In principle, this method is a kind of learning by analogy, which and the deep learning that belongs to inductive learning can complement each other, and for some problems, the two can even have an effect of “different approaches but equal results” in big data and cloud computing environment. Thus, the learning using ADB interpolation can also be regarded as a kind of “wide learning” that is dual to deep learning.

scholarly journals Prior knowledge-based deep learning method for indoor object recognition and application

2018 ◽  
Vol 6 (1) ◽  
pp. 249-257 ◽  
Author(s):  
Xintao Ding ◽  
Yonglong Luo ◽  
Qingde Li ◽  
Yongqiang Cheng ◽  
Guorong Cai ◽  
...  
Keyword(s):  
Deep Learning ◽  
Object Recognition ◽  
Prior Knowledge ◽  
Learning Method ◽  
Knowledge Based

Review of the Applications of Deep Learning in Bioinformatics

2021 ◽  
Vol 15 (8) ◽  
pp. 898-911
Author(s):  
Yongqing Zhang ◽  
Jianrong Yan ◽  
Siyu Chen ◽  
Meiqin Gong ◽  
Dongrui Gao ◽  
...  
Keyword(s):  
Deep Learning ◽  
Drug Discovery ◽  
Biomedical Imaging ◽  
State Of The Art ◽  
Black Box ◽  
Medical Data ◽  
Biological Data ◽  
High Dimensional ◽  
Biological Research ◽  
Process Data

Rapid advances in biological research over recent years have significantly enriched biological and medical data resources. Deep learning-based techniques have been successfully utilized to process data in this field, and they have exhibited state-of-the-art performances even on high-dimensional, nonstructural, and black-box biological data. The aim of the current study is to provide an overview of the deep learning-based techniques used in biology and medicine and their state-of-the-art applications. In particular, we introduce the fundamentals of deep learning and then review the success of applying such methods to bioinformatics, biomedical imaging, biomedicine, and drug discovery. We also discuss the challenges and limitations of this field, and outline possible directions for further research.

scholarly journals Siamese Reconstruction Network: Accurate Image Reconstruction from Human Brain Activity by Learning to Compare

2019 ◽  
Vol 9 (22) ◽  
pp. 4749
Author(s):  
Lingyun Jiang ◽  
Kai Qiao ◽  
Linyuan Wang ◽  
Chi Zhang ◽  
Jian Chen ◽  
...  
Keyword(s):  
Deep Learning ◽  
Human Brain ◽  
Brain Activity ◽  
Feature Space ◽  
Training Data ◽  
Reconstruction Method ◽  
Learning Method ◽  
Training Samples ◽  
Visual Reconstruction ◽  
Relationship Of

Decoding human brain activities, especially reconstructing human visual stimuli via functional magnetic resonance imaging (fMRI), has gained increasing attention in recent years. However, the high dimensionality and small quantity of fMRI data impose restrictions on satisfactory reconstruction, especially for the reconstruction method with deep learning requiring huge amounts of labelled samples. When compared with the deep learning method, humans can recognize a new image because our human visual system is naturally capable of extracting features from any object and comparing them. Inspired by this visual mechanism, we introduced the mechanism of comparison into deep learning method to realize better visual reconstruction by making full use of each sample and the relationship of the sample pair by learning to compare. In this way, we proposed a Siamese reconstruction network (SRN) method. By using the SRN, we improved upon the satisfying results on two fMRI recording datasets, providing 72.5% accuracy on the digit dataset and 44.6% accuracy on the character dataset. Essentially, this manner can increase the training data about from n samples to 2n sample pairs, which takes full advantage of the limited quantity of training samples. The SRN learns to converge sample pairs of the same class or disperse sample pairs of different class in feature space.

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