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 Approximation-Degree-Based Interpolation: A New Interpolation Method

2020 ◽  
Author(s):  
Shiyou Lian
Keyword(s):  
Interpolation Method ◽  
High Dimensional ◽  
Learning Method ◽  
One Dimensional ◽  
A Value ◽  
Instance Based Learning ◽  
Difference Formula ◽  
Degree Function ◽  
Convenient Approach ◽  
The One

This paper introduces the measure of approximate-degree and the concept of approximate-degree function between numerical values, thus developing a new interpolation method —— approximation-degree-based interpolation, i.e., AD <a></a><a>interpolation</a>. One-dimensional AD interpolation is done directly by using correlative interpolation formulas; <i>n</i>(<i>n</i>>1)-dimensional AD interpolation is firstly separated into <i>n</i> parallel one-dimensional AD interpolation computations to do respectively, and then got results are synthesized by Sum-Times-Difference formula into a value as the result value of the<i> n</i>-dimensional interpolation. If the parallel processing is used, the efficiency of <i>n</i>-dimensional AD interpolation is almost the same as that of the one-dimensional AD interpolation. Thus it starts a feasible and convenient approach and provides an effective method for high-dimensional interpolations. <a></a><a>Furthermore</a>, if AD interpolation is introduced into machine learning, a new instance-based learning method is <a></a><a>expecte</a>d to be<a></a><a> realize</a>d.

scholarly journals Approximation-Degree-Based Interpolation: A New Interpolation Method

2020 ◽  
Author(s):  
Shiyou Lian
Keyword(s):  
Interpolation Method ◽  
High Dimensional ◽  
Learning Method ◽  
One Dimensional ◽  
A Value ◽  
Instance Based Learning ◽  
Difference Formula ◽  
Degree Function ◽  
Convenient Approach ◽  
The One

This paper introduces the measure of approximate-degree and the concept of approximate-degree function between numerical values, thus developing a new interpolation method —— approximation-degree-based interpolation, i.e., AD <a></a><a>interpolation</a>. One-dimensional AD interpolation is done directly by using correlative interpolation formulas; <i>n</i>(<i>n</i>>1)-dimensional AD interpolation is firstly separated into <i>n</i> parallel one-dimensional AD interpolation computations to do respectively, and then got results are synthesized by Sum-Times-Difference formula into a value as the result value of the<i> n</i>-dimensional interpolation. If the parallel processing is used, the efficiency of <i>n</i>-dimensional AD interpolation is almost the same as that of the one-dimensional AD interpolation. Thus it starts a feasible and convenient approach and provides an effective method for high-dimensional interpolations. <a></a><a>Furthermore</a>, if AD interpolation is introduced into machine learning, a new instance-based learning method is <a></a><a>expecte</a>d to be<a></a><a> realize</a>d.

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 Understanding the onset of hot streaks across artistic, cultural, and scientific careers

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Lu Liu ◽  
Nima Dehmamy ◽  
Jillian Chown ◽  
C. Lee Giles ◽  
Dashun Wang
Keyword(s):  
Deep Learning ◽  
Network Science ◽  
High Impact ◽  
High Dimensional ◽  
Science Methods ◽  
Scientific Careers ◽  
Wide Range ◽  
Film Directors ◽  
Hot Streak

AbstractAcross a range of creative domains, individual careers are characterized by hot streaks, which are bursts of high-impact works clustered together in close succession. Yet it remains unclear if there are any regularities underlying the beginning of hot streaks. Here, we analyze career histories of artists, film directors, and scientists, and develop deep learning and network science methods to build high-dimensional representations of their creative outputs. We find that across all three domains, individuals tend to explore diverse styles or topics before their hot streak, but become notably more focused after the hot streak begins. Crucially, hot streaks appear to be associated with neither exploration nor exploitation behavior in isolation, but a particular sequence of exploration followed by exploitation, where the transition from exploration to exploitation closely traces the onset of a hot streak. Overall, these results may have implications for identifying and nurturing talents across a wide range of creative domains.

scholarly journals Addressing Noise and Skewness in Interpretable Health-Condition Assessment by Learning Model Confidence

Sensors ◽  
2020 ◽  
Vol 20 (24) ◽  
pp. 7307
Author(s):  
Yuxi Zhou ◽  
Shenda Hong ◽  
Junyuan Shang ◽  
Meng Wu ◽  
Qingyun Wang ◽  
...  
Keyword(s):  
Deep Learning ◽  
Domain Knowledge ◽  
High Efficiency ◽  
Condition Assessment ◽  
Health Condition ◽  
Assessment Task ◽  
Wide Range ◽  
Real World Applications ◽  
Interpretation Method ◽  
Assessment Research

Assessing the health condition has a wide range of applications in healthcare, military, aerospace, and industrial fields. Nevertheless, traditional feature-engineered techniques involve manual feature extraction, which are too cumbersome to adapt to the changes caused by the development of sensor network technology. Recently, deep-learning-based methods have achieved initial success in health-condition assessment research, but insufficient considerations for problems such as class skewness, noisy segments, and result interpretability make it difficult to apply them to real-world applications. In this paper, we propose a K-margin-based Interpretable Learning approach for health-condition assessment. In detail, a skewness-aware RCR-Net model is employed to handle problems of class skewness. Furthermore, we present a diagnosis model based on K-margin to automatically handle noisy segments by naturally exploiting expected consistency among the segments associated with each record. Additionally, a knowledge-directed interpretation method is presented to learn domain knowledge-level features automatically without the help of human experts which can be used as an interpretable decision-making basis. Finally, through experimental validation in the field of both medical and aerospace, the proposed method has a better generality and high efficiency with 0.7974 and 0.8005 F1 scores, which outperform all state-of-the-art deep learning methods for health-condition assessment task by 3.30% and 2.99%, respectively.

scholarly journals A Deep Learning Approach for MIMO-NOMA Downlink Signal Detection

Sensors ◽  
2019 ◽  
Vol 19 (11) ◽  
pp. 2526 ◽  
Author(s):  
Chuan Lin ◽  
Qing Chang ◽  
Xianxu Li
Keyword(s):  
Deep Learning ◽  
Signal Detection ◽  
Power Allocation ◽  
Interference Cancellation ◽  
Communication Systems ◽  
High Efficiency ◽  
Optimal Solution ◽  
Optimal Order ◽  
Learning Method ◽  
Allocation Factor

As a key candidate technique for fifth-generation (5G) mobile communication systems, non-orthogonal multiple access (NOMA) has attracted considerable attention in the field of wireless communication. Successive interference cancellation (SIC) is the main NOMA detection method applied at receivers for both uplink and downlink NOMA transmissions. However, SIC is limited by the receiver complex and error propagation problems. Toward this end, we explore a high-performance, high-efficiency tool—deep learning (DL). In this paper, we propose a learning method that automatically analyzes the channel state information (CSI) of the communication system and detects the original transmit sequences. In contrast to existing SIC schemes, which must search for the optimal order of the channel gain and remove the signal with higher power allocation factor while detecting a signal with a lower power allocation factor, the proposed deep learning method can combine the channel estimation process with recovery of the desired signal suffering from channel distortion and multiuser signal superposition. Extensive performance simulations were conducted for the proposed MIMO-NOMA-DL system, and the results were compared with those of the conventional SIC method. According to our simulation results, the deep learning method can successfully address channel impairment and achieve good detection performance. In contrast to implementing well-designed detection algorithms, MIMO-NOMA-DL searches for the optimal solution via a neural network (NN). Consequently, deep learning is a powerful and effective tool for NOMA signal detection.

Deep-learning-based image registration for nano-resolution tomographic reconstruction

2021 ◽  
Vol 28 (6) ◽  
Author(s):  
Tianyu Fu ◽  
Kai Zhang ◽  
Yan Wang ◽  
Jizhou Li ◽  
Jin Zhang ◽  
...  
Keyword(s):  
Deep Learning ◽  
Image Registration ◽  
High Efficiency ◽  
Tomographic Reconstruction ◽  
3D Structure ◽  
Correction Method ◽  
Full Field ◽  
Research Fields ◽  
Wide Range

Nano-resolution full-field transmission X-ray microscopy has been successfully applied to a wide range of research fields thanks to its capability of non-destructively reconstructing the 3D structure with high resolution. Due to constraints in the practical implementations, the nano-tomography data is often associated with a random image jitter, resulting from imperfections in the hardware setup. Without a proper image registration process prior to the reconstruction, the quality of the result will be compromised. Here a deep-learning-based image jitter correction method is presented, which registers the projective images with high efficiency and accuracy, facilitating a high-quality tomographic reconstruction. This development is demonstrated and validated using synthetic and experimental datasets. The method is effective and readily applicable to a broad range of applications. Together with this paper, the source code is published and adoptions and improvements from our colleagues in this field are welcomed.

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