Source: Deep Learning on Medium
Bye to Trial and Error Activation Functions of Neural Networks II: Proposed Jameel’s ANNAF Stochastic Criterion
Artist Hans Hoffman wrote, “The ability to simplify means to eliminate the unnecessary so that the necessary may speak.”
Casper Hansen (2019) says “Better optimized neural network; choose the right activation function, and your neural network can perform vastly better”.
In my second article entitled “Scientific Facts that prove the existing set of Activation Functions formed the Neural Networks’ Black-Box”, we stopped at a point where we are about to introduce the proposed “Jameel’s ANNAF Stochastic Criterion (2019)”.
Jamilu (2019) proposed “JAMEEL’S ANNAF STOCHASTIC CRITERION” as follows. Note that ANNAF means Artificial Neural Network Activation Functions.
This stated that under this criterion, we run the goodness of fits test on our referenced PURIFIED AL-ML-DATA SET such that:
(1) We accept if the Average of the ranks of Kolmogorov Smirnor, Anderson Darling and Chi-squared is less than or equal to Three (3);
(2) We must choose the fat-tailed Probability Distribution follows by our referenced PURIFIED AL-ML-DATA SET ITSELF regardless of its Rankings;
(3) If there is a tie, we include both the fat-tailed Probability Distributions in the selection;
(4) At least two (2) fat-tailed Probability Distributions must be included in the selection;
(5) We select the most occur Probability Distribution as the qualified candidate in each case of a test of goodness of fit on our referenced PURIFIED AL-ML-DATA SET;
More so, Jamilu (2019) proposed “Jameel’s Stochastic Lemma” as follows:
All the TOP-RANKED Fat-tailed Monotone Continuously Differentiable Stochastic Functions EMANATED from referenced AI-ML-Purified Data satisfies Proposed “Jameel’s Stochastic ANNAF Criterion” are EXCELLENT STOCHASTIC ACTIVATION FUNCTIONS to perform well-informed Forward and Backward Propagations of a Deep Learning Neural Network.
In July 2015, the author considered STOCKS PRICES of Eleven (11) out of Fifty (50) World’s Biggest Public Companies by FORBES as of 2015, applied “Jameel’s Criterion (first version)” to came up with the following Stochastic Functions which he subsequently proposed in October, 2019 are INDEED EXCELLENT set of STOCKS PRICES ACTIVATION FUNCTIONS to conducts STOCKS PRICES DEEP LEARNING NEURAL NETWORKS. Thus, the RANKING of the Stocks Prices Advanced Optimized Activation Functions are as follows:
First Derivative of Log — Logistic (3P) Probability Distribution (1st):
First Derivative of Pearson 5 (3P) Probability Distribution (3rd):
First Derivative of Burr (4P) Probability Distribution (4th):
First Derivative of Fatique Life (3P) Probability Distribution (5th):
Here, you will apply Product and Chain Rules. The following gives the Derivative of a Normal Distribution, this idea can be applied to solve the above problem.
First Derivative of Dagum (4P) Probability Distribution (7th):
First Derivative of Lognormal (3P) Probability Distribution (8th):
NOTE: The First Derivatives’ of the above EIGHT(8) Activation Functions’ LIMITS (RANGES) are not stated in this article.
Note that the author did not check the Monotone Differentiability of the functions presented above. However, the market trends are very volatile, many things had happened from 2019–2015. The distribution time series Data was from 2014–1990, was shown in (2015) showed. Different results may be obtained when conducted in the year 2019. Anyway, the author adopted the fat-tailed probability distributions obtained as per as 2015.
This research work was published in the “Risk and Financial Management Journal, IDEASPREAD.ORG, USA” and available online: https://j.ideasspread.org/index.php/rfm/article/view/387
To be continued in the next article.
Jamilu Auwalu Adamu, FIMC, CMC, FIMS (UK), FICA (in view)
Associate Editor, Risk and Financial Management Journal, USA
Editor, Journal of Economics and Management Sciences, USA
Former Associate Editor, Journal of Risk Model Validation, UK
PEER-REVIEWER, RISK.NET Journals, London
Former, Steering Committee Member, PRMIA Nigeria Chapter
Correspondence: Mathematics Programme Building, 118 National Mathematical Centre, Small Sheda, Kwali, 904105, FCT-Abuja, Nigeria. Tel: +2348038679094. E-mail: firstname.lastname@example.org
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Jamilu Auwalu Adamu (2019), Superintelligent Deep Learning Artificial Neural Networks, accepted for publication in the International Journal of Applied Science, IDEAS SPREAD. INC, USA (https://j.ideasspread.org/index.php/ijas), preprint available on https://www.preprints.org/manuscript/201912.0263/v1 with doi: 10.20944/preprints201912.0263.v1
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Backward propagation and Activation Functions: