Advanced Stochastic Optimization Algorithm for Deep Learning Artificial Neural Networks in Banking and Finance Industries

One of the objectives of this paper is to incorporate fat-tail effects into, for instance, Sigmoid in order to introduce Transparency and Stability into the existing stochastic Activation Functions. Secondly, according to the available literature reviewed, the existing set of Activation Functions were introduced into the Deep learning Artificial Neural Network through the “Window” not properly through the “Legitimate Door” since they are “Trial and Error “and “Arbitrary Assumptions”, thus, the Author proposed a “Scientific Facts”, “Definite Rules: Jameel’s Stochastic ANNAF Criterion”, and a “Lemma” to substitute not necessarily replace the existing set of stochastic Activation Functions, for instance, the Sigmoid among others. This research is expected to open the “Black-Box” of Deep Learning Artificial Neural networks. The author proposed a new set of advanced optimized fat-tailed Stochastic Activation Functions EMANATED from the AI-ML-Purified Stocks Data  namely; the Log – Logistic (3P) Probability Distribution (1st), Cauchy Probability Distribution (2nd), Pearson 5 (3P) Probability Distribution (3rd), Burr (4P) Probability Distribution (4th), Fatigue Life (3P) Probability Distribution (5th), Inv. Gaussian (3P) Probability Distribution (6th), Dagum (4P) Probability Distribution (7th), and Lognormal (3P) Probability Distribution (8th) for the successful conduct of both Forward and Backward Propagations of Deep Learning Artificial Neural Network. However, this paper did not check the Monotone Differentiability of the proposed distributions. Appendix A, B, and C presented and tested the performances of the stressed Sigmoid and the Optimized Activation Functions using Stocks Data (2014-1991) of Microsoft Corporation (MSFT), Exxon Mobil (XOM), Chevron Corporation (CVX), Honda Motor Corporation (HMC), General Electric (GE), and U.S. Fundamental Macroeconomic Parameters, the results were found fascinating. Thus, guarantee, the first three distributions are excellent Activation Functions to successfully conduct any Stock Deep Learning Artificial Neural Network. Distributions Number 4 to 8 are also good Advanced Optimized Activation Functions. Generally, this research revealed that the Advanced Optimized Activation Functions satisfied Jameel’s ANNAF Stochastic Criterion depends on the Referenced Purified AI Data Set, Time Change and Area of Application which is against the existing “Trial and Error “and “Arbitrary Assumptions” of Sigmoid, Tanh, Softmax, ReLu, and Leaky ReLu

Stochastic Reinforcement Learning

In reinforcement learning episodes, the rewards and punishments are often non-deterministic, and there are invariably stochastic elements governing the underlying situation. Such stochastic elements are often numerous and cannot be known in advance, and they have a tendency to obscure the underlying rewards and punishments patterns. Indeed, if stochastic elements were absent, the same outcome would occur every time and the learning problems involved could be greatly simplified. In addition, in most practical situations, the cost of an observation to receive either a reward or punishment can be significant, and one would wish to arrive at the correct learning conclusion by incurring minimum cost. In this paper, we present a stochastic approach to reinforcement learning which explicitly models the variability present in the learning environment and the cost of observation. Criteria and rules for learning success are quantitatively analyzed, and probabilities of exceeding the observation cost bounds are also obtained.Comment: AIKE 201

Network Inference with Hidden Units

We derive learning rules for finding the connections between units in stochastic dynamical networks from the recorded history of a ``visible'' subset of the units. We consider two models. In both of them, the visible units are binary and stochastic. In one model the ``hidden'' units are continuous-valued, with sigmoidal activation functions, and in the other they are binary and stochastic like the visible ones. We derive exact learning rules for both cases. For the stochastic case, performing the exact calculation requires, in general, repeated summations over an number of configurations that grows exponentially with the size of the system and the data length, which is not feasible for large systems. We derive a mean field theory, based on a factorized ansatz for the distribution of hidden-unit states, which offers an attractive alternative for large systems. We present the results of some numerical calculations that illustrate key features of the two models and, for the stochastic case, the exact and approximate calculations

MIHash: Online Hashing with Mutual Information

Learning-based hashing methods are widely used for nearest neighbor retrieval, and recently, online hashing methods have demonstrated good performance-complexity trade-offs by learning hash functions from streaming data. In this paper, we first address a key challenge for online hashing: the binary codes for indexed data must be recomputed to keep pace with updates to the hash functions. We propose an efficient quality measure for hash functions, based on an information-theoretic quantity, mutual information, and use it successfully as a criterion to eliminate unnecessary hash table updates. Next, we also show how to optimize the mutual information objective using stochastic gradient descent. We thus develop a novel hashing method, MIHash, that can be used in both online and batch settings. Experiments on image retrieval benchmarks (including a 2.5M image dataset) confirm the effectiveness of our formulation, both in reducing hash table recomputations and in learning high-quality hash functions.Comment: International Conference on Computer Vision (ICCV), 201

Functional Bipartite Ranking: a Wavelet-Based Filtering Approach

It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is randomly assigned, the objective is to learn a scoring function s with optimal ROC curve. Based on linear/nonlinear wavelet-based approximations, it is shown how to select compact finite dimensional representations of the input curves adaptively, in order to build accurate ranking rules, using recent advances in the ranking problem for multivariate data with binary feedback. Beyond theoretical considerations, the performance of the learning methods for functional bipartite ranking proposed in this paper are illustrated by numerical experiments