Tuesday, 17 February 2015

The Genetic Algorithm - Explained

Paradigm of Evolution

Every organism contains an array of traits - called DNA, when 2 parents mate they produce a child containing a mixture of their DNA. Depending on how well those traits work together to help the child survive so that he may reproduce, will determine if those traits will pass into future generation. Rarely a random trait enters a child's DNA that was not inherited from the parents, we call this mutation. If the mutation is beneficial, the organism will survive long enough to carry the mutation over to future generations. So the cycle continues, after many generations we continue to optimize the population by "mixing and matching", "trial and error" of  DNA.

Introduction

Genetic Algorithms are used to find optimal solution by method of evolution-inspired search and optimization; Generally used in problems where linear/brute-force searches are not viable in terms of time, such as – Travelling Salesman Problem, Timetable Scheduling, Finding Neural Network Weights, Sudoku, Trees(data-structure) etc..  The first requirement is a encoding scheme suitable for representing individuals, second requirement being a evaluation function for representing the fitness of an individual.

Thursday, 8 January 2015

Neural Network Illustrated – Step by Step

I1 and I2 are the inputs scaled to [-1,1] or [0, 1], depending on the activation function used
f()=Activation Function=Tanh(), Sigmoid() or any differential-able function
W=Current neurons input weights, initialized randomly between [-1, 1].
Wb=Bias Weight, connected to nothing, used as a threshold, initialized same as W
N=The output of the current neuron.


Markov Chains - Explained

Markov Chains is a probabilistic process, that relies on the current state to predict the next state. For Markov chains to be effective the current state has to be dependent on the previous state in some way; For instance, from experience we know that if it looks cloudy outside, the next state we expect is rain. We can also say that when the rain starts to subside into cloudiness, the next state will most likely be sunny. Not every process has the Markov Property, such as the Lottery, this weeks winning numbers have no dependence to the previous weeks winning numbers.

Bloom Filters - Explained

The Bloom filter is a space efficient, probabilistic data structure, designed to test the membership of elements to a set. The trade-off for being a space efficient data structure is it may return false positives, but always returns definite negatives: Meaning Bloom filters can accurately test an element for non-membership to a set, but can only with probability test an element for membership. Bloom filters find application in circumstances where testing for non-membership saves resources such as calls to a web server, checking a proxy cache. Google uses Bloom filters in the Chrome browser as a preliminary check for malicious URL's.