Machine Learning (ML)

Artificial Neural Networks

An Artificial Neural Network is a form of computing system that vaguely resembles the biological nervous system. It is composed of very many neurons that are centres of computation and learn by a sort of hit and trial method over the course of many epochs. ANN can be seen as a network of perceptrons

Restricted Boltzmann Machines

Boltzmann Machines are bidirectionally connected networks of stochastic processing units. It can be used to learn important aspects of an unknown probability distribution based on samples from the distribution. We explore Gibbs Sampling and Contrastive Divergence.

Machine Learning (ML)

Perceptron, the building block of modern AI

A perceptron is an artificial neuron that essentially receives input from an input layer, processes the input with the help of an activation function (the Heaviside step function) and gives out the output in the form of either a 0 or 1. The perceptron was invented in 1957 by Frank Rosenblatt

matrix multiplication

Cannon’s algorithm for distributed matrix multiplication

Cannon's algorithm is a distributed algorithm for matrix multiplication for two-dimensional meshes. It is especially suitable for computers laid out in an N × N mesh. The main advantage of the algorithm is that its storage requirements remain constant and are independent of the number of processors.

matrix multiplication

Freivalds’ algorithm for verifying Matrix Multiplication

Freivalds' algorithm is a probabilistic randomized algorithm used to verify matrix multiplication. Given three n x n matrices, Freivalds' algorithm determines in O(kn^2) whether the matrices are equal for a chosen k value with a probability of failure less than 2^-k.

matrix multiplication

Russian peasant multiplication algorithm

Russian peasant multiplication is an interesting way to multiply numbers that uses a process of halving and doubling without using multiplication operator. The idea is to double the first number and halve the second number repeatedly till the second number doesn’t become 1

matrix multiplication

Strassen’s Matrix Multiplication algorithm

Strassen’s Matrix Multiplication algorithm is the first algorithm to prove that matrix multiplication can be done at a time faster than O(N^3). It utilizes the strategy of divide and conquer to reduce the number of recursive multiplication calls from 8 to 7 and hence, the improvement.

Artificial Intelligence

L1 and L2 Regularization Methods

A regression model that uses L1 regularization technique is called Lasso Regression and model which uses L2 is called Ridge Regression. The key difference between these two is the penalty term. Lasso shrinks the less important feature’s coefficient to zero

Artificial Intelligence

Gradient descent: Mathematical view

Gradient descent algorithm is one of the most popuarl algorithms for finding optimal parameters for most machine learning models including neural networks. The basic method that this algorithm uses is to find optimal values for the parameters that define your ‘cost function’.

Artificial Intelligence

Regularization

Regularization is a method used to reduce the variance of your model and increase the bias. It is used when your model overfits the training data. Another method to do regularization is called Lasso regression. This is the solution to Biase-Variance Dilemma.

Artificial Intelligence

Cross Validation

Cross Validation is a procedure used to evaluate your machine learning model on limited sample of data. With the help of this, we can actually tell how well our model performs on unseen data. Other variants are stratified cross validation and leave one out cross validation. Learn through an example

Artificial Intelligence

Decision Trees

Decision Tree is a popular machine learning algorithm mainly used for classification. Concepts of entropy and information gain are required to apply decision tree for a data set. It is used for non-linear classification and regression Learn through an example