The noblest pleasure is the joy of understanding
In this era, everything is influenced by Artificial Intelligence, Machine Learning, and deep learning. Nowadays it is common to use very big datasets and we need fast and efficient optimization algorithms to get the leverage of this big amount of data. Training Neural Network is generally much harder than the other optimization problems in deep learning, A good optimization algorithm is easy to implement and…
Most real-world data sets have outliers that have unusually small or big values then the typical values of the data set. Outliers can have a negative impact on data analysis if not detected correctly and also outliers can provide significant information at the same time. There are several methods to detect an outlier in the data set. It is important to understand the characteristics of…
Statistics is very important in our day to day life. There are so many applications of statistics in sectors like predictive analytics, machine learning, etc. It is really important to understand statistics well in order to understand these high-level concepts. In this post, we will introduce different parts of statistics, and then in later posts, we will describe them briefly. Statistics Statistics is the discipline that…
Logistic regression is one of the most commonly used algorithms for machine learning and is a building block for neural networks. It is really important to understand the concepts and the derivations of logistic regression. In this post we will explore the fundamentals of logistic regression and also concepts like maximum likelihood function, cross-entropy are covered briefly. Previously, we have covered linear classifier models and…
Previously, we have discussed briefly the simple linear regression. Here we will discuss multiple regression or multivariable regression and how to get the solution of the multivariable regression. At the end of the post, we will provide the python code from scratch for multivariable regression. Motivation A single variable linear regression model can learn to predict an output variable \(y\) when there is only one…
Regression is a very fundamental concept in statistics, machine learning and in Neural Network. Imagine plotting the correlation between rainfall frequency and agriculture production in high school. Increase in rainfall generally increases agriculture production. Fitting a line to those points enables us to predict the production rate under different rain conditions. It was actually a very simplest form of linear regression. In simple words, regression…
To build an accurate machine learning model we need to have a proper understanding of the error. In forming predictions of a model there are three sources of error: noise, bias, and variance. Having proper knowledge of error and bias-variance would help us building accurate models and avoiding mistakes of overfitting and underfitting. In this tutorial, our case study is discussing how to predict house…
In the earlier era of machine learning, there used to be a lot of discussion on the bias-variance trade-off and the reason for that was we could increase bias and reduce variance, or reduce bias and increase variance. But back in the pre-deep learning era, we didn’t have many tools that just reduce bias or just reduce variance without hurting the other one. But in the modern deep learning, neural network or big data…
Neural Network has become a crucial part of modern technology. It has influenced our daily life in a way that we have never imagined. From e-commerce and solving classification problems to autonomous driving, it has touched everything. In this tutorial, we are gonna discuss all the important aspects of neural networks in the simplest way possible and at the end of the tutorial, we have…
Differential Equations An equation involving derivatives of one or more dependent variables with respect to one or more independent variables is called a differential equation. For example: \begin{equation} \frac{d^{2}y}{dx^2} + xy \left( \frac{dy}{dx}\right)^2 = 0 \end{equation} \begin{equation} \frac{d^{4}x}{dt^4} + 5 \frac{d^{2}x}{dt^2} + 3x = \sin t \end{equation} \begin{equation}\frac{\partial v}{\partial s} + \frac{\partial v}{\partial t} = v \end{equation} \begin{equation}\frac{\partial^{2}u}{\partial x^2} + \frac{\partial^{2}u}{\partial y^2} + \frac{\partial^{2}u}{\partial z^2}…