Artificial Neural Network: Julia, Python and R

In this post, we will attempt to explain the most famous model for deep learning, the artificial neural network (ANN). This is part of the deep learning series that we plan to publish in this blog. The typical ANN model as we all know is inspired by the biological neural network, but in a feedforward fashion, which means input signals are passed into the layers of neurons up into the output layer without recurring at any given layer. Sample Mathematically, this expectation function looks complicated and sometimes difficult to understand. However, this is actually easy to grasp if we relate this to a simple model, say any nonlinear model like Michaelis-Menten model. For regression modeling, any given dataset $\mathscr{D}=\{(\mathbf{x}_i, t_i): \mathbf{x}_i\in\mathbb{R}^{d}, t_i\in\mathbb{R}, i=1,\cdots,n\}$, where $\mathbf{x}$ is the input vector and $t$ is the corresponding target variable, we can relate the two variables ($\mathbf{x}$ and $t$) as follows: \begin{equation} t_i= f(\mathbf{x}_i)+\varepsilon_i, \quad i = 1,\cdots, n \end{equation}