Basic Elements of Linear Regression Model

Linear regression may be both the simplest and most popular among the standard tools to regression.Dating back to the dawn of the 19th century, linear regression flows from a few simpleassumptions. First, we assume that the relationship between the independent variables x and thedependent variable y is linear, i.e., that y can be expressed as … Continue reading Basic Elements of Linear Regression Model

Affine Function

Affine functions is a vector-valued functions of the form f(x_1,…,x_n)=A_1x_1+…+A_nx_n+b These coefficients can be scalar or dense or sparse matrices. The constant term is a scalar or a column vector. In geometry, an affine transformation or affine map (from the Latin, affinis, "connected with") between two vector spaces consists of a linear transformation followed by … Continue reading Affine Function

Softmax Operation

The main approach that we are going to take here is to interpret the outputs of our model as probabilities. We will optimize our parameters to produce probabilities that maximize the likelihood ofthe observed data. Then, to generate predictions, we will set a threshold, for example, choosingthe label with the maximum predicted probabilities. Put formally, … Continue reading Softmax Operation