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Given a set of data points $\{x {(1)}, ..., x {(m)}\}$ associated to a set of outcomes $\{y {(1)}, ..., y {(m)}\}$, we want to build a classifier that learns how to predict $y$ from $x$. Hypothesis The hypothesis is noted $h_\theta$ and is the model that we choose. For a given input data $x {(i)}$ the model prediction output is $h_\theta(x {(i)})$. Loss function A loss function is a function $L:(z,y)\in\mathbb{R}\times Y\longmapsto L(z,y)\in\mathbb{R}$ that takes as inputs the predicted value $z$ corresponding to the real data value $y$ and outputs how different they are. Remark: Stochastic gradient descent (SGD) is updating the parameter based on each training example, and batch gradient descent is on a batch of training examples.

Given a set of data points $\{x {(1)}, ..., x {(m)}\}$ associated to a set of outcomes $\{y {(1)}, ..., y {(m)}\}$, we want to build a classifier that learns how to predict $y$ from $x$. Hypothesis ― The hypothesis is noted $h_\theta$ and is the model that we choose. For a given input data $x {(i)}$ the model prediction output is $h_\theta(x {(i)})$. Loss function ― A loss function is a function $L:(z,y)\in\mathbb{R}\times Y\longmapsto L(z,y)\in\mathbb{R}$ that takes as inputs the predicted value $z$ corresponding to the real data value $y$ and outputs how different they are. Remark: Stochastic gradient descent (SGD) is updating the parameter based on each training example, and batch gradient descent is on a batch of training examples.