# What's the name of this classification algorithm?

We are given a training dataset consisting of a list of feature vectors $$x_1, \ldots, x_N \in \mathbb R^d$$ and corresponding labels $$y_1, \ldots, y_N \in \{-1, 1\}$$. Let $$\hat x_i$$ be the augmented feature vector obtained by prepending a $$1$$ to the vector $$x_i$$. We seek to find a vector $$\beta \in \mathbb R^{d+1}$$ such that if $$y_i = 1$$ then $$\hat x_i^T \beta > 0$$, and if $$y_i = -1$$ then $$\hat x_i^T \beta < 0$$. We choose $$\beta$$ to be a minimizer of the function $$L(\beta) = \sum_{I=1}^N e^{-y_i \hat x_i^T \beta}.$$ What is the name of this particular binary classification algorithm, where $$\beta$$ is chosen to minimize this cost function $$L$$? Is this a popular algorithm?

• I'd just call it a linear classifier that minimizes the exponential loss. No name AFAIK, since it's not a common thing to do. One common use of the exponential loss is Adaboost. It's not particularly popular anymore compared to other forms of boosting, but is still regarded as an important historical development. In any case, what you're proposing is not equivalent to Adaboost, even though it uses the same loss function. Mar 6, 2020 at 23:32
• Correct, it's just linear regression, with a log-linear transform. It's just function minimization on the log scale.
– user32398
Mar 7, 2020 at 3:10