Julian M. Del Fiore

Cartesian and polar coordinates [Read More]

It all starts with a simple question: given $n + 1$ points $\left\{p_0, p_1, \ldots, p_j, \ldots, p_n\right\}$ where $p_j = (x_j, y_j)$, how can we find the unique polnoymium of degree $n$ that traverses such points? [Read More]

Softmax regression is a supervised machine learning algorithm used in classification tasks where a target variable $y$ may take $K$ values, and we are interested in labeling an observation composed of $N$ features/predictors. While workarounds such as OvR and OvO allow to use binary classifiers (e.g. logistic regression) in multinomial... [Read More]

Linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA) are supervised machine learning algorithms used for multinomial classification tasks. Both LDA and QDA estimate $P(y \;\vert\;\mathbf{x})$ relying on Bayes theorem, i.e., first calculating $P(\mathbf{x} \;\vert\; y)$, and eventually $P(y)$ too. For each class $k \in \{1, \ldots, K\}$, LDA assumes... [Read More]

A training set $X$ composed of $m$ samples, i.e., $X = (x^{(1)}, \ldots, x^{(m)})$, can be modeled as the outcome of a random variable $\mathcal{X}$. If we knew how this variable behaves, we would then be able to characterize the dataset. The behavior of a random variable is determined by... [Read More]