Julian M. Del FioreBlog, research, projects and teaching material
https://julian10m.github.io
Lagrange Interpolation
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? Let’s begin easy: “polnoymium of degree $n$” means that we are looking for...
Sat, 02 Apr 2022 00:00:00 +0200
https://julian10m.github.io/2022-04-02-Lagrange-Interpolation/
https://julian10m.github.io/2022-04-02-Lagrange-Interpolation/Softmax Regression
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...
Fri, 23 Apr 2021 00:00:00 +0200
https://julian10m.github.io/2021-04-23-Softmax-Regression/
https://julian10m.github.io/2021-04-23-Softmax-Regression/Linear and Quadratic Discriminant Analysis
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...
Sun, 21 Mar 2021 00:00:00 +0100
https://julian10m.github.io/2021-03-21-Linear-Quadratic-Discriminant-Analysis/
https://julian10m.github.io/2021-03-21-Linear-Quadratic-Discriminant-Analysis/Maximum Likelihood and Bayesian Estimation
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...
Sat, 13 Mar 2021 00:00:00 +0100
https://julian10m.github.io/2021-03-13-Maximum-Likelihood-Estimation-Bayesian-Estimation/
https://julian10m.github.io/2021-03-13-Maximum-Likelihood-Estimation-Bayesian-Estimation/Logistic Regression
Logistic regression is a supervised machine learning algorithm used in classification tasks where a target variable $y$ may take $K$ possible values, and we are interested in labeling an observation $\mathbf{x}$ composed of $N$ features/predictors. In particular, logistic regression is used in binary classification tasks, i.e., cases where $K=2$. However,...
Sun, 07 Mar 2021 00:00:00 +0100
https://julian10m.github.io/2021-03-07-Logistic-Regression/
https://julian10m.github.io/2021-03-07-Logistic-Regression/Linear and Polynomial Regression
Linear and polynomial regression are supervised machine learning algorithms used, as their names indicate, to perform regression tasks, i.e., to estimate the values of a continuous response/target variable $y$. Linear Regression To obtain the estimate $\hat{y}$ of $y$, given a sample $x$ with $n$ features, the model simply proposes to...
Fri, 05 Mar 2021 00:00:00 +0100
https://julian10m.github.io/2021-03-05-Linear-Polynomial-Regression/
https://julian10m.github.io/2021-03-05-Linear-Polynomial-Regression/Machine Learning and Pattern Recognition
As human beings, we like understanding what surrounds us, either for the simple sake of knowing or because this gives us predictability. In that sense, in many situations it arrives that we have a problem that we want to model, e.g., from a phenomenon that depends only on basic physics...
Wed, 03 Mar 2021 00:00:00 +0100
https://julian10m.github.io/2021-03-03-Machine-Learning-Pattern-Recognition/
https://julian10m.github.io/2021-03-03-Machine-Learning-Pattern-Recognition/Classification relying on Bayes or Bayes classifiers
The objective is to determine to which class $\hat{y}$ an unlabelled observation $x$ belongs to, out of $K$ available. We assume that $x$ is composed of $n$ features/predictors, i.e., $x=(x_1,\ldots,x_n)$. Bayes classifier The Bayes classifier assigns an observation $x$ to class $y_k$ when the likelihood of this being true is...
Thu, 25 Feb 2021 00:00:00 +0100
https://julian10m.github.io/2021-02-25-bayes-classifier/
https://julian10m.github.io/2021-02-25-bayes-classifier/Finally a PhD, no longer a candidate!
I am glad to tell you that I finished my PhD with a defense that went great a couple of days ago, I am very happy :)
I was lucky and my presentation got recorded, thus I want to share it with you! I hope you enjoy it!
Wed, 10 Feb 2021 00:00:00 +0100
https://julian10m.github.io/2021-02-10-End-of-PhD/
https://julian10m.github.io/2021-02-10-End-of-PhD/Back on Track
After a very long time, I am trying to finally dedicate some time to my website! It’s not that I didn’t want before, but I’ve been working SO much! I’ve decided to keep the Blog section. I feel this might encourage me to post stuff…we shall see, stay tuned :)...
Sun, 14 Jul 2019 00:00:00 +0200
https://julian10m.github.io/2019-07-14-back-in-track/
https://julian10m.github.io/2019-07-14-back-in-track/