Author: Arthur Charpentier

Can we diversify extremal events?

This post was originaly written in French and translated below. In a financial context, diversifying risks means investing in a variety of assets, sectors, or geographic regions to avoid having the poor performance of a single investment significantly affect the overall portfolio. Diversification allows for risk reduction, or, in its…

Fairness and discrimination, PhD Course, #9 Mitigation, Pre-processing and In-processing

Finally, after defining (and quantifying) “group fairness“ and “individual fairness“, we can now start to discuss the idea of mitigating a possible discrimination. Here, we will see, how based on some data that were initially collected, and a model (a pricing model), it is possible to remove the discrimination in…

Fairness and discrimination, PhD Course, #1 Motivation

This week, we will start our MAT998P course, in Montréal, entitled “équité et discrimination des modèles prédictifs“. It will mainly be based on the forthcoming textbook, I can also mention the R package > library(devtools) > install_github("freakonometrics/InsurFair") And because it is the first course, this week, I will start with…

Econometrics Seminars at Université de Montréal

This Thursday, I will present at the CIREQ Séminaire Marcel-Dagenais en Économétrie at Université de Montréal, ou paper Optimal Transport for Counterfactual Estimation: A Method for Causal Inference, written with Emmanuel Flachaire and Ewen Gallic. Many problems ask a question that can be formulated as a causal question: “what would…

Interpretability and explainability of predictive models

In 400 AD, in his Confessiones, Augustine wrote quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio that can be translated as What then is time? If no one asks me, I know what it is. If I wish to explain it to him…

Could there be incentives to cycle through a red light?

This is of course a rhetorical question! Because cyclists must stop when the light is red! … But … there is always that moment, on a bicycle, when you stop, and  then you say to yourself the worst part is that the lights are badly regulated, and I know that…

Regression discontinuity model for TV series

In September, we are usually happy to see our favorite TV series back on air… Or not? Because, admit it, if we are happy to see those characters back, most of the time, we are disappointed, too. So why not look at the data, to confirm this feeling? Nazareno Andrade…

Testing for Covid-19 in the U.S.

For almost a month, on a daily basis, we are working with colleagues (Romuald, Chi and Mathieu) on modeling the dynamics of the recent pandemic. I learn of lot of things discussing with them, but we keep struggling with the tests. Paul, in Montréal, helped me a little bit, but…

Qui a survécu au naufrage du Titanic?

also known as quiz numéro 4 du cours STT5100 (de la session d’hiver). Vendredi dernier, alors que nous terminions le cours vers midi, François Legault a décrété l’état d’urgence sanitaire pour une quinzaine de jours. Le cours est donc sur la glace depuis une semaine, et (pour l’instant) encore une…

Modeling Pandemics (3)

In Statistical Inference in a Stochastic Epidemic SEIR Model with Control Intervention, a more complex model than the one we’ve seen yesterday was considered (and is called the SEIR model). Consider a population of size N, and assume that S is the number of susceptible, E the number of exposed,…

Modeling pandemics (2)

When introducing the SIR model, in our initial post, we got an ordinary differential equation, but we did not really discuss stability, and periodicity. It has to do with the Jacobian matrix of the system. But first of all, we had three equations for three function, but actually\displaystyle{{\frac{dS}{dt}}+{\frac {dI}{dt}}+{\frac {dR}{dt}}=0}so…

Modeling pandemics (1)

The most popular model to model epidemics is the so-called SIR model – or Kermack-McKendrick. Consider a population of size N, and assume that S is the number of susceptible, I the number of infectious, and R for the number recovered (or immune) individuals, \displaystyle {\begin{aligned}&{\frac {dS}{dt}}=-{\frac {\beta IS}{N}},\\[6pt]&{\frac {dI}{dt}}={\frac…

Function basis and regression

In the first part of the course on linear models, we’ve seen how to construct a linear model when the vector of covariates \boldsymbol{x} is given, so that \mathbb{E}(Y|\boldsymbol{X}=\boldsymbol{x}) is either simply \boldsymbol{x}^\top\boldsymbol{\beta} (for standard linear models) or a functional of \boldsymbol{x}^\top\boldsymbol{\beta} (in GLMs). But more generally, we can consider…

Gini index, poverty and top shares

Consider some ordered income \{y_1,y_2,\dots,y_n\}, with y_1\leq y_2\leq\dots\leq y_n. A classical tool to visualize inequality is Lorenz curve: define the proportion of people F_{i}=i/n (with the convention F_{0}=0); then the cumulated wealth S_{i}=\sum_{j=1}^{i}y_{j} and the fraction of cumulated wealth L_{i}=S_{i}/S_{n} (with again {\displaystyle L_{0}=0}). Then Lorenz curve is simply the…

Testing for a causal effect (with 2 time series)

A few days ago, I came back on a sentence I found (in a French newspaper), where someone was claiming that “… an old variable explains 85% of the change in a new variable. So we can talk about causality” and I tried to explain that it was just stupid…

Lasso Regression (home made)

Again, this post is related to my MAT7381 course, where we will see that it is actually possible to write our own code to compute Lasso regression, \min\left\lbrace\frac{1}{2}\|\mathbf{y}-\mathbf{X}\mathbf{\beta}\|_{\ell_2}^2+\lambda\|\mathbf{\beta}\|_{\ell_1}\right\rbraceWe have to define the soft-thresholding functionS(z,\gamma)=\text{sign}(z)\cdot(|z|-\gamma)_+=\begin{cases}z-\gamma&\text{ if }\gamma>|z|\text{ and }z<0\\z+\gamma&\text{ if }\gamma<|z|\text{ and }z<0 \\0&\text{ if }\gamma\geq|z|\end{cases}The R function would be soft_thresholding…
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