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Benjamin Cohen's Projects

case_study_operations_intern icon case_study_operations_intern

Statistical description of a dataset containing transactions (passed/failed) with their amounts for the business Voodoo. Ways to work daily against frauds and ways to determine a user’s value by his level of engagement.

causal-inference-and-missing-values-multiple-treatment-or-continuous-treatment icon causal-inference-and-missing-values-multiple-treatment-or-continuous-treatment

Several methods to estimate the average effect (IPW, g-estimators, AIPW) and heterogeneous effects in the context of binary treatment already exist. The objective of this project was to make a state of the art of the available methods to manage multiple treatments or even continuous treatments (doses). On the one hand we listed the main estimators and their characteristics. On the other hand we listed their implementations to compare them empirically by reproducing simulations of a real dataset. It will help us to create recommendations to the users. We proved some results empirically using a notebook written in Python and also try to suggest improvements if needed.

control-variates-with-kernel-smoothing-toward-faster-than-root-n-rates icon control-variates-with-kernel-smoothing-toward-faster-than-root-n-rates

This document is the summary of our work on Control variates with Kernel smoothing. The goal of this project is to see if Kernel smoothing enables us to be more efficient than other control variates in approximating the integral : \begin{equation} \displaystyle I = \int g f d\lambda \end{equation}. Where $f$ is a density function on $\mathbb{R}^d$ and $g$ a function on $\mathbb{R}^d \mapsto \mathbb{R}$. As we might not be able to draw random variables directly from $f$, we consider a sampler $q$ of the density $f$. \paragraph{ } In a first part we create conventional control variates and compute the approximation of $I$. Then we will be taking the Kernel smoothing estimators as control variates (in order to control the variance ~\cite{article1}). In a third time we will implement the OLS to those control variables in order to select the best $q$, the ultimate goal being to compare the efficiency of the different control variables.

differentiable-ranks-and-sorting-using-optimal-transport icon differentiable-ranks-and-sorting-using-optimal-transport

Sorting is a necessary tool for machine learning, to create algorithms (k-NN) or test-time metrics like top-k classification accuracy or losses based on the rank. Nevertheless it seems to be a difficult task for automatically differentiable pipelines in DL. Sorting gives us two vectors, this application is not differentiable as we are working with integer-valued permutation. In the paper they aim to implement a differentiable proxy of the basic approach. The article conceive this proxy by thinking of an optimal assignment problem. We sort n values by matching them to a probability measure supported on any increasing family of n target values. Therefore we are considering Optimal Transport (OT) as a relaxation of the basic problem allowing us to extend rank and sort operators using probability measures. The auxiliary measure will be supported on m increasing values with m $\ne$ n. Introducing regularization with an entropic penalty and applying Sinkhorn iterations will allow to gain back differentiable operators. The smooth approximation of rank and sort allow to use the 0/1 loss and the quantile regression loss.

differential-equations-numerical-resolution icon differential-equations-numerical-resolution

Resolution of differential equations using various integration methods as explicit Euler, implicit Euler, various numerical Runge-Kutta methods, search of an equilibrium point. Behavior of the equations close to the equilibrium point.

epidemiologic-study icon epidemiologic-study

Deterministic model based on differential equations, Markov modelisation, test on parameters gamma and beta for contamination/healing/infection

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