## Portfolio item number 1

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Published in *ECML PKDD 2017, Skopje, Macedonia*, 2017

co-authors: S. Clémençon, A. Garivier, A. Sabourin, C. Vernade

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Published in *NeurIPS 2017, Long Beach, USA*, 2017

co-author: S. Clémençon

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Published in *ACML 2018, Beijing, China*, 2018

co-authors: S. Clémençon, A. Garivier

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Published in *ALT 2019, Chicago, USA*, 2019

co-authors: A. Korba, S. Clémençon

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Published in *ICMA 2020*, 2020

co-authors: R. Vogel, S. Clémençon, C. Tillier

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Published in *Institut polytechnique de Paris*, 2020

supervisors: Stephan Clémençon, Aurélien Garivier and Anne Sabourin

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Published in *preprint*, 2021

co-author: Gergely Neu

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Published in *preprint*, 2022

Abstract. This paper introduces the checkered regression model, a nonlinear generalization of logistic regression. More precisely, this new binary classifier relies on the multivariate function $\frac{1}{2}\left( 1 + \tanh(\frac{z_1}{2})\times\dots\times\tanh(\frac{z_m}{2}) \right)$, which coincides with the usual sigmoid function in the univariate case $m=1$. While the decision boundary of logistic regression consists of a single hyperplane, our method is shown to tessellate the feature space by any given number $m\ge 1$ of hyperplanes. In order to fit the model’s parameters to some labeled data, we describe a classic empirical risk minimization framework based on the cross entropy loss. A multiclass version of our approach is also proposed.

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Published in *Deep Reinforcement Learning Workshop at NeurIPS 2022*, 2022

co-authors: R. Alami, Y.A. Dahou Djilali, K. Fedyanin, E. Moulines, M. Panov

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Published in *preprint*, 2023

co-authors: M.E.A. Seddik, H. Goulart, M. Debbah

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Published in *Transactions on Machine Learning Research*, 2023

co-authors: R. Alami, Y.A. Dahou Djilali, K. Fedyanin, E. Moulines

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Published in *preprint*, 2023

Abstract. This paper extends the classic theory of convex optimization to the minimization of functions that are equal to the negated logarithm of what we term as a “sum-log-concave” function, i.e., a sum of log-concave functions. In particular, we show that such functions are in general not convex but still satisfy generalized convexity inequalities. These inequalities unveil the key importance of a certain vector that we call the “cross-gradient” and that is, in general, distinct from the usual gradient. Thus, we propose the Cross Gradient Descent (XGD) algorithm moving in the opposite direction of the cross-gradient and derive a convergence analysis. As an application of our sum-log-concave framework, we introduce the so-called “checkered regression” method relying on a sum-log-concave function. This classifier extends (multiclass) logistic regression to non-linearly separable problems since it is capable of tessellating the feature space by using any given number of hyperplanes, creating a checkerboard-like pattern of decision regions.

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** Published:**

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Undergraduate course, *University 1, Department*, 2014

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Workshop, *University 1, Department*, 2015

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