PAC-Bayesian High Dimensional Bipartite Ranking

This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive scoring functions, and we derive non-asymptotic risk bounds under a sparsity assumption. In particular, oracle inequalities in probability holding under a margin condition assess the performance of our procedure, and prove its minimax optimality. An MCMC-flavored algorithm is proposed to implement our method, along with its behavior on synthetic and real-life datasets

Invariant currents and dynamical Lelong numbers

Let $f$ be a polynomial automorphism of ${\Bbb C}^k$ of degree $\lambda$, whose rational extension to ${\Bbb P}^k$ maps the hyperplane at infinity to a single point. Given any positive closed current $S$ on ${\Bbb P}^k$ of bidegree (1,1), we show that the sequence $\lambda^{-n}(f^n)^\star S$ converges in the sense of currents on ${\Bbb P}^k$ to a linear combination of the Green current $T_+$ of $f$ and the current of integration along the hyperplane at infinity. We give an interpretation of the coefficients in terms of generalized Lelong numbers with respect to an invariant dynamical current for $f^{-1}$.Comment: 15 page

An Oracle Inequality for Quasi-Bayesian Non-Negative Matrix Factorization

The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods non-negative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general class of prior distributions and shows how the prior affects the rate of convergence.Comment: This is the corrected version of the published paper P. Alquier, B. Guedj, An Oracle Inequality for Quasi-Bayesian Non-negative Matrix Factorization, Mathematical Methods of Statistics, 2017, vol. 26, no. 1, pp. 55-67. Since then Arnak Dalalyan (ENSAE) found a mistake in the proofs. We fixed the mistake at the price of a slightly different logarithmic term in the boun

Pycobra: A Python Toolbox for Ensemble Learning and Visualisation

We introduce \texttt{pycobra}, a Python library devoted to ensemble learning (regression and classification) and visualisation. Its main assets are the implementation of several ensemble learning algorithms, a flexible and generic interface to compare and blend any existing machine learning algorithm available in Python libraries (as long as a \texttt{predict} method is given), and visualisation tools such as Voronoi tessellations. \texttt{pycobra} is fully \texttt{scikit-learn} compatible and is released under the MIT open-source license. \texttt{pycobra} can be downloaded from the Python Package Index (PyPi) and Machine Learning Open Source Software (MLOSS). The current version (along with Jupyter notebooks, extensive documentation, and continuous integration tests) is available at \href{https://github.com/bhargavvader/pycobra}{https://github.com/bhargavvader/pycobra} and official documentation website is \href{https://modal.lille.inria.fr/pycobra}{https://modal.lille.inria.fr/pycobra}