2020-02-20 Articles

La librairie deslib implémente plusieurs algorithme de sélection de modèles sur des problèmes de classifications. Mais plutôt que de sélectionner un modèle ou un ensemble de modèle sur toutes la base, elle sélectionne les meilleurs modèles localement. On appelle cela la sélection dynamique de classifieurs (voir Sélection dynamique de modèles).

Quelques lectures plus loin (Generalized probabilistic principal component analysis of correlated data), j’ai découvert PPCA = Probabilistic PCA qui produit des résultats équivalents mais formule le problème d’une façon plus interprétable (voir aussi edwards - probabilistic pca.

Je suis tombé aussi sur cet article A Unified Framework for Structured Graph Learning via Spectral Constraints. Il m’a fait découvrir la forme des valeurs propres de la matrice Laplacien construite à partir d’un graphe bi-partite. La première équation m’a intrigué car je manque de culture dans ce domaine :

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\mathcal{S}^p_{++} est l’ensemble des matrices dans

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définies positives pour me demander le maximum de \max_x f(x) = \log x - s x \Rightarrow x = \frac{1}{s} et f(\frac{1}{s}) = - log s - 1.

L’article suivant essaye de faire du clustering Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms en utilisant l’arc le plus long parmi dans le chemin le plus court reliant deux noeuds. L’algorithme résultat est apparemment capable de séparer deux spirales enlacées.

Deux autres articles Online Sufficient Dimension Reduction Through Sliced Inverse Regression, Online PCA with Optimal Regret m’ont ramené à quelques idées développées pour l’implémentation d’une régression linéaire par morceaux.

Le dernier article apprend lui-aussi à réduire les dimensions Perturbation Bounds for Procrustes, Classical Scaling, and Trilateration, with Applications to Manifold Learning. Je l’ai ouvert car certains mots du titres me faisait penser à formules magiques tirées de Harry Potter.