Modèle probit

En statistiques, le modèle probit est un modèle de régression binomiale. Le modèle probit a été introduit par Chester Bliss en 1934. C'est un cas particulier du modèle linéaire généralisé. Cadre conceptuel Soit Y une variable aléatoire binaire (i.e. prenant pour valeur 0 ou 1) et X un vecteur de variables dont on suppose qu'il influence Y. On fait l'hypothèse que le modèle s'écrit de la manière suivante :

P(Y=1 \mid X) = \Phi(X'\beta),

où \Phi désigne la fonction de répartition de la loi normale centrée réduite. Voir aussi

Régression logistique

Notes et références Catégorie:Modèle statistique Catégorie:Régression

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Robust Binary Models by Pruning Randomly-initialized Networks

Chen Liu, Mathieu Salzmann, Sabine Süsstrunk, Ziqi Zhao

Robustness to adversarial attacks was shown to require a larger model capacity, and thus a larger memory footprint. In this paper, we introduce an approach to obtain robust yet compact models by pruning randomly-initialized binary networks. Unlike adversarial training, which learns the model parameters, we initialize the model parameters as either +1 or −1, keep them fixed, and find a subnetwork structure that is robust to attacks. Our method confirms the Strong Lottery Ticket Hypothesis in the presence of adversarial attacks, and extends this to binary networks. Furthermore, it yields more compact networks with competitive performance than existing works by 1) adaptively pruning different network layers; 2) exploiting an effective binary initialization scheme; 3) incorporating a last batch normalization layer to improve training stability. Our experiments demonstrate that our approach not only always outperforms the state-of-the-art robust binary networks, but also can achieve accuracy better than full-precision ones on some datasets. Finally, we show the structured patterns of our pruned binary networks.

2022

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Learning and generation of slow sequences: an application to music composition

Florian François Colombo

Human brains can deal with sequences with temporal dependencies on a broad range of timescales, many of which are several order of magnitude longer than neuronal timescales. Here we introduce an artificial intelligence that learns and produces the complex structure of music, a specific type of slow sequence. Our model employs a separation of fundamental features and multi-layer networks of gated recurrent units. We separate the information contained in monophonic melodies into their rhythm and melody features. The model processes these features in parallel while modelling the relation between them, effectively splitting the joint distribution over note duration and pitch into conditional probabilities. Using such an approach, we were able to automatically learn the temporal dependencies inherent of large corpora of Irish folk songs. We could use the extracted structural rules to generate interesting complete melodies or suggest possible continuations of melody fragments that are coherent with the characteristics of the fragments themselves.

2016

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Principled Detection-by-Classification from Multiple Views

Jérôme Berclaz, François Fleuret, Pascal Fua

Machine-learning based classification techniques have been shown to be effective at detecting objects in complex scenes. However, the final results are often obtained from the alarms produced by the classifiers through a post-processing which typically relies on ad hoc heuristics. Spatially close alarms are assumed to be triggered by the same target and grouped together. Here we replace those heuristics by a principled Bayesian approach, which uses knowledge about both the classifier response model and the scene geometry to combine multiple classification answers. We demonstrate its effectiveness for multi-view pedestrian detection. We estimate the marginal probabilities of presence of people at any location in a scene, given the responses of classifiers evaluated in each view. Our approach naturally takes into account both the occlusions and the very low metric accuracy of the classifiers due to their invariance to translation and scale. Results show our method produces one order of magnitude fewer false positives than a method that is representative of typical state-of-the-art approaches. Moreover, the framework we propose is generic and could be applied to any detection-by-classification task.

2008

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Régression logistique

En statistiques, la régression logistique ou modèle logit est un modèle de régression binomiale. Comme pour tous les modèles de régression binomiale, il s'agit d'expliquer au mieux une variable bin

Régression (statistiques)

En mathématiques, la régression recouvre plusieurs méthodes d’analyse statistique permettant d’approcher une variable à partir d’autres qui lui sont corrélées. Par extension, le terme est aussi uti

Régression linéaire

En statistiques, en économétrie et en apprentissage automatique, un modèle de régression linéaire est un modèle de régression qui cherche à établir une relation linéaire entre une variable, dite exp

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