Probit model

Summary

In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit. The purpose of the model is to estimate the probability that an observation with particular characteristics will fall into a specific one of the categories; moreover, classifying observations based on their predicted probabilities is a type of binary classification model. A probit model is a popular specification for a binary response model. As such it treats the same set of problems as does logistic regression using similar techniques. When viewed in the generalized linear model framework, the probit model employs a probit link function. It is most often estimated using the maximum likelihood procedure, such an estimation being called a probit regression. Conceptual framework Suppose a response variable Y is binary, that is it can have only two possible outcomes which we

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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

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

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