@conference {arribas2003neural,
	title = {Neural posterior probabilities for microcalcification detection in breast cancer diagnoses},
	booktitle = {Neural Engineering, 2003. Conference Proceedings. First International IEEE EMBS Conference on},
	year = {2003},
	pages = {660{\textendash}663},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {We apply the a Posteriori Probability Model Selection (PPMS) algorithm with the help of Generalized Softmax Perceptron (GSP) neural architecture in order to obtain estimates of the posterior class probabilities at its outputs, in the binary problem of microcalcification detection in a hospital digitalized mammogram database. We first detect windowed images with high probability to belong to the class microcalcification is present, then we locally segment the shape of the calcifications, and finally show the segmented microcalcifications to the radiologist. The segmented images together with the posterior probabilities for each window image can be employed as a valuable information to help predicting a breast diagnosis, in order to distinguish between benignant calcium deposit and malignant accumulation, that is, breast carcinoma.},
	doi = {https://doi.org/10.1109/CNE.2003.1196915},
	url = {https://ieeexplore.ieee.org/abstract/document/1196915},
	author = {J I Arribas and Carlos Alberola L{\'o}pez and Mateos-Marcos, A and Jes{\'u}s Cid-Sueiro}
}
@conference {411,
	title = {Neural architectures for parametric estimation of a posteriori probabilities by constrained conditional density functions},
	booktitle = {Neural Networks for Signal Processing - Proceedings of the IEEE Workshop},
	year = {1999},
	publisher = {IEEE, Piscataway, NJ, United States},
	organization = {IEEE, Piscataway, NJ, United States},
	address = {Madison, WI, USA},
	abstract = {<p>A new approach to the estimation of {\textquoteright}a posteriori{\textquoteright} class probabilities using neural networks, the Joint Network and Data Density Estimation (JNDDE), is presented in this paper. It is based on the estimation of the conditional data density functions, with some restrictions imposed by the classifier structure; the Bayes{\textquoteright} rule is used to obtain the {\textquoteright}a posteriori{\textquoteright} probabilities from these densities. The proposed method is applied to three different network structures: the logistic perceptron (for the binary case), the softmax perceptron (for multi-class problems) and a generalized softmax perceptron (that can be used to map arbitrarily complex probability functions). Gaussian mixture models are used for the conditional densities. The method has the advantage of establishing a distinction between the network parameters and the model parameters. Complexity on any of them can be fixed as desired. Maximum Likelihood gradient-based rules for the estimation of the parameters can be obtained. It is shown that JNDDE exhibits a more robust convergence characteristics than other methods of a posteriori probability estimation, such as those based on the minimization of a Strict Sense Bayesian (SSB) cost function.</p>
},
	keywords = {Asymptotic stability, Constraint theory, Data structures, Gaussian mixture models, Joint network and data density estimation, Mathematical models, Maximum likelihood estimation, Neural networks, Probability},
	doi = {https://doi.org/10.1109/NNSP.1999.788145},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033321049\&partnerID=40\&md5=7967fa377810cc0c3e6a4d9020024b80},
	author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and A R Figueiras-Vidal}
}
@conference {410,
	title = {Neural networks to estimate ML multi-class constrained conditional probability density functions},
	booktitle = {Proceedings of the International Joint Conference on Neural Networks},
	year = {1999},
	publisher = {IEEE, United States},
	organization = {IEEE, United States},
	address = {Washington, DC, USA},
	abstract = {<p>In this paper, a new algorithm, the Joint Network and Data Density Estimation (JNDDE), is proposed to estimate the {\textquoteleft}a posteriori{\textquoteright} probabilities of the targets with neural networks in multiple classes problems. It is based on the estimation of conditional density functions for each class with some restrictions or constraints imposed by the classifier structure and the use Bayes rule to force the a posteriori probabilities at the output of the network, known here as a implicit set. The method is applied to train perceptrons by means of Gaussian mixture inputs, as a particular example for the Generalized Softmax Perceptron (GSP) network. The method has the advantage of providing a clear distinction between the network architecture and the model of the data constraints, giving network parameters or weights on one side and data over parameters on the other. MLE stochastic gradient based rules are obtained for JNDDE. This algorithm can be applied to hybrid labeled and unlabeled learning in a natural fashion.</p>
},
	keywords = {Generalized softmax perceptron (GSP) network, Joint network and data density estimation (JNDDE), Mathematical models, Maximum likelihood estimation, Neural networks, Probability density function, Random processes},
	doi = {https://doi.org/10.1109/IJCNN.1999.831174},
	url = {http://www.scopus.com/inward/record.url?eid=2-s2.0-0033326060\&partnerID=40\&md5=bb38c144dac0872f3a467dc12170e6b6},
	author = {J I Arribas and Jes{\'u}s Cid-Sueiro and T Adali and A R Figueiras-Vidal}
}
