Regularization methods are characterized by loss functions measuring data fits and penalty terms constraining model parameters. The commonly used quadratic loss is not suitable for classification with binary responses, whereas the loglikelihood function is not readily applicable to models where the exact distribution of observations is unknown or not fully specified. We introduce the penalized ...

purpose: to report a case who had optic disc duplication, a rare congenital disorder characterized by two well-defined discs in one eye. case report: a 19 months-old child presented with unilateral epiphora in the right eye since birthday. the right eye was smaller than the left eye and mild ptosis was apparent. nasolacrimal duct probing was performed under general anesthesia. the examination r...

The performance of the likelihood ratio test is considered for a many-point interaction point process featuring a reduced number of isolated points. Limit theorems are proved that establish the Poissonian asymptotic distribution of the loglikelihood function for point processes with the isolated-pointpenalization joint probability density function. The asymptotic distribution is used to approxi...

Here we show that the one-sided chi-square test used for evaluating the significance of the overlap between the RH network and other existing datasets and the Bayesian loglikelihood score (LLS) approach used for integrating diverse datasets [1,2] are closely related. The Fisher’s exact test was used instead of the chi-square test when the expected value in a cell of the contingency table was ≤ ...

We immediately notice the similarity between the empirical risk we had seen before and the negative loglikelihood. We will see that we can regard maximum likelihood estimation as our familiar minimal empirical risk when the loss function is chosen appropriately. In the meantime note that minimizing (1) yields our familiar square-error loss if Wi’s are Gaussian. If the Wi’s are Laplacian (pW (w)...

We introduce the matrix exponential as a way of modelling spatially dependent data. The matrix exponential spatial specification simplifies the loglikelihood allowing a closed form solution to the problem of maximum likelihood estimation, and greatly simplifies Bayesian estimation of the model. The matrix exponential spatial specification can produce estimates and inferences similar to those fr...

As shown recently, the structural optimization of probabilistic neural networks can be included into EM algorithm by introducing a special type of multivariate Bernoulli mixtures. However, the underlying loglikelihood criterion is known to be multimodal in case of mixtures and therefore the EM iteration process may be starting-point dependent. In the present paper we discuss the possibility of ...

This paper proposes a learning method of translation rules from parallel corpora. This method applies the maximum entropy principle to a probabilistic model of translation rules. First, we define feature functions which express statistical properties of this model. Next, in order to optimize the model, the system iterates following steps: (1) selects a feature function which maximizes loglikeli...

Kernel discriminant analysis (KDA) is an effective approach for supervised nonlinear dimensionality reduction. Probabilistic models can be used with KDA to improve its robustness. However, the state of the art of such models could only handle binary class problems, which confines their application in many real world problems. To overcome this limitation, we propose a novel nonparametric probabi...