E. Curbelo

L. Martino, M. M. Garcia, P. S. Paradas et al.

Counting immunopositive cells on biological tissues generally requires either manual annotation or (when available) automatic rough systems, for scanning signal surface and intensity in whole slide imaging. In this work, we tackle the problem of counting microglial cells in lumbar spinal cord cross-sections of rats by omitting cell detection and focusing only on the counting task. Manual cell counting is, however, a time-consuming task and additionally entails extensive personnel training. The classic automatic color-based methods roughly inform about the total labeled area and intensity (protein quantification) but do not specifically provide information on cell number. Since the images to be analyzed have a high resolution but a huge amount of pixels contain just noise or artifacts, we first perform a pre-processing generating several filtered images {(providing a tailored, efficient feature extraction)}. Then, we design an automatic kernel counter that is a non-parametric and non-linear method. The proposed scheme can be easily trained in small datasets since, in its basic version, it relies only on one hyper-parameter. However, being non-parametric and non-linear, the proposed algorithm is flexible enough to express all the information contained in rich and heterogeneous datasets as well (providing the maximum overfit if required). Furthermore, the proposed kernel counter also provides uncertainty estimation of the given prediction, and can directly tackle the case of receiving several expert opinions over the same image. Different numerical experiments with artificial and real datasets show very promising results. Related Matlab code is also provided.

L. Martino, F. Llorente, E. Curbelo et al.

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure, alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the actual estimation of the noise power. A complete Bayesian study over the model parameters and the scale parameter can be also performed. Numerical experiments show the benefits of the proposed approach.

F. Llorente, E. Curbelo, L. Martino et al.

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of Layered Adaptive Importance Sampling (LAIS) scheme, which is a family of adaptive importance samplers where Markov chain Monte Carlo algorithms are employed to drive an underlying multiple importance sampling scheme. The modular nature of LAIS allows for different possible implementations, yielding a variety of different performance and computational costs. In this work, we propose different enhancements of the classical LAIS setting in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants address computational challenges arising in real-world applications, for instance with highly concentrated posterior distributions. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer. Different numerical experiments, considering several challenging scenarios, show the benefits of the proposed schemes comparing with benchmark methods presented in the literature.