Complementary sum sampling for likelihood approximation in large scale classification

We consider training probabilistic classifiers in the case that the number of classes is too large to perform exact normalisation over all classes. We show that the source of high variance in standard sampling approximations is due to simply not including the correct class of the datapoint into the approximation. To account for this we explicitly sum over a subset of classes and sample the remaining. We show that this simple approach is competitive with recently introduced non likelihood-based approximations

Adaptive Markov random fields for joint unmixing and segmentation of hyperspectral image

Linear spectral unmixing is a challenging problem in hyperspectral imaging that consists of decomposing an observed pixel into a linear combination of pure spectra (or endmembers) with their corresponding proportions (or abundances). Endmember extraction algorithms can be employed for recovering the spectral signatures while abundances are estimated using an inversion step. Recent works have shown that exploiting spatial dependencies between image pixels can improve spectral unmixing. Markov random fields (MRF) are classically used to model these spatial correlations and partition the image into multiple classes with homogeneous abundances. This paper proposes to define the MRF sites using similarity regions. These regions are built using a self-complementary area filter that stems from the morphological theory. This kind of filter divides the original image into flat zones where the underlying pixels have the same spectral values. Once the MRF has been clearly established, a hierarchical Bayesian algorithm is proposed to estimate the abundances, the class labels, the noise variance, and the corresponding hyperparameters. A hybrid Gibbs sampler is constructed to generate samples according to the corresponding posterior distribution of the unknown parameters and hyperparameters. Simulations conducted on synthetic and real AVIRIS data demonstrate the good performance of the algorithm

Resampled Priors for Variational Autoencoders

We propose Learned Accept/Reject Sampling (LARS), a method for constructing richer priors using rejection sampling with a learned acceptance function. This work is motivated by recent analyses of the VAE objective, which pointed out that commonly used simple priors can lead to underfitting. As the distribution induced by LARS involves an intractable normalizing constant, we show how to estimate it and its gradients efficiently. We demonstrate that LARS priors improve VAE performance on several standard datasets both when they are learned jointly with the rest of the model and when they are fitted to a pretrained model. Finally, we show that LARS can be combined with existing methods for defining flexible priors for an additional boost in performance