Here, we present a novel approach to solve the problem of reconstructing perceived stimuli from brain responses by combining probabilistic inference with deep learning. Our approach first inverts the linear transformation from latent features to brain responses with maximum a posteriori estimation and then inverts the nonlinear transformation from perceived stimuli to latent features with adver...

An extension of the "prior density for path" (Onsager-Machlup functional) is defined and shown to exist for Gaussian fields generated by solutions of elliptic PDE's driven by white noise. This functional is then used to define and solve the MAP estimation of such fields observed via nonlinear noisy sensors. Existence results and a representation of the estimator are derived for this model. AMS ...

Abstract — A semilinear second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for a difference scheme that uses Backward-Euler in time and central differencing in space. Sharp L1-norm bounds for the Green’s function of the parabolic operator and its derivatives are derived...

This paper studies the asymptotic performance of maximum-a-posteriori estimation in the presence of prior information. The problem arises in several applications such as recovery of signals with non-uniform sparsity pattern from underdetermined measurements. With prior information, the maximum-a-posteriori estimator might have asymmetric penalty. We consider a generic form of this estimator and...

Soft-Output Viterbi Algorithm (SOVA) is one type of recovery memory-less Markov Chain and is used widely to decode convolutional codes. Fundamentally, conventional SOVA is designed on the basis of Maximum A-Posteriori Probability (APP) with the assumption of normal distribution. Therefore, conventional SOVA fails miserably in the presence of symmetric alpha stable noise S S α which is one form ...

Few-shot learning aims to train an effective classifier in a small data regime. Due the scarcity of training samples (usually as 1 or 5), traditional deep solutions often suffer from overfitting. To address this issue, intuitive idea is augment hallucinate sufficient data. For purpose, paper, we propose simple yet method build model for novel categories with few samples. Specifically, assume th...

In this paper a new method for noise removal from singletrial event-related potentials recorded with a multi-channel electroencephalogram is addressed. An observed signal is separated into multiple signals with a multi-channel Wiener filter whose coefficients are estimated based on parameter estimation of a probabilistic generative model that locally models the amplitude of each separated signa...