Understanding the neural processing of natural speech processing is an important first step for designing Brain-Computer Interface (BCI) based speech enhancement and speech recognition systems. Complex neural signals like electroencephalography (EEG) are time-varying and has a non-linear relationship with continuous speech. Linear models can decode stimulus features reliably, but the correlation between the reconstructed signal and continuous EEG remain low despite attempts at optimization. In the current application, we demonstrate the utility of a Recurrent Neural Networks (RNN) model to relate various stimuli features such as the envelope, spectrogram to the continuous EEG in a cocktail party scenario. We use a Long Short-Term Memory (LSTM) neural network architecture that has self-connecting loops which help in preserving past information to predict future value. Given that predictability plays a critical role in speech comprehension, we posit that such a neural network architecture yield better results. In attended condition, for native participants, the LSTM models yield 30% and 22% mean correlation improvement and for non-native participants, 43% and 37% improvement over linear models for envelope and spectrogram respectively with EEG. Finally, we have trained a single model to predict the native language of a participant using EEG and it yielded 95% accuracy.

We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph G on p vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with vertices lying along a path in G. From a statistical perspective, information on the underlying network may potentially reduce the number of observations required to recover the population principal component. We consider the canonical estimator which optimally exploits the prior knowledge by solving a non-convex quadratic maximization on the empirical covariance. We introduce a simple network and analyze the estimator under the spiked covariance model for sparse PCA. We show that side information potentially improves the statistical complexity. We propose two algorithms to approximate the solution of the constrained quadratic maximization, and recover a component with the desired properties. We empirically evaluate our schemes on synthetic and real datasets.