Starting with a simple generative model and the assumption of statistical independence of the underlying components, independent component analysis (ICA) decomposes a given set of observations by making use of the diversity in the data, typically in terms of statistical properties of the signal. Most of the ICA algorithms introduced to date have considered one of the two types of diversity: non-Gaussianity-i.e., higherorder-statistics-or, sample dependence. A recent generalization of ICA, independent vector analysis (IVA), generalizes ICA to multiple data sets and adds the use of one more diversity, dependence across multiple data sets for achieving an independent decomposition, jointly across multiple data sets. Finally, both ICA and IVA, when implemented in the complex domain, enjoy the addition of yet another type of diversity, noncircularity of the sources-underlying components. Mutual information rate provides a unifying framework such that all these statistical properties-types of diversity-can be jointly taken into account for achieving the independent decomposition. Most of the ICA methods developed to date can be cast as special cases under this umbrella, as well as the more recently developed IVA methods. In addition, this formulation allows us to make use of maximum likelihood theory to study large sample properties of the estimator, derive the Cramér-Rao lower bound (CRLB) and determine the conditions for the identifiability of the ICA and IVA models. In this overview paper, we first present ICA, and then its generalization to multiple data sets, IVA, both using mutual information rate, present conditions for the identifiability of the given linear mixing model and derive the performance bounds. We address how various methods fall under this umbrella and give examples of performance for a few sample algorithms compared with the performance bound. We then discuss the importance of approaching the performance bound depending on the goal, and use medical image analysis as the motivating example.

Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the identification conditions for a general IVA formulation, which accounts for linear, nonlinear, and sample-to-sample dependencies. The identification conditions are a generalization of previous results for ICA and for IVA when samples are independently and identically distributed. Furthermore, a principal aim of IVA is the identification of dependent sources between datasets. Thus, we provide the additional conditions for when the arbitrary ordering of the sources within each dataset is common. Performance bounds in terms of the Cramér-Rao lower bound are also provided for the demixing matrices and interference to source ratio. The performance of two IVA algorithms are compared to the theoretical bounds.

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We propose a max-pooling based loss function for training Long Short-Term Memory (LSTM) networks for smallfootprint keyword spotting (KWS), with low CPU, memory, and latency requirements. The max-pooling loss training can be further guided by initializing with a cross-entropy loss trained network. A posterior smoothing based evaluation approach is employed to measure keyword spotting performance. Our experimental results show that LSTM models trained using cross-entropy loss or max-pooling loss outperform a cross-entropy loss trained baseline feed-forward Deep Neural Network (DNN). In addition, max-pooling loss trained LSTM with randomly initialized network performs better compared to cross-entropy loss trained LSTM. Finally, the max-pooling loss trained LSTM initialized with a crossentropy pre-trained network shows the best performance, which yields 67.6% relative reduction compared to baseline feed-forward DNN in Area Under the Curve (AUC) measure.