Lukáš Samuel Marták

Lukáš Samuel Marták, Rainer Kelz, Gerhard Widmer

We introduce a novel way to incorporate prior information into (semi-) supervised non-negative matrix factorization, which we call differentiable dictionary search. It enables general, highly flexible and principled modelling of mixtures where non-linear sources are linearly mixed. We study its behavior on an audio decomposition task, and conduct an extensive, highly controlled study of its modelling capabilities.

Lukáš Samuel Marták, Rainer Kelz, Gerhard Widmer

This paper describes several improvements to a new method for signal decomposition that we recently formulated under the name of Differentiable Dictionary Search (DDS). The fundamental idea of DDS is to exploit a class of powerful deep invertible density estimators called normalizing flows, to model the dictionary in a linear decomposition method such as NMF, effectively creating a bijection between the space of dictionary elements and the associated probability space, allowing a differentiable search through the dictionary space, guided by the estimated densities. As the initial formulation was a proof of concept with some practical limitations, we will present several steps towards making it scalable, hoping to improve both the computational complexity of the method and its signal decomposition capabilities. As a testbed for experimental evaluation, we choose the task of frame-level piano transcription, where the signal is to be decomposed into sources whose activity is attributed to individual piano notes. To highlight the impact of improved non-linear modelling of sources, we compare variants of our method to a linear overcomplete NMF baseline. Experimental results will show that even in the absence of additional constraints, our models produce increasingly sparse and precise decompositions, according to two pertinent evaluation measures.

Martin Stano, Wanda Benesova, Lukas Samuel Martak

In many practical applications, deep neural networks have been typically deployed to operate as a black box predictor. Despite the high amount of work on interpretability and high demand on the reliability of these systems, they typically still have to include a human actor in the loop, to validate the decisions and handle unpredictable failures and unexpected corner cases. This is true in particular for failure-critical application domains, such as medical diagnosis. We present a novel approach to explain and support an interpretation of the decision-making process to a human expert operating a deep learning system based on Convolutional Neural Network (CNN). By modeling activation statistics on selected layers of a trained CNN via Gaussian Mixture Models (GMM), we develop a novel perceptual code in binary vector space that describes how the input sample is processed by the CNN. By measuring distances between pairs of samples in this perceptual encoding space, for any new input sample, we can now retrieve a set of most perceptually similar and dissimilar samples from an existing atlas of labeled samples, to support and clarify the decision made by the CNN model. Possible uses of this approach include for example Computer-Aided Diagnosis (CAD) systems working with medical imaging data, such as Magnetic Resonance Imaging (MRI) or Computed Tomography (CT) scans. We demonstrate the viability of our method in the domain of medical imaging for patient condition diagnosis, as the proposed decision explanation method via similar ground truth domain examples (e.g. from existing diagnosis archives) will be interpretable by the operating medical personnel. Our results indicate that our method is capable of detecting distinct prediction strategies that enable us to identify the most similar predictions from an existing atlas.