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Register a new userData-driven Estimation of Sinusoid Frequencies
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Frequency estimation is a fundamental problem in signal processing, with applications in radar imaging, underwater acoustics, seismic imaging, and spectroscopy. The goal is to estimate the frequency of each component in a multisinusoidal signal from a finite number of noisy samples. A recent machine-learning approach uses a neural network to output a learned representation with local maxima at the position of the frequency estimates. In this work, we propose a novel neural-network architecture that produces a significantly more accurate representation, and combine it with an additional neural-network module trained to detect the number of frequencies. This yields a fast, fully-automatic method for frequency estimation that achieves state-of-the-art results. In particular, it outperforms existing techniques by a substantial margin at medium-to-high noise levels.
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We study the relationship between the frequency of a function and the speed at which a neural network learns it. We build on recent results that show that the dynamics of overparameterized neural networks trained with gradient descent can be well approximated by a linear system. When normalized training data is uniformly distributed on a hypersphere, the eigenfunctions of this linear system are spherical harmonic functions. We derive the corresponding eigenvalues for each frequency after introducing a bias term in the model. This bias term had been omitted from the linear network model without significantly affecting previous theoretical results. However, we show theoretically and experimentally that a shallow neural network without bias cannot represent or learn simple, low frequency functions with odd frequencies. Our results lead to specific predictions of the time it will take a network to learn functions of varying frequency. These predictions match the empirical behavior of both shallow and deep networks.
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Assessment of mental workload in real world conditions is key to ensure the performance of workers executing tasks which demand sustained attention. Previous literature has employed electroencephalography (EEG) to this end. However, EEG correlates of mental workload vary across subjects and physical strain, thus making it difficult to devise models capable of simultaneously presenting reliable performance across users. The field of domain adaptation (DA) aims at developing methods that allow for generalization across different domains by learning domain-invariant representations. Such DA methods, however, rely on the so-called covariate shift assumption, which typically does not hold for EEG-based applications. As such, in this paper we propose a way to measure the statistical (marginal and conditional) shift observed on data obtained from different users and use this measure to quantitatively assess the effectiveness of different adaptation strategies. In particular, we use EEG data collected from individuals performing a mental task while running in a treadmill and explore the effects of different normalization strategies commonly used to mitigate cross-subject variability. We show the effects that different normalization schemes have on statistical shifts and their relationship with the accuracy of mental workload prediction as assessed on unseen participants at train time.
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