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Abstract / Description of output
Solving an illposed linear inverse problem requires knowledge about the underlying signal model. In many applications, this model is a priori unknown and has to be learned from data. However, it is impossible to learn the model using observations obtained via a single incomplete measurement operator, as there is no information about the signal model in the nullspace of the operator, resulting in a chickenandegg problem: to learn the model we need reconstructed signals, but to reconstruct the signals we need to know the model. Two ways to overcome this limitation are using multiple measurement operators or assuming that the signal model is invariant to a certain group action. In this paper, we present necessary and sufficient sensing conditions for learning the signal model from measurement data alone which only depend on the dimension of the model and the number of operators or properties of the group action that the model is invariant to. As our results are agnostic of the learning algorithm, they shed light into the fundamental limitations of learning from incomplete data and have implications in a wide range set of practical algorithms, such as
dictionary learning, matrix completion and deep neural networks.
dictionary learning, matrix completion and deep neural networks.
Original language  English 

Number of pages  45 
Journal  Journal of Machine Learning Research 
Volume  24 
Early online date  23 Jan 2023 
Publication status  Epub ahead of print  23 Jan 2023 
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Dive into the research topics of 'Sensing Theorems for Unsupervised Learning in Linear Inverse Problems'. Together they form a unique fingerprint.Projects
 1 Finished

CSENSE: Exploiting low dimensional models in sensing, computation and signal processing
1/09/16 → 31/08/22
Project: Research