Preeti
The content discusses non-convex optimizations for machine learning with theoretical guarantees, focusing on robust matrix completion and neural network learning. The challenge lies in the non-linearity of real data, leading to non-convex loss functions that trap gradient descent algorithms in spurious local minima. This makes it difficult to develop explainable algorithms for non-convex optimization problems.
In the first study, graph-based matrix completion is applied to weather data, where low-rank matrix completion is used to recover unknown entries of a matrix by incorporating additional information in the form of weighted graphs. This approach significantly improves completion accuracy in air temperature data recorded by weather stations.
The second study explores fermionic reduced density low-rank matrix completion for quantum simulations, focusing on reconstructing the two-particle reduced density matrix from partial information. The experiments show that the 2-RDM can be efficiently reconstructed even with reduced information, leading to a significant reduction in the number of measurements needed for accurate results. These techniques have applications in both classical and quantum algorithms for quantum simulations.
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Source link: https://medium.com/@monocosmo77/research-on-matrix-completion-part3-machine-learning-core-3ce926fed447?source=rss——artificial_intelligence-5
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