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Partial Trace Regression and Low-Rank Kraus Decomposition

Authors: Hachem Kadri, Stephane Ayache, Riikka Huusari, Alain Rakotomamonjy, Ralaivola Liva

ICML 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable	Result	LLM Response
Research Type	Experimental	We show the relevance of our framework with synthetic and real-world experiments conducted for both i) matrix-to-matrix regression and ii) positive semideﬁnite matrix completion, two tasks which can be formulated as partial trace regression problems.
Researcher Affiliation	Collaboration	1Aix-Marseille University, CNRS, LIS, Marseille, France 2Helsinki Institute for Information Technology HIIT, Department of Computer Science, Aalto University, Espoo, Finland 3Université Rouen Normandie, LITIS, Rouen, France 4Criteo AI Lab, Paris, France.
Pseudocode	No	The paper describes optimization methods and procedures in narrative text but does not include structured pseudocode or algorithm blocks.
Open Source Code	Yes	Our code is available at https://github.com/Stef-hub/ partial_trace_kraus.
Open Datasets	Yes	We consider the multiple features digits dataset, available online.3
Dataset Splits	No	The paper mentions training data (e.g., "use the training examples (230 samples) for learning the covariance mapping") and testing data, but does not explicitly specify a validation dataset split.
Hardware Specification	No	The paper mentions leveraging "efﬁcient computational hardware, like GPUs" but does not provide specific details such as GPU models, CPU models, or memory specifications.
Software Dependencies	No	The paper states that the PTR model is implemented in "keras/Tensorﬂow framework" but does not provide specific version numbers for these software dependencies.
Experiment Setup	Yes	In all the experiments, the PTR model is implemented in a keras/Tensorﬂow framework and learned with Adam with default learning rate (0.001) and for 100 epochs. Batch size is typically 16.