41,921 research outputs found
Bayesian Robust Tensor Factorization for Incomplete Multiway Data
We propose a generative model for robust tensor factorization in the presence
of both missing data and outliers. The objective is to explicitly infer the
underlying low-CP-rank tensor capturing the global information and a sparse
tensor capturing the local information (also considered as outliers), thus
providing the robust predictive distribution over missing entries. The
low-CP-rank tensor is modeled by multilinear interactions between multiple
latent factors on which the column sparsity is enforced by a hierarchical
prior, while the sparse tensor is modeled by a hierarchical view of Student-
distribution that associates an individual hyperparameter with each element
independently. For model learning, we develop an efficient closed-form
variational inference under a fully Bayesian treatment, which can effectively
prevent the overfitting problem and scales linearly with data size. In contrast
to existing related works, our method can perform model selection automatically
and implicitly without need of tuning parameters. More specifically, it can
discover the groundtruth of CP rank and automatically adapt the sparsity
inducing priors to various types of outliers. In addition, the tradeoff between
the low-rank approximation and the sparse representation can be optimized in
the sense of maximum model evidence. The extensive experiments and comparisons
with many state-of-the-art algorithms on both synthetic and real-world datasets
demonstrate the superiorities of our method from several perspectives.Comment: in IEEE Transactions on Neural Networks and Learning Systems, 201
Experimentally exploring compressed sensing quantum tomography
In the light of the progress in quantum technologies, the task of verifying
the correct functioning of processes and obtaining accurate tomographic
information about quantum states becomes increasingly important. Compressed
sensing, a machinery derived from the theory of signal processing, has emerged
as a feasible tool to perform robust and significantly more resource-economical
quantum state tomography for intermediate-sized quantum systems. In this work,
we provide a comprehensive analysis of compressed sensing tomography in the
regime in which tomographically complete data is available with reliable
statistics from experimental observations of a multi-mode photonic
architecture. Due to the fact that the data is known with high statistical
significance, we are in a position to systematically explore the quality of
reconstruction depending on the number of employed measurement settings,
randomly selected from the complete set of data, and on different model
assumptions. We present and test a complete prescription to perform efficient
compressed sensing and are able to reliably use notions of model selection and
cross-validation to account for experimental imperfections and finite counting
statistics. Thus, we establish compressed sensing as an effective tool for
quantum state tomography, specifically suited for photonic systems.Comment: 12 pages, 5 figure
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