1,171 research outputs found
The supervised hierarchical Dirichlet process
We propose the supervised hierarchical Dirichlet process (sHDP), a
nonparametric generative model for the joint distribution of a group of
observations and a response variable directly associated with that whole group.
We compare the sHDP with another leading method for regression on grouped data,
the supervised latent Dirichlet allocation (sLDA) model. We evaluate our method
on two real-world classification problems and two real-world regression
problems. Bayesian nonparametric regression models based on the Dirichlet
process, such as the Dirichlet process-generalised linear models (DP-GLM) have
previously been explored; these models allow flexibility in modelling nonlinear
relationships. However, until now, Hierarchical Dirichlet Process (HDP)
mixtures have not seen significant use in supervised problems with grouped data
since a straightforward application of the HDP on the grouped data results in
learnt clusters that are not predictive of the responses. The sHDP solves this
problem by allowing for clusters to be learnt jointly from the group structure
and from the label assigned to each group.Comment: 14 page
Magnetic Bulk Photovoltaic Effect: Strong and Weak Field
Shift current and ballistic current have been proposed to explain the bulk
photovoltaic effect (BPVE), and there have been experiments designed to
separate the two mechanisms. These experiments are based on the assumption that
under magnetic field, ballistic current can have a Hall effect while the shift
current cannot, which is from some energy-scale arguments and has never been
proven. A recent work [Phys. Rev. B 103, 195203 (2021)] using quantum transport
formalism achieves a conclusion that shift current indeed has a Hall current,
seemingly contradicting the previous assumption and making the situation more
confusing. Moreover, the behavior of BPVE under strong magnetic field is still
unexplored. In this Letter, using a minimal 2D tight-binding model, we carry
out a systematic numerical study of the BPVE under weak and strong magnetic
field by treating the field in a non-perturbative way. Our model clearly shows
the appearance of the magnetically-induced ballistic current along the
transverse direction, which agrees with the previous predictions, and
interestingly a sizable longitudinal response of the shift current is also
observed, a phenomenon that is not captured by any existing theories where the
magnetic field is treated perturbatively. More surprisingly, drastically
different shift current is found in the strong-field regime, and the evolution
from weak to strong field resembles a phase transition. We hope that our work
could resolve the debate over the behavior of BPVE under magnetic field, and
the strong-field behavior of shift current is expected to inspire more studies
on the relation between nonlinear optics and quantum geometry
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