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

Who Said What: Modeling Individual Labelers Improves Classification

Data are often labeled by many different experts with each expert only labeling a small fraction of the data and each data point being labeled by several experts. This reduces the workload on individual experts and also gives a better estimate of the unobserved ground truth. When experts disagree, the standard approaches are to treat the majority opinion as the correct label or to model the correct label as a distribution. These approaches, however, do not make any use of potentially valuable information about which expert produced which label. To make use of this extra information, we propose modeling the experts individually and then learning averaging weights for combining them, possibly in sample-specific ways. This allows us to give more weight to more reliable experts and take advantage of the unique strengths of individual experts at classifying certain types of data. Here we show that our approach leads to improvements in computer-aided diagnosis of diabetic retinopathy. We also show that our method performs better than competing algorithms by Welinder and Perona (2010), and by Mnih and Hinton (2012). Our work offers an innovative approach for dealing with the myriad real-world settings that use expert opinions to define labels for training.Comment: AAAI 201

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