Learning Mixtures of Plackett-Luce Models with Features from Top-ll Orders

Plackett-Luce model (PL) is one of the most popular models for preference learning. In this paper, we consider PL with features and its mixture models, where each alternative has a vector of features, possibly different across agents. Such models significantly generalize the standard PL, but are not as well investigated in the literature. We extend mixtures of PLs with features to models that generate top-$l$ and characterize their identifiability. We further prove that when PL with features is identifiable, its MLE is consistent with a strictly concave objective function under mild assumptions. Our experiments on synthetic data demonstrate the effectiveness of MLE on PL with features with tradeoffs between statistical efficiency and computational efficiency when $l$ takes different values. For mixtures of PL with features, we show that an EM algorithm outperforms MLE in MSE and runtime.Comment: 16 pages, 2 figure

Three-dimensional super-resolution correlation-differential confocal microscopy with nanometer axial focusing accuracy

We present a correlation-differential confocal microscopy (CDCM), a novel method that can simultaneously improve the three-dimensional spatial resolution and axial focusing accuracy of confocal microscopy (CM). CDCM divides the CM imaging light path into two paths, where the detectors are before and after the focus with an equal axial offset in opposite directions. Then, the light intensity signals received from the two paths are processed by the correlation product and differential subtraction to improve the CM spatial resolution and axial focusing accuracy, respectively. Theoretical analyses and preliminary experiments indicate that, for the excitation wavelength of λ = 405 nm, numerical aperture of NA = 0.95, and the normalized axial offset of uM = 5.21, the CDCM resolution is improved by more than 20% and more than 30% in the lateral and axial directions, respectively, compared with that of the CM. Also, the axial focusing resolution important for the imaging of sample surface profiles is improved to 1 nm

Improving spatial resolution of confocal Raman microscopy by super-resolution image restoration

A new super-resolution image restoration confocal Raman microscopy method (SRIR-RAMAN) is proposed for improving the spatial resolution of confocal Raman microscopy. This method can recover the lost high spatial frequency of the confocal Raman microscopy by using Poisson-MAP super-resolution imaging restoration, thereby improving the spatial resolution of confocal Raman microscopy and realizing its super-resolution imaging. Simulation analyses and experimental results indicate that the spatial resolution of SRIR-RAMAN can be improved by 65% to achieve 200 nm with the same confocal Raman microscopy system. This method can provide a new tool for high spatial resolution micro-probe structure detection in physical chemistry, materials science, biomedical science and other areas

Confocal Raman image method with maximum likelihood method

With the increasing interest in nano microscopic area, such as DNA sequencing, micro structure detection of molecular nano devices, a higher requirement for the spatial resolution of Raman spectroscopy is demanded. However, because of the weak Raman signal, the pinhole size of confocal Raman microscopy is usually a few hundreds microns to ensure a relatively higher spectrum throughput, but the large pinhole size limits the improvements of spatial resolution of confoal Raman spectroscopy. As a result, the convential confocal Raman spectroscopy has been unable to meet the needs of science development. Therefore, a confocal Raman image method with Maximum Likelihood image restoration algorithm based on the convential confocal Raman microscope is propose. This method combines super-resolution image restoration technology and confocal Raman microscopy to realize super-resolution imaging, by using Maximum Likelihood image restoration algorithm based on Poisson-Markov model to conduct image restoration processing on the Raman image, and the high frequency information of the image is recovered, and then the spatial resolution of Raman image is improved and the super-resolution image is realized. Simulation analyses and experimental results indicate that the proposed confocal Raman image method with Maximum Likelihood image restoration algorithm can improve the spatial resolution to 200 nm without losing any Raman spectral signal under the same condition with convential confocal Raman microscopy, moreover it has strong noise suppression capability. In conclusion, the method can provide a new approach for material science, life sciences, biomedicine and other frontiers areas. This method is an effective confocal Raman image method with high spatial resolution