A Bayesian approach to parameter estimation for kernel density estimation via transformations

In this paper, we present a Markov chain Monte Carlo (MCMC) simulation algorithm for estimating parameters in the kernel density estimation of bivariate insurance claim data via transformations. Our data set consists of two types of auto insurance claim costs and exhibit a high-level of skewness in the marginal empirical distributions. Therefore, the kernel density estimator based on original data does not perform well. However, the density of the original data can be estimated through estimating the density of the transformed data using kernels. It is well known that the performance of a kernel density estimator is mainly determined by the bandwidth, and only in a minor way by the kernel choice. In the current literature, there have been some developments in the area of estimating densities based on transformed data, but bandwidth selection depends on pre-determined transformation parameters. Moreover, in the bivariate situation, each dimension is considered separately and the correlation between the two dimensions is largely ignored. We extend the Bayesian sampling algorithm proposed by Zhang, King and Hyndman (2006) and present a Metropolis-Hastings sampling procedure to sample the bandwidth and transformation parameters from their posterior density. Our contribution is to estimate the bandwidths and transformation parameters within a Metropolis-Hastings sampling procedure. Moreover, we demonstrate that the correlation between the two dimensions is well captured through the bivariate density estimator based on transformed data.Bandwidth parameter; kernel density estimator; Markov chain Monte Carlo; Metropolis-Hastings algorithm; power transformation; transformation parameter.

Necessary and sufficient conditions for local creation of quantum correlation

Quantum correlation can be created by a local operation from some initially classical states. We prove that the necessary and sufficient condition for a local trace-preserving channel to create quantum correlation is that it is not a commutativity-preserving channel. This condition is valid for arbitrary finite dimension systems. We also derive the explicit form of commutativity-preserving channels. For a qubit, a commutativity-preserving channel is either a completely decohering channel or a mixing channel. For a three-dimensional system (qutrit), a commutativity-preserving channel is either a completely decohering channel or an isotropic channel.Comment: Theorem 2 has been modifie

Electromagnetic Response Design With Plasmonic Metamaterials

Thesis advisor: Krzysztof KempaPlasmons are quantized quasiparticles of the electron density waves. When coupled with photons, plasmons become another type of quasiparticles called plasmon polaritons. At the surface of a metal, surface plasmons can be formed. They have confined propagation on the surface, analogous to water waves in a pool. Plasmonic metamaterials manipulate the surface plasmon resonances, achieving a variety of unseen optical properties in nature. For the sake of fast emerging of nano fabrication and characterization techniques in recent years, plasmonic metamaterials have been applied in a wide range of fields, such as broadband absorption in solar cells, negative index materials for cloaking, subwavelength imaging, and wave modulations. One unique property of plasmonic metamaterial is offering remarkable flexibility in controlling effective dielectric properties of matter, depending on the composite design. In this thesis, several concepts of EM response manipulation using plasmonic metamaterials are proposed and studied. These studies include: (1) a scheme assuring topologically protected photonic edge states in the visible range utilizing epsilon-near-zero (ENZ) gyroelectric metamaterials; (2) engineering low frequency dielectric function with extremely subwavelength magnetic resonators; and (3) tailoring the electron-phonon interactions (including controlling superconductivity) by introducing plasmonic resonators into the phonon systems. These works may enable a broad range of applications in both photonic and phonon systems.Thesis (PhD) — Boston College, 2018.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Physics

SEGA: Structural Entropy Guided Anchor View for Graph Contrastive Learning

In contrastive learning, the choice of ``view'' controls the information that the representation captures and influences the performance of the model. However, leading graph contrastive learning methods generally produce views via random corruption or learning, which could lead to the loss of essential information and alteration of semantic information. An anchor view that maintains the essential information of input graphs for contrastive learning has been hardly investigated. In this paper, based on the theory of graph information bottleneck, we deduce the definition of this anchor view; put differently, \textit{the anchor view with essential information of input graph is supposed to have the minimal structural uncertainty}. Furthermore, guided by structural entropy, we implement the anchor view, termed \textbf{SEGA}, for graph contrastive learning. We extensively validate the proposed anchor view on various benchmarks regarding graph classification under unsupervised, semi-supervised, and transfer learning and achieve significant performance boosts compared to the state-of-the-art methods.Comment: ICML'2

Exploiting Audio-Visual Features with Pretrained AV-HuBERT for Multi-Modal Dysarthric Speech Reconstruction

Dysarthric speech reconstruction (DSR) aims to transform dysarthric speech into normal speech by improving the intelligibility and naturalness. This is a challenging task especially for patients with severe dysarthria and speaking in complex, noisy acoustic environments. To address these challenges, we propose a novel multi-modal framework to utilize visual information, e.g., lip movements, in DSR as extra clues for reconstructing the highly abnormal pronunciations. The multi-modal framework consists of: (i) a multi-modal encoder to extract robust phoneme embeddings from dysarthric speech with auxiliary visual features; (ii) a variance adaptor to infer the normal phoneme duration and pitch contour from the extracted phoneme embeddings; (iii) a speaker encoder to encode the speaker's voice characteristics; and (iv) a mel-decoder to generate the reconstructed mel-spectrogram based on the extracted phoneme embeddings, prosodic features and speaker embeddings. Both objective and subjective evaluations conducted on the commonly used UASpeech corpus show that our proposed approach can achieve significant improvements over baseline systems in terms of speech intelligibility and naturalness, especially for the speakers with more severe symptoms. Compared with original dysarthric speech, the reconstructed speech achieves 42.1\% absolute word error rate reduction for patients with more severe dysarthria levels.Comment: Accepted by ICASSP 202