6,961 research outputs found
Nonparametric Estimation of Multi-View Latent Variable Models
Spectral methods have greatly advanced the estimation of latent variable
models, generating a sequence of novel and efficient algorithms with strong
theoretical guarantees. However, current spectral algorithms are largely
restricted to mixtures of discrete or Gaussian distributions. In this paper, we
propose a kernel method for learning multi-view latent variable models,
allowing each mixture component to be nonparametric. The key idea of the method
is to embed the joint distribution of a multi-view latent variable into a
reproducing kernel Hilbert space, and then the latent parameters are recovered
using a robust tensor power method. We establish that the sample complexity for
the proposed method is quadratic in the number of latent components and is a
low order polynomial in the other relevant parameters. Thus, our non-parametric
tensor approach to learning latent variable models enjoys good sample and
computational efficiencies. Moreover, the non-parametric tensor power method
compares favorably to EM algorithm and other existing spectral algorithms in
our experiments
Kinetic Ballooning Mode Under Steep Gradient: High Order Eigenstates and Mode Structure Parity Transition
The existence of kinetic ballooning mode (KBM) high order (non-ground)
eigenstates for tokamak plasmas with steep gradient is demonstrated via
gyrokinetic electromagnetic eigenvalue solutions, which reveals that eigenmode
parity transition is an intrinsic property of electromagnetic plasmas. The
eigenstates with quantum number for ground state and for
non-ground states are found to coexist and the most unstable one can be the
high order states (). The conventional KBM is the state. It is
shown that the KBM has the same mode structure parity as the
micro-tearing mode (MTM). In contrast to the MTM, the KBM can be driven
by pressure gradient even without collisions and electron temperature gradient.
The relevance between various eigenstates of KBM under steep gradient and edge
plasma physics is discussed.Comment: 6 pages, 6 figure
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