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Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) methods have been widely used to sample from certain probability distributions, incorporating (kernel) density derivatives and/or given datasets. Instead of exploring new samples from kernel spaces, this piece of work proposed a novel SGHMC sampler, namely Spectral Hamiltonian Monte Carlo (SpHMC), that produces the high dimensional sparse representations of given datasets through sparse sensing and SGHMC. Inspired by compressed sensing, we<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1609/aaai.v33i01.33015516">doi:10.1609/aaai.v33i01.33015516</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ztmooaau6rbyjjmdaamjypzbxy">fatcat:ztmooaau6rbyjjmdaamjypzbxy</a> </span>
more »... me all given samples are low-dimensional measurements of certain high-dimensional sparse vectors, while a continuous probability distribution exists in such high-dimensional space. Specifically, given a dictionary for sparse coding, SpHMC first derives a novel likelihood evaluator of the probability distribution from the loss function of LASSO, then samples from the high-dimensional distribution using stochastic Langevin dynamics with derivatives of the logarithm likelihood and Metropolis–Hastings sampling. In addition, new samples in low-dimensional measuring spaces can be regenerated using the sampled high-dimensional vectors and the dictionary. Extensive experiments have been conducted to evaluate the proposed algorithm using real-world datasets. The performance comparisons on three real-world applications demonstrate the superior performance of SpHMC beyond baseline methods.
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