A unified performance analysis of likelihood-informed subspace methods
نویسندگان
چکیده
The likelihood-informed subspace (LIS) method offers a viable route to reducing the dimensionality of high-dimensional probability distributions arising in Bayesian inference. LIS identifies an intrinsic low-dimensional linear where target distribution differs most from some tractable reference distribution. Such can be identified using leading eigenvectors Gram matrix gradient log-likelihood function. Then, original is approximated through various forms marginalization likelihood function, which only has support on subspace. This approximation enables design inference algorithms that scale sub-linearly with apparent problem. Intuitively, accuracy approximation, and hence performance algorithms, are influenced by three factors—the dimension truncation error identifying subspace, Monte Carlo estimating matrices, constructing marginalizations. work establishes unified framework analyze each these factors their interplay. Under mild technical assumptions, we establish bounds for range existing reduction techniques based principle LIS. Our also provide useful insights into methods. In addition, integration sampling methods such as Markov Chain (MCMC) sequential (SMC). We demonstrate applicability our analysis inverse problem Gaussian prior, shows all estimates dimension-independent if prior covariance trace-class operator. Finally, aspects theoretical claims two nonlinear problems.
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2022
ISSN: ['1573-9759', '1350-7265']
DOI: https://doi.org/10.3150/21-bej1437