Subsampling is commonly used to mitigate costs associated with data
acquisition, such as time or energy requirements, motivating the development of
algorithms for estimating the fully-sampled signal of interest $x$ from
partially observed measurements $y$. In maximum-entropy sampling, one selects
measurement locations that are expected to have the highest entropy, so as to
minimize uncertainty about $x$. This approach relies on an accurate model of
the posterior distribution over future measurements, given the measurements
observed so far. Recently, diffusion models have been shown to produce
high-quality posterior samples of high-dimensional signals using guided
diffusion. In this work, we propose Active Diffusion Subsampling (ADS), a
method for performing active subsampling using guided diffusion in which the
model tracks a distribution of beliefs over the true state of $x$ throughout
the reverse diffusion process, progressively decreasing its uncertainty by
choosing to acquire measurements with maximum expected entropy, and ultimately
generating the posterior distribution $p(x | y)$. ADS can be applied using
pre-trained diffusion models for any subsampling rate, and does not require
task-specific retraining - just the specification of a measurement model.
Furthermore, the maximum entropy sampling policy employed by ADS is
interpretable, enhancing transparency relative to existing methods using
black-box policies. Experimentally, we show that ADS outperforms fixed sampling
strategies, and study an application of ADS in Magnetic Resonance Imaging
acceleration using the fastMRI dataset, finding that ADS performs competitively
with supervised methods. Code available at
this https URL

在本文中，我们提出了一种名为 Active Diffusion Subsampling (ADS) 的方法，该方法使用引导扩散进行主动子采样，该模型通过选择具有最大期望熵的测量来逐步减小不确定性，并最终生成后验分布 p (x | y)。我们实验证明 ADS 优于固定采样策略，并在快速核磁共振成像的应用中研究了 ADS 的性能，发现 ADS 与监督方法具有竞争力。

主动扩散下采样

Active Diffusion Subsampling

We design new approximation algorithms for the problems of optimizing
submodular and supermodular functions subject to a single matroid constraint.
Specifically, we consider the case in which we wish to maximize a nondecreasing
submodular function or minimize a nonincreasing supermodular function in the
setting of bounded total curvature $c$. In the case of submodular maximization
with curvature $c$, we obtain a $(1-c/e)$-approximation --- the first
improvement over the greedy $(1-e^{-c})/c$-approximation of Conforti and
Cornuejols from 1984, which holds for a cardinality constraint, as well as
recent approaches that hold for an arbitrary matroid constraint.
Our approach is based on modifications of the continuous greedy algorithm and
non-oblivious local search, and allows us to approximately maximize the sum of
a nonnegative, nondecreasing submodular function and a (possibly negative)
linear function. We show how to reduce both submodular maximization and
supermodular minimization to this general problem when the objective function
has bounded total curvature. We prove that the approximation results we obtain
are the best possible in the value oracle model, even in the case of a
cardinality constraint.
We define an extension of the notion of curvature to general monotone set
functions and show $(1-c)$-approximation for maximization and
$1/(1-c)$-approximation for minimization cases. Finally, we give two concrete
applications of our results in the settings of maximum entropy sampling, and
the column-subset selection problem.

论文设计了一种新的逼近算法来解决在单一拟阵约束下优化子模和超模函数的问题，特别地，当目标函数有闭合总曲率时，获得了一个 (1-c/e)- 近似的结果；该算法基于连续贪心算法和非随机局部搜索的修改，并进行了扩展以包括在一些特定场景下的应用，例如最大熵抽样和列子集选择问题。