This work is concerned with the following fundamental question in scientific
machine learning: Can deep-learning-based methods solve noise-free inverse
problems to near-perfect accuracy? Positive evidence is provided for the first
time, focusing on a prototypical computed tomography (CT) setup. We demonstrate
that an iterative end-to-end network scheme enables reconstructions close to
numerical precision, comparable to classical compressed sensing strategies. Our
results build on our winning submission to the recent AAPM DL-Sparse-View CT
Challenge. Its goal was to identify the state-of-the-art in solving the
sparse-view CT inverse problem with data-driven techniques. A specific
difficulty of the challenge setup was that the precise forward model remained
unknown to the participants. Therefore, a key feature of our approach was to
initially estimate the unknown fanbeam geometry in a data-driven calibration
step. Apart from an in-depth analysis of our methodology, we also demonstrate
its state-of-the-art performance on the open-access real-world dataset LoDoPaB
CT.

本文旨在探讨科学机器学习中的一个基本问题，即基于深度学习的方法是否能够将无噪声的反问题精确解决。作者通过提供证据证明了这一问题。本文着重研究了一个典型的计算机断层扫描（CT）问题，并且通过迭代的端到端网络方案以及数据驱动的校准步骤，展示了该方案能够使 CT 重建达到数值精度，与基于压缩感知策略的方法相当。作者同时也在本文中展示了方法的优越表现。

通过深度学习实现对于层析成像逆问题的几乎精确恢复

Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning

We study the out-of-sample properties of robust empirical optimization
problems with smooth $\phi$-divergence penalties and smooth concave objective
functions, and develop a theory for data-driven calibration of the non-negative
"robustness parameter" $\delta$ that controls the size of the deviations from
the nominal model. Building on the intuition that robust optimization reduces
the sensitivity of the expected reward to errors in the model by controlling
the spread of the reward distribution, we show that the first-order benefit of
``little bit of robustness" (i.e., $\delta$ small, positive) is a significant
reduction in the variance of the out-of-sample reward while the corresponding
impact on the mean is almost an order of magnitude smaller. One implication is
that substantial variance (sensitivity) reduction is possible at little cost if
the robustness parameter is properly calibrated. To this end, we introduce the
notion of a robust mean-variance frontier to select the robustness parameter
and show that it can be approximated using resampling methods like the
bootstrap. Our examples show that robust solutions resulting from "open loop"
calibration methods (e.g., selecting a $90\%$ confidence level regardless of
the data and objective function) can be very conservative out-of-sample, while
those corresponding to the robustness parameter that optimizes an estimate of
the out-of-sample expected reward (e.g., via the bootstrap) with no regard for
the variance are often insufficiently robust.

研究了平滑的 phi - 散度惩罚和平滑的凸目标函数的鲁棒经验优化问题的样本外性质，并开发了一种理论来数据驱动地校准非负 “鲁棒性参数”，以控制偏离名义模型的大小。

分布鲁棒经验优化模型的校准

Calibration of Distributionally Robust Empirical Optimization Models

The aim of this paper is to provide a new method for the detection of either
favored or avoided distances between genomic events along DNA sequences. These
events are modeled by a Hawkes process. The biological problem is actually
complex enough to need a nonasymptotic penalized model selection approach. We
provide a theoretical penalty that satisfies an oracle inequality even for
quite complex families of models. The consecutive theoretical estimator is
shown to be adaptive minimax for H\"{o}lderian functions with regularity in
$(1/2,1]$: those aspects have not yet been studied for the Hawkes' process.
Moreover, we introduce an efficient strategy, named Islands, which is not
classically used in model selection, but that happens to be particularly
relevant to the biological question we want to answer. Since a multiplicative
constant in the theoretical penalty is not computable in practice, we provide
extensive simulations to find a data-driven calibration of this constant. The
results obtained on real genomic data are coherent with biological knowledge
and eventually refine them.

本文提供了一种新的方法，可以使用 Hawkes 过程检测 DNA 序列中基因组事件之间的首选或避免距离，使用非渐近惩罚模型选择方法，该模型选择能够适应 Hawkes' 过程的 Hölderian 函数，并且引入了一种有效的名为 Islands 的策略，用于数据驱动的惩罚校准，实验证明结果与生物学知识一致并完善了结果。