Importance sampling is widely used in machine learning and statistics, but
its power is limited by the restriction of using simple proposals for which the
importance weights can be tractably calculated. We address this problem by
studying black-box importance sampling methods that calculate importance
weights for samples generated from any unknown proposal or black-box mechanism.
Our method allows us to use better and richer proposals to solve difficult
problems, and (somewhat counter-intuitively) also has the additional benefit of
improving the estimation accuracy beyond typical importance sampling. Both
theoretical and empirical analyses are provided.

本文研究黑盒重要性抽样方法，可计算从任何未知提议或黑盒机制生成的样本的重要性权重，允许我们使用更好更丰富的提议来解决困难问题，并提高了估计精度。

黑盒重要性采样

Black-box Importance Sampling

It is commonly believed that increasing the interpretability of a machine
learning model may decrease its predictive power. However, inspecting
input-output relationships of those models using visual analytics, while
treating them as black-box, can help to understand the reasoning behind
outcomes without sacrificing predictive quality. We identify a space of
possible solutions and provide two examples of where such techniques have been
successfully used in practice.

通过视觉分析技术，我们可以在不牺牲预测质量的情况下理解黑盒机器学习模型的推理过程，从而提高模型的可解释性。

运用视觉分析解释预测机器学习模型

Using Visual Analytics to Interpret Predictive Machine Learning Models

We present general methods for simulating black-box Hamiltonians using
quantum walks. These techniques have two main applications: simulating sparse
Hamiltonians and implementing black-box unitary operations. In particular, we
give the best known simulation of sparse Hamiltonians with constant precision.
Our method has complexity linear in both the sparseness D (the maximum number
of nonzero elements in a column) and the evolution time t, whereas previous
methods had complexity scaling as D^4 and were superlinear in t. We also
consider the task of implementing an arbitrary unitary operation given a
black-box description of its matrix elements. Whereas standard methods for
performing an explicitly specified N x N unitary operation use O(N^2)
elementary gates, we show that a black-box unitary can be performed with
bounded error using O(N^{2/3} (log log N)^{4/3}) queries to its matrix
elements. In fact, except for pathological cases, it appears that most
unitaries can be performed with only O(sqrt{N}) queries, which is optimal.

本文提出了用量子行走模拟黑箱哈密顿量的一般方法。这些技术具有两个主要应用：模拟稀疏哈密顿量和实现黑箱酉操作。我们给出了稀疏 Hamiltonians 常数精度下最好的已知模拟方法，复杂度线性地随着稀疏矩阵的最大非零元素数 D 和演化时间 t 增长，并且我们还研究了给定黑箱描述矩阵元素的任意酉操作实现的任务。