In this note we give proofs for results relating to the Instrumental Variable
(IV) model with binary response $Y$ and binary treatment $X$, but with an
instrument $Z$ that takes $K$ states that were originally stated in Richardson
& Robins (2014), "ACE Bounds; SEMS with Equilibrium Conditions,"
arXiv:1410.0470.

本文为结合二进制反应 $Y$、二进制处理 $X$ 和多状态仪器 $Z$ 的工具变量（IV）模型的结果提供了证明，这些结果最初在 Richardson 和 Robins 的文章 “ACE Bounds; SEMS with Equilibrium Conditions”，arXiv:1410.0470 中提出。

工具变量模型中的假设和界限

Assumptions and Bounds in the Instrumental Variable Model

Recent progress in deep learning for audio synthesis opens the way to models
that directly produce the waveform, shifting away from the traditional paradigm
of relying on vocoders or MIDI synthesizers for speech or music generation.
Despite their successes, current state-of-the-art neural audio synthesizers
such as WaveNet and SampleRNN suffer from prohibitive training and inference
times because they are based on autoregressive models that generate audio
samples one at a time at a rate of 16kHz. In this work, we study the more
computationally efficient alternative of generating the waveform frame-by-frame
with large strides. We present SING, a lightweight neural audio synthesizer for
the original task of generating musical notes given desired instrument, pitch
and velocity. Our model is trained end-to-end to generate notes from nearly
1000 instruments with a single decoder, thanks to a new loss function that
minimizes the distances between the log spectrograms of the generated and
target waveforms. On the generalization task of synthesizing notes for pairs of
pitch and instrument not seen during training, SING produces audio with
significantly improved perceptual quality compared to a state-of-the-art
autoencoder based on WaveNet as measured by a Mean Opinion Score (MOS), and is
about 32 times faster for training and 2, 500 times faster for inference.

本研究提出了一种基于深度学习的轻量级神经音频合成器 SING，其可以通过单一解码器从近 1000 种乐器中生成音符，并且通过新的损失函数将生成的和目标波形的对数谱距离最小化，提高了音质的感知品质。与基于 WaveNet 的最新自动编码器相比，在训练和推理方面分别快 32 倍和快 2500 倍。