In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
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Question: Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Rate-optimal procedures such as Tukey's median and other estimators based on statistical depth functions are impractical because of their computational intractability. In this paper, we establish an intriguing connection between f-GANs and various depth functions through the lens of f-Learning. Similar to the derivation of f-GAN, we show that these depth functions that lead to rate-optimal robust estimators can all be viewed as variational lower bounds of the total variation distance in the framework of f-Learning. This connection opens the door of computing robust estimators using tools developed for training GANs. In particular, we show that a JS-GAN that uses a neural network discriminator with at least one hidden layer is able to achieve the minimax rate of robust mean estimation under Huber's $\epsilon$-contamination model. Interestingly, the hidden layers of the neural net structure in the discriminator class are shown to be necessary for robust estimation.

Answer: GANs are shown to provide us a new effective robust mean estimate against agnostic contaminations with both statistical optimality and practical tractability.

Question: Capturing high-level structure in audio waveforms is challenging because a single second of audio spans tens of thousands of timesteps. While long-range dependencies are difficult to model directly in the time domain, we show that they can be more tractably modelled in two-dimensional time-frequency representations such as spectrograms. By leveraging this representational advantage, in conjunction with a highly expressive probabilistic model and a multiscale generation procedure, we design a model capable of generating high-fidelity audio samples which capture structure at timescales which time-domain models have yet to achieve. We demonstrate that our model captures longer-range dependencies than time-domain models such as WaveNet across a diverse set of unconditional generation tasks, including single-speaker speech generation, multi-speaker speech generation, and music generation.

Answer: We introduce an autoregressive generative model for spectrograms and demonstrate applications to speech and music generation

Question: Deep neural networks have achieved impressive performance in handling complicated semantics in natural language, while mostly treated as black boxes. To explain how the model handles compositional semantics of words and phrases, we study the hierarchical explanation problem. We highlight the key challenge is to compute non-additive and context-independent importance for individual words and phrases. We show some prior efforts on hierarchical explanations, e.g. contextual decomposition, do not satisfy the desired properties mathematically, leading to inconsistent explanation quality in different models. In this paper, we propose a formal way to quantify the importance of each word or phrase to generate hierarchical explanations. We modify contextual decomposition algorithms according to our formulation, and propose a model-agnostic explanation algorithm with competitive performance. Human evaluation and automatic metrics evaluation on both LSTM models and fine-tuned BERT Transformer models on multiple datasets show that our algorithms robustly outperform prior works on hierarchical explanations. We show our algorithms help explain compositionality of semantics, extract classification rules, and improve human trust of models.

Answer:
We propose measurement of phrase importance and algorithms for hierarchical explanation of neural sequence model predictions