You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Deep Neural Networks have achieved huge success at a wide spectrum of applications from language modeling, computer vision to speech recognition. However, nowadays, good performance alone is not enough to satisfy the needs of practical deployment where interpretability is demanded for cases involving ethics and mission critical applications. The complex models of Deep Neural Networks make it hard to understand and reason the predictions, which hinders its further progress. To tackle this problem, we apply the Knowledge Distillation technique to distill Deep Neural Networks into decision trees in order to attain good performance and interpretability simultaneously. We formulate the problem at hand as a multi-output regression problem and the experiments demonstrate that the student model achieves significantly better accuracy performance (about 1 to 5 ) than vanilla decision trees at the same level of tree depth. The experiments are implemented on the TensorFlow platform to make it scalable to big datasets. To the best of our knowledge, we are the first to distill Deep Neural Networks into vanilla decision trees on multi-class datasets.

Cited Abstract(s):
[1]: Black-box risk scoring models permeate our lives, yet are typically proprietary or opaque. We propose a transparent model distillation approach to audit such models. Model distillation was first introduced to transfer knowledge from a large, complex teacher model to a faster, simpler student model without significant loss in prediction accuracy. To this we add a third criterion - transparency. To gain insight into black-box models, we treat them as teachers, training transparent student models to mimic the risk scores assigned by the teacher. Moreover, we use side information in the form of the actual outcomes the teacher scoring model was intended to predict in the first place. By training a second transparent model on the outcomes, we can compare the two models to each other. When comparing models trained on risk scores to models trained on outcomes, we show that it is necessary to calibrate the risk-scoring model's predictions to remove distortion that may have been added to the black-box risk-scoring model during or after its training process. We also show how to compute confidence intervals for the particular class of transparent student models we use - tree-based additive models with pairwise interactions (GA2Ms) - to support comparison of the two transparent models. We demonstrate the methods on four public datasets: COMPAS, Lending Club, Stop-and-Frisk, and Chicago Police.

[2]: 

[3]: Gradient boosting constructs additive regression models by sequentially fitting a simple parameterized function (base learner) to current "pseudo'-residuals by least squares at each iteration. The pseudo-residuals are the gradient of the loss functional being minimized, with respect to the model values at each training data point evaluated at the current step. It is shown that both the approximation accuracy and execution speed of gradient boosting can be substantially improved by incorporating randomization into the procedure. Specifically, at each iteration a subsample of the training data is drawn at random (without replacement) from the full training data set. This randomly selected subsample is then used in place of the full sample to fit the base learner and compute the model update for the current iteration. This randomized approach also increases robustness against overcapacity of the base learner.

[4]: Function estimation approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest-descent minimization. A general gradient descent boosting paradigm is developed for additive expansions based on any fitting criterion. Specific algorithms are presented for least-squares, least absolute deviation, and Huber-M loss functions for regression, and multiclass logistic likelihood for classification. Special enhancements are derived for the particular case where the individual additive components are regression trees, and tools for interpreting such TreeBoost models are presented. Gradient boosting of regression trees produces competitive, highly robust, interpretable procedures for both regression and classification, especially appropriate for mining less than clean data. Connections between this approach and the boosting methods of Freund and Shapire and Friedman, Hastie and Tibshirani are discussed.

[5]: Exponential growth in Electronic Healthcare Records (EHR) has resulted in new opportunities and urgent needs for discovery of meaningful data-driven representations and patterns of diseases in Computational Phenotyping research. Deep Learning models have shown superior performance for robust prediction in computational phenotyping tasks, but suffer from the issue of model interpretability which is crucial for clinicians involved in decision-making. In this paper, we introduce a novel knowledge-distillation approach called Interpretable Mimic Learning, to learn interpretable phenotype features for making robust prediction while mimicking the performance of deep learning models. Our framework uses Gradient Boosting Trees to learn interpretable features from deep learning models such as Stacked Denoising Autoencoder and Long Short-Term Memory. Exhaustive experiments on a real-world clinical time-series dataset show that our method obtains similar or better performance than the deep learning models, and it provides interpretable phenotypes for clinical decision making.
In the health care domain, two pipelines [5] [2] are proposed to distill the knowledge from a DNN to Gradient Boosting Trees (GBTs) [4] [3] . One of them extracts the logits from a learned DNN and uses the logits and the true labels of the original training data to train a logistic regression algorithm to obtain the soft prediction scores. The next step is to train GBTs with the original training data's features and the soft predictions. The second pipeline directly applies the soft prediction scores of the trained DNN on the original training data as targets for training a mimic model with GBTs. However, GBTs lack transparency as they rely on post-hoc determinations: partial dependence [4] , which would result in bias in this process [1] . The differences between their approach and ours are apparent. The strategy we applied when training the mimic model is matching logits, not the soft targets. Also, our student model is decision tree.