While the success of deep neural networks (DNNs) is well-established across a variety of domains, our ability to explain and interpret these methods is limited. Unlike previously proposed local methods which try to explain particular classification decisions, we focus on global interpretability and ask a universally applicable question: given a trained model, which features are the most important? In the context of neural networks, a feature is rarely important on its own, so our strategy is specifically designed to leverage partial covariance structures and incorporate variable dependence into feature ranking. Our methodological contributions in this paper are two-fold. First, we propose an effect size analogue for DNNs that is appropriate for applications with highly collinear predictors (ubiquitous in computer vision). Second, we extend the recently proposed "RelATive cEntrality" (RATE) measure (, 2019) to the Bayesian deep learning setting. RATE applies an information theoretic criterion to the posterior distribution of effect sizes to assess feature significance. We apply our framework to three broad application areas: computer vision, natural language processing, and social science.
One viable approach for achieving global interpretability is to train more conventional statistical methods to mimic the predictive behavior of a DNN. This imitation model is then retrospectively used to explain the predictions that a DNN would make. For example, using a decision tree @cite_18 or falling rule list @cite_24 can yield straightforward characterizations of predictive outcomes. Unfortunately, these simple models can struggle to mimic the accuracy of DNNs effectively. A random forest, on the other hand, is much more capable of matching the predictive power of neural networks. Here, measures of feature selection can be computed by permuting information within the input variables and examining this null effect on test accuracy or Gini impurity @cite_23 . The ability establish variable importance in random forests is a significant reason for their popularity in fields such as the life sciences @cite_28 --- thus, providing motivation for developing analogous approaches for DNNs.
@cite_24 @cite_18 @cite_28 @cite_23
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As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modeling uncertainty is one of the key features of Bayesian methods. Using Bernoulli dropout with sampling at prediction time has recently been proposed as an efficient and well performing variational inference method for DNNs. However, sampling from other multiplicative noise based variational distributions has not been investigated in depth. We evaluated Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We tested the calibration of the probabilistic predictions of Bayesian convolutional neural networks (CNNs) on MNIST and CIFAR-10. Sampling at prediction time increased the calibration of the DNNs' probabalistic predictions. Sampling weights, whether Gaussian or Bernoulli, led to more robust representation of uncertainty compared to sampling of units. However, using either Gaussian or Bernoulli dropout led to increased test set classification accuracy. Based on these findings we used both Bernoulli dropout and Gaussian dropconnect concurrently, which we show approximates the use of a spike-and-slab variational distribution without increasing the number of learned parameters. We found that spike-and-slab sampling had higher test set performance than Gaussian dropconnect and more robustly represented its uncertainty compared to Bernoulli dropout. Sometimes it is not enough for a DNN to produce an outcome. For example, in applications such as healthcare, users need to understand the rationale of the decisions. Therefore, it is imperative to develop algorithms to learn models with good interpretability (Doshi-Velez 2017). An important factor that leads to the lack of interpretability of DNNs is the ambiguity of neurons, where a neuron may fire for various unrelated concepts. This work aims to increase the interpretability of DNNs on the whole image space by reducing the ambiguity of neurons. In this paper, we make the following contributions: 1) We propose a metric to evaluate the consistency level of neurons in a network quantitatively. 2) We find that the learned features of neurons are ambiguous by leveraging adversarial examples. 3) We propose to improve the consistency of neurons on adversarial example subset by an adversarial training algorithm with a consistent loss. This paper proposes an effective segmentation-free approach using a hybrid neural network hidden Markov model (NN-HMM) for offline handwritten Chinese text recognition (HCTR). In the general Bayesian framework, the handwritten Chinese text line is sequentially modeled by HMMs with each representing one character class, while the NN-based classifier is adopted to calculate the posterior probability of all HMM states. The key issues in feature extraction, character modeling, and language modeling are comprehensively investigated to show the effectiveness of NN-HMM framework for offline HCTR. First, a conventional deep neural network (DNN) architecture is studied with a well-designed feature extractor. As for the training procedure, the label refinement using forced alignment and the sequence training can yield significant gains on top of the frame-level cross-entropy criterion. Second, a deep convolutional neural network (DCNN) with automatically learned discriminative features demonstrates its superiority to DNN in the HMM framework. Moreover, to solve the challenging problem of distinguishing quite confusing classes due to the large vocabulary of Chinese characters, NN-based classifier should output 19900 HMM states as the classification units via a high-resolution modeling within each character. On the ICDAR 2013 competition task of CASIA-HWDB database, DNN-HMM yields a promising character error rate (CER) of 5.24 by making a good trade-off between the computational complexity and recognition accuracy. To the best of our knowledge, DCNN-HMM can achieve a best published CER of 3.53 . As deep neural networks (DNNs) are applied to increasingly challenging problems, they will need to be able to represent their own uncertainty. Modelling uncertainty is one of the key features of Bayesian methods. Bayesian DNNs that use dropout-based variational distributions and scale to complex tasks have recently been proposed. We evaluate Bayesian DNNs trained with Bernoulli or Gaussian multiplicative masking of either the units (dropout) or the weights (dropconnect). We compare these Bayesian DNNs ability to represent their uncertainty about their outputs through sampling during inference. We tested the calibration of these Bayesian fully connected and convolutional DNNs on two visual inference tasks (MNIST and CIFAR-10). By adding different levels of Gaussian noise to the test images, we assessed how these DNNs represented their uncertainty about regions of input space not covered by the training set. These Bayesian DNNs represented their own uncertainty more accurately than traditional DNNs with a softmax output. We find that sampling of weights, whether Gaussian or Bernoulli, led to more accurate representation of uncertainty compared to sampling of units. However, sampling units using either Gaussian or Bernoulli dropout led to increased convolutional neural network (CNN) classification accuracy. Based on these findings we use both Bernoulli dropout and Gaussian dropconnect concurrently, which approximates the use of a spike-and-slab variational distribution. We find that networks with spike-and-slab sampling combine the advantages of the other methods: they classify with high accuracy and robustly represent the uncertainty of their classifications for all tested architectures.