Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Interpretable machine learning tackles the important problem that humans cannot understand the behaviors of complex machine learning models and how these models arrive at a particular decision. Although many approaches have been proposed, a comprehensive understanding of the achievements and challenges is still lacking. We provide a survey covering existing techniques to increase the interpretability of machine learning models. We also discuss crucial issues that the community should consider in future work such as designing user-friendly explanations and developing comprehensive evaluation metrics to further push forward the area of interpretable machine learning.

pdf/techniques-for-interpretable-machine-learning-3krci1pgpm.pdf

Techniques for interpretable machine learning

The need for interpretable and accountable intelligent systems grows along with the prevalence of artificial intelligence applications used in everyday life. Explainable intelligent systems are designed to self-explain the reasoning behind system decisions and predictions, and researchers from different disciplines work together to define, design, and evaluate interpretable systems. However, scholars from different disciplines focus on different objectives and fairly independent topics of interpretable machine learning research, which poses challenges for identifying appropriate design and evaluation methodology and consolidating knowledge across efforts. To this end, this paper presents a survey and framework intended to share knowledge and experiences of XAI design and evaluation methods across multiple disciplines. Aiming to support diverse design goals and evaluation methods in XAI research, after a thorough review of XAI related papers in the fields of machine learning, visualization, and human-computer interaction, we present a categorization of interpretable machine learning design goals and evaluation methods to show a mapping between design goals for different XAI user groups and their evaluation methods. From our findings, we develop a framework with step-by-step design guidelines paired with evaluation methods to close the iterative design and evaluation cycles in multidisciplinary XAI teams. Further, we provide summarized ready-to-use tables of evaluation methods and recommendations for different goals in XAI research.

A Multidisciplinary Survey and Framework for Design and Evaluation of Explainable AI Systems

Deep learning (DL) defines a new data-driven programming paradigm where the internal system logic is largely shaped by the training data. The standard way of evaluating DL models is to examine their performance on a test dataset. The quality of the test dataset is of great importance to gain confidence of the trained models. Using an inadequate test dataset, DL models that have achieved high test accuracy may still lack generality and robustness. In traditional software testing, mutation testing is a well-established technique for quality evaluation of test suites, which analyzes to what extent a test suite detects the injected faults. However, due to the fundamental difference between traditional software and deep learning-based software, traditional mutation testing techniques cannot be directly applied to DL systems. In this paper, we propose a mutation testing framework specialized for DL systems to measure the quality of test data. To do this, by sharing the same spirit of mutation testing in traditional software, we first define a set of source-level mutation operators to inject faults to the source of DL (i.e., training data and training programs). Then we design a set of model-level mutation operators that directly inject faults into DL models without a training process. Eventually, the quality of test data could be evaluated from the analysis on to what extent the injected faults could be detected. The usefulness of the proposed mutation testing techniques is demonstrated on two public datasets, namely MNIST and CIFAR-10, with three DL models.

DeepMutation: Mutation Testing of Deep Learning Systems

https://pureadmin.qub.ac.uk/ws/files/213055682/A_Survey_of_Safety_and_Trustworthiness_of_Deep_Neural_Networks.pdf

A Survey of Safety and Trustworthiness of Deep Neural Networks: Verification, Testing, Adversarial Attack and Defence, and Interpretability

Model complexity is a fundamental problem in deep learning. In this paper, we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive capacity and effective model complexity. We review the existing studies on those two categories along four important factors, including model framework, model size, optimization process, and data complexity. We also discuss the applications of deep learning model complexity including understanding model generalization, model optimization, and model selection and design. We conclude by proposing several interesting future directions.

Model complexity of deep learning: a survey

It is fundamental to measure model complexity of deep neural networks. A good model complexity measure can help to tackle many challenging problems, such as overfitting detection, model selection, and performance improvement. The existing literature on model complexity mainly focuses on neural networks with piecewise linear activation functions. Model complexity of neural networks with general curve activation functions remains an open problem. To tackle the challenge, in this paper, we first propose linear approximation neural network (LANN for short), a piecewise linear framework to approximate a given deep model with curve activation function. LANN constructs individual piecewise linear approximation for the activation function of each neuron, and minimizes the number of linear regions to satisfy a required approximation degree. Then, we analyze the upper bound of the number of linear regions formed by LANNs, and derive the complexity measure based on the upper bound. To examine the usefulness of the complexity measure, we experimentally explore the training process of neural networks and detect overfitting. Our results demonstrate that the occurrence of overfitting is positively correlated with the increase of model complexity during training. We find that the L1 and L2 regularizations suppress the increase of model complexity. Finally, we propose two approaches to prevent overfitting by directly constraining model complexity, namely neuron pruning and customized L1 regularization.

Measuring Model Complexity of Neural Networks with Curve Activation Functions

Strong intelligent machines powered by deep neural networks are increasingly deployed as black boxes to make decisions in risk-sensitive domains, such as finance and medical. To reduce potential risk and build trust with users, it is critical to interpret how such machines make their decisions. Existing works interpret a pre-trained neural network by analyzing hidden neurons, mimicking pre-trained models or approximating local predictions. However, these methods do not provide a guarantee on the exactness and consistency of their interpretation. In this paper, we propose an elegant closed form solution named $OpenBox$ to compute exact and consistent interpretations for the family of Piecewise Linear Neural Networks (PLNN). The major idea is to first transform a PLNN into a mathematically equivalent set of linear classifiers, then interpret each linear classifier by the features that dominate its prediction. We further apply $OpenBox$ to demonstrate the effectiveness of non-negative and sparse constraints on improving the interpretability of PLNNs. The extensive experiments on both synthetic and real world data sets clearly demonstrate the exactness and consistency of our interpretation.

Exact and Consistent Interpretation for Piecewise Linear Neural Networks: A Closed Form Solution

It is fundamental to measure model complexity of deep neural networks. The existing literature on model complexity mainly focuses on neural networks with piecewise linear activation functions. Model complexity of neural networks with general curve activation functions remains an open problem. To tackle the challenge, in this paper, we first propose the linear approximation neural network (LANN for short), a piecewise linear framework to approximate a given deep model with curve activation function. LANN constructs individual piecewise linear approximation for the activation function of each neuron, and minimizes the number of linear regions to satisfy a required approximation degree. Then, we analyze the upper bound of the number of linear regions formed by LANNs, and derive the complexity measure based on the upper bound. To examine the usefulness of the complexity measure, we experimentally explore the training process of neural networks and detect overfitting. Our results demonstrate that the occurrence of overfitting is positively correlated with the increase of model complexity during training. We find that the $L^1$ and $L^2$ regularizations suppress the increase of model complexity. Finally, we propose two approaches to prevent overfitting by directly constraining model complexity, namely neuron pruning and customized $L^1$ regularization.

Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive capacity and effective model complexity. We review the existing studies on those two categories along four important factors, including model framework, model size, optimization process and data complexity. We also discuss the applications of deep learning model complexity including understanding model generalization, model optimization, and model selection and design. We conclude by proposing several interesting future directions.

Model Complexity of Deep Learning: A Survey

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Papers

Model complexity of deep learning: a survey

Measuring Model Complexity of Neural Networks with Curve Activation Functions

Exact and Consistent Interpretation for Piecewise Linear Neural Networks: A Closed Form Solution

Measuring Model Complexity of Neural Networks with Curve Activation Functions

Model Complexity of Deep Learning: A Survey