We introduce a family of interpretable machine learning models, with two broad additions: Linearised Additive Models (LAMs) which replace the ubiquitous logistic link function in General Additive Models (GAMs); and SubscaleHedge, an expert advice algorithm for combining base models trained on subsets of features called subscales. LAMs can augment any additive binary classification model equipped with a sigmoid link function. Moreover, they afford direct global and local attributions of additive components to the model output in probability space. We argue that LAMs and SubscaleHedge improve the interpretability of their base algorithms. Using rigorous null-hypothesis significance testing on a broad suite of financial modelling data, we show that our algorithms do not suffer from large performance penalties in terms of ROC-AUC and calibration.
Explainable artificial intelligence (XAI) provides explanations for not interpretable machine learning (ML) models. While many technical approaches exist, there is a lack of validation of these techniques on real-world datasets. In this work, we present a use-case of XAI: an ML model which is trained to estimate electrification rates based on mobile phone data in Senegal. The data originate from the Data for Development challenge by Orange in 2014/15. We apply two model-agnostic, local explanation techniques and find that while the model can be verified, it is biased with respect to the population density. We conclude our paper by pointing to the two main challenges we encountered during our work: data processing and model design that might be restricted by currently available XAI methods, and the importance of domain knowledge to interpret explanations.
Classical artificial neural networks have witnessed widespread successes in machine-learning applications. Here, we propose fermion neural networks (FNNs) whose physical properties, such as local density of states or conditional conductance, serve as outputs, once the inputs are incorporated as an initial layer. Comparable to back-propagation, we establish an efficient optimization, which entitles FNNs to competitive performance on challenging machine-learning benchmarks. FNNs also directly apply to quantum systems, including hard ones with interactions, and offer in-situ analysis without preprocessing or presumption. Following machine learning, FNNs precisely determine topological phases and emergent charge orders. Their quantum nature also brings various advantages: quantum correlation entitles more general network connectivity and insight into the vanishing gradient problem, quantum entanglement opens up novel avenues for interpretable machine learning, etc.
Interpretability provides a means for humans to verify aspects of machine learning (ML) models and empower human+ML teaming in situations where the task cannot be fully automated. Different contexts require explanations with different properties. For example, the kind of explanation required to determine if an early cardiac arrest warning system is ready to be integrated into a care setting is very different from the type of explanation required for a loan applicant to help determine the actions they might need to take to make their application successful. Unfortunately, there is a lack of standardization when it comes to properties of explanations: different papers may use the same term to mean different quantities, and different terms to mean the same quantity. This lack of a standardized terminology and categorization of the properties of ML explanations prevents us from both rigorously comparing interpretable machine learning methods and identifying what properties are needed in what contexts. In this work, we survey properties defined in interpretable machine learning papers, synthesize them based on what they actually measure, and describe the trade-offs between different formulations of these properties. In doing so, we enable more informed selection of task-appropriate formulations of explanation properties as well as standardization for future work in interpretable machine learning.
In this paper, negatively inclined buoyant jets, which appear during the discharge of wastewater from processes such as desalination, are observed. To minimize harmful effects and assess environmental impact, a detailed numerical investigation is necessary. The selection of appropriate geometry and working conditions for minimizing such effects often requires numerous experiments and numerical simulations. For this reason, the application of machine learning models is proposed. Several models including Support Vector Regression, Artificial Neural Networks, Random Forests, XGBoost, CatBoost and LightGBM were trained. The dataset was built with numerous OpenFOAM simulations, which were validated by experimental data from previous research. The best prediction was obtained by Artificial Neural Network with an average of R2 0.98 and RMSE 0.28. In order to understand the working of the machine learning model and the influence of all parameters on the geometrical characteristics of inclined buoyant jets, the SHAP feature interpretation method was used.
In intensive care units (ICUs), critically ill patients are monitored with electroencephalograms (EEGs) to prevent serious brain injury. The number of patients who can be monitored is constrained by the availability of trained physicians to read EEGs, and EEG interpretation can be subjective and prone to inter-observer variability. Automated deep learning systems for EEG could reduce human bias and accelerate the diagnostic process. However, black box deep learning models are untrustworthy, difficult to troubleshoot, and lack accountability in real-world applications, leading to a lack of trust and adoption by clinicians. To address these challenges, we propose a novel interpretable deep learning model that not only predicts the presence of harmful brainwave patterns but also provides high-quality case-based explanations of its decisions. Our model performs better than the corresponding black box model, despite being constrained to be interpretable. The learned 2D embedded space provides the first global overview of the structure of ictal-interictal-injury continuum brainwave patterns. The ability to understand how our model arrived at its decisions will not only help clinicians to diagnose and treat harmful brain activities more accurately but also increase their trust and adoption of machine learning models in clinical practice; this could be an integral component of the ICU neurologists' standard workflow.
With the rising need of interpretable machine learning methods, there is a necessity for a rise in human effort to provide diverse explanations of the influencing factors of the model decisions. To improve the trust and transparency of AI-based systems, the EXplainable Artificial Intelligence (XAI) field has emerged. The XAI paradigm is bifurcated into two main categories: feature attribution and counterfactual explanation methods. While feature attribution methods are based on explaining the reason behind a model decision, counterfactual explanation methods discover the smallest input changes that will result in a different decision. In this paper, we aim at building trust and transparency in time series models by using motifs to generate counterfactual explanations. We propose Motif-Guided Counterfactual Explanation (MG-CF), a novel model that generates intuitive post-hoc counterfactual explanations that make full use of important motifs to provide interpretive information in decision-making processes. To the best of our knowledge, this is the first effort that leverages motifs to guide the counterfactual explanation generation. We validated our model using five real-world time-series datasets from the UCR repository. Our experimental results show the superiority of MG-CF in balancing all the desirable counterfactual explanations properties in comparison with other competing state-of-the-art baselines.
Interpretable and explainable machine learning has seen a recent surge of interest. We focus on safety as a key motivation behind the surge and make the relationship between interpretability and safety more quantitative. Toward assessing safety, we introduce the concept of maximum deviation via an optimization problem to find the largest deviation of a supervised learning model from a reference model regarded as safe. We then show how interpretability facilitates this safety assessment. For models including decision trees, generalized linear and additive models, the maximum deviation can be computed exactly and efficiently. For tree ensembles, which are not regarded as interpretable, discrete optimization techniques can still provide informative bounds. For a broader class of piecewise Lipschitz functions, we leverage the multi-armed bandit literature to show that interpretability produces tighter (regret) bounds on the maximum deviation. We present case studies, including one on mortgage approval, to illustrate our methods and the insights about models that may be obtained from deviation maximization.
Developing interpretable machine learning models has become an increasingly important issue. One way in which data scientists have been able to develop interpretable models has been to use dimension reduction techniques. In this paper, we examine several dimension reduction techniques including two recent approaches developed in the network psychometrics literature called exploratory graph analysis (EGA) and unique variable analysis (UVA). We compared EGA and UVA with two other dimension reduction techniques common in the machine learning literature (principal component analysis and independent component analysis) as well as no reduction to the variables real data. We show that EGA and UVA perform as well as the other reduction techniques or no reduction. Consistent with previous literature, we show that dimension reduction can decrease, increase, or provide the same accuracy as no reduction of variables. Our tentative results find that dimension reduction tends to lead to better performance when used for classification tasks.
Ransomware has appeared as one of the major global threats in recent days. The alarming increasing rate of ransomware attacks and new ransomware variants intrigue the researchers to constantly examine the distinguishing traits of ransomware and refine their detection strategies. Application Programming Interface (API) is a way for one program to collaborate with another; API calls are the medium by which they communicate. Ransomware uses this strategy to interact with the OS and makes a significantly higher number of calls in different sequences to ask for taking action. This research work utilizes the frequencies of different API calls to detect and classify ransomware families. First, a Web-Crawler is developed to automate collecting the Windows Portable Executable (PE) files of 15 different ransomware families. By extracting different frequencies of 68 API calls, we develop our dataset in the first phase of the two-phase feature engineering process. After selecting the most significant features in the second phase of the feature engineering process, we deploy six Supervised Machine Learning models: Na"ive Bayes, Logistic Regression, Random Forest, Stochastic Gradient Descent, K-Nearest Neighbor, and Support Vector Machine. Then, the performances of all the classifiers are compared to select the best model. The results reveal that Logistic Regression can efficiently classify ransomware into their corresponding families securing 99.15% overall accuracy. Finally, instead of relying on the 'Black box' characteristic of the Machine Learning models, we present the post-hoc analysis of our best-performing model using 'SHapley Additive exPlanations' or SHAP values to ascertain the transparency and trustworthiness of the model's prediction.
In recent years, there has been growing attention to interpretable machine learning models which can give explanatory insights on their behaviour. Thanks to their interpretability, decision trees have been intensively studied for classification tasks and, due to the remarkable advances in mixed integer programming (MIP), various approaches have been proposed to formulate the problem of training an Optimal Classification Tree (OCT) as a MIP model. We present a novel mixed integer quadratic formulation for the OCT problem, which exploits the generalization capabilities of Support Vector Machines for binary classification. Our model, denoted as Margin Optimal Classification Tree (MARGOT), encompasses maximum margin multivariate hyperplanes nested in a binary tree structure. To enhance the interpretability of our approach, we analyse two alternative versions of MARGOT, which include feature selection constraints inducing sparsity of the hyperplanes' coefficients. First, MARGOT has been tested on non-linearly separable synthetic datasets in a 2-dimensional feature space to provide a graphical representation of the maximum margin approach. Finally, the proposed models have been tested on benchmark datasets from the UCI repository. The MARGOT formulation turns out to be easier to solve than other OCT approaches, and the generated tree better generalizes on new observations. The two interpretable versions effectively select the most relevant features, maintaining good prediction quality.
Anomaly detection in sequential data has been studied for a long time because of its potential in various applications, such as detecting abnormal system behaviors from log data. Although many approaches can achieve good performance on anomalous sequence detection, how to identify the anomalous entries in sequences is still challenging due to a lack of information at the entry-level. In this work, we propose a novel framework called CFDet for fine-grained anomalous entry detection. CFDet leverages the idea of interpretable machine learning. Given a sequence that is detected as anomalous, we can consider anomalous entry detection as an interpretable machine learning task because identifying anomalous entries in the sequence is to provide an interpretation to the detection result. We make use of the deep support vector data description (Deep SVDD) approach to detect anomalous sequences and propose a novel counterfactual interpretation-based approach to identify anomalous entries in the sequences. Experimental results on three datasets show that CFDet can correctly detect anomalous entries.
Interpretable machine learning plays a key role in healthcare because it is challenging in understanding feature importance in deep learning model predictions. We propose a novel framework that uses deep learning to study feature sensitivity for model predictions. This work combines sensitivity analysis with heterogeneous time-series deep learning model prediction, which corresponds to the interpretations of spatio-temporal features. We forecast county-level COVID-19 infection using the Temporal Fusion Transformer. We then use the sensitivity analysis extending Morris Method to see how sensitive the outputs are with respect to perturbation to our static and dynamic input features. The significance of the work is grounded in a real-world COVID-19 infection prediction with highly non-stationary, finely granular, and heterogeneous data. 1) Our model can capture the detailed daily changes of temporal and spatial model behaviors and achieves high prediction performance compared to a PyTorch baseline. 2) By analyzing the Morris sensitivity indices and attention patterns, we decipher the meaning of feature importance with observational population and dynamic model changes. 3) We have collected 2.5 years of socioeconomic and health features over 3142 US counties, such as observed cases and deaths, and a number of static (age distribution, health disparity, and industry) and dynamic features (vaccination, disease spread, transmissible cases, and social distancing). Using the proposed framework, we conduct extensive experiments and show our model can learn complex interactions and perform predictions for daily infection at the county level. Being able to model the disease infection with a hybrid prediction and description accuracy measurement with Morris index at the county level is a central idea that sheds light on individual feature interpretation via sensitivity analysis.
Despite the popularity of feature importance (FI) measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analyzing a variable's importance before and after adjusting for covariates - i.e., between $\textit{marginal}$ and $\textit{conditional}$ measures. Our work draws attention to this rarely acknowledged, yet crucial distinction and showcases its implications. Further, we reveal that for testing conditional FI, only few methods are available and practitioners have hitherto been severely restricted in method application due to mismatching data requirements. Most real-world data exhibits complex feature dependencies and incorporates both continuous and categorical data (mixed data). Both properties are oftentimes neglected by conditional FI measures. To fill this gap, we propose to combine the conditional predictive impact (CPI) framework with sequential knockoff sampling. The CPI enables conditional FI measurement that controls for any feature dependencies by sampling valid knockoffs - hence, generating synthetic data with similar statistical properties - for the data to be analyzed. Sequential knockoffs were deliberately designed to handle mixed data and thus allow us to extend the CPI approach to such datasets. We demonstrate through numerous simulations and a real-world example that our proposed workflow controls type I error, achieves high power and is in line with results given by other conditional FI measures, whereas marginal FI metrics result in misleading interpretations. Our findings highlight the necessity of developing statistically adequate, specialized methods for mixed data.
Shapley values are ubiquitous in interpretable Machine Learning due to their strong theoretical background and efficient implementation in the SHAP library. Computing these values previously induced an exponential cost with respect to the number of input features of an opaque model. Now, with efficient implementations such as Interventional TreeSHAP, this exponential burden is alleviated assuming one is explaining ensembles of decision trees. Although Interventional TreeSHAP has risen in popularity, it still lacks a formal proof of how/why it works. We provide such proof with the aim of not only increasing the transparency of the algorithm but also to encourage further development of these ideas. Notably, our proof for Interventional TreeSHAP is easily adapted to Shapley-Taylor indices and one-hot-encoded features.
Black-box models, such as deep neural networks, exhibit superior predictive performances, but understanding their behavior is notoriously difficult. Many explainable artificial intelligence methods have been proposed to reveal the decision-making processes of black box models. However, their applications in high-stakes domains remain limited. Recently proposed neural additive models (NAM) have achieved state-of-the-art interpretable machine learning. NAM can provide straightforward interpretations with slight performance sacrifices compared with multi-layer perceptron. However, NAM can only model 1$^{\text{st}}$-order feature interactions; thus, it cannot capture the co-relationships between input features. To overcome this problem, we propose a novel interpretable machine learning method called higher-order neural additive models (HONAM) and a feature interaction method for high interpretability. HONAM can model arbitrary orders of feature interactions. Therefore, it can provide the high predictive performance and interpretability that high-stakes domains need. In addition, we propose a novel hidden unit to effectively learn sharp-shape functions. We conducted experiments using various real-world datasets to examine the effectiveness of HONAM. Furthermore, we demonstrate that HONAM can achieve fair AI with a slight performance sacrifice. The source code for HONAM is publicly available.
Interpretable machine learning seeks to understand the reasoning process of complex black-box systems that are long notorious for lack of explainability. One flourishing approach is through counterfactual explanations, which provide suggestions on what a user can do to alter an outcome. Not only must a counterfactual example counter the original prediction from the black-box classifier but it should also satisfy various constraints for practical applications. Diversity is one of the critical constraints that however remains less discussed. While diverse counterfactuals are ideal, it is computationally challenging to simultaneously address some other constraints. Furthermore, there is a growing privacy concern over the released counterfactual data. To this end, we propose a feature-based learning framework that effectively handles the counterfactual constraints and contributes itself to the limited pool of private explanation models. We demonstrate the flexibility and effectiveness of our method in generating diverse counterfactuals of actionability and plausibility. Our counterfactual engine is more efficient than counterparts of the same capacity while yielding the lowest re-identification risks.
While machine learning methods have significantly improved model performance over traditional methods, their black-box structure makes it difficult for researchers to interpret results. For highly regulated financial industries, model transparency is equally important to accuracy. Without understanding how models work, even highly accurate machine learning methods are unlikely to be accepted. We address this issue by introducing a novel class of transparent machine learning models known as generalized groves of neural additive models. The generalized groves of neural additive models separate features into three categories: linear features, individual nonlinear features, and interacted nonlinear features. Additionally, interactions in the last category are only local. A stepwise selection algorithm distinguishes the linear and nonlinear components, and interacted groups are carefully verified by applying additive separation criteria. Through some empirical examples in finance, we demonstrate that generalized grove of neural additive models exhibit high accuracy and transparency with predominantly linear terms and only sparse nonlinear ones.
Most existing Time series classification (TSC) models lack interpretability and are difficult to inspect. Interpretable machine learning models can aid in discovering patterns in data as well as give easy-to-understand insights to domain specialists. In this study, we present Neuro-Symbolic Time Series Classification (NSTSC), a neuro-symbolic model that leverages signal temporal logic (STL) and neural network (NN) to accomplish TSC tasks using multi-view data representation and expresses the model as a human-readable, interpretable formula. In NSTSC, each neuron is linked to a symbolic expression, i.e., an STL (sub)formula. The output of NSTSC is thus interpretable as an STL formula akin to natural language, describing temporal and logical relations hidden in the data. We propose an NSTSC-based classifier that adopts a decision-tree approach to learn formula structures and accomplish a multiclass TSC task. The proposed smooth activation functions for wSTL allow the model to be learned in an end-to-end fashion. We test NSTSC on a real-world wound healing dataset from mice and benchmark datasets from the UCR time-series repository, demonstrating that NSTSC achieves comparable performance with the state-of-the-art models. Furthermore, NSTSC can generate interpretable formulas that match with domain knowledge.
Interpretable Machine Learning (IML) is expected to remove significant barriers for the application of Machine Learning (ML) algorithms in power systems. This letter first seeks to showcase the benefits of SHapley Additive exPlanations (SHAP) for understanding the outcomes of ML models, which are increasingly being used. Second, we seek to demonstrate that SHAP explanations are able to capture the underlying physics of the power system. To do so, we demonstrate that the Power Transfer Distribution Factors (PTDF) -- a physics-based linear sensitivity index -- can be derived from the SHAP values. To do so, we take the derivatives of SHAP values from a ML model trained to learn line flows from generator power injections, using a simple DC power flow case in the 9-bus 3-generator test network. In demonstrating that SHAP values can be related back to the physics that underpin the power system, we build confidence in the explanations SHAP can offer.