Interpretable architectures can have advantages over black-box architectures, and interpretability is essential for the application of machine learning in critical settings, such as aviation or medicine. However, the simplest, most commonly used interpretable architectures, such as LASSO or elastic net (EN), are limited to linear predictions and have poor feature selection capabilities. In this work, we introduce the LASSO-Clip-EN (LCEN) algorithm for the creation of nonlinear, interpretable machine learning models. LCEN is tested on a wide variety of artificial and empirical datasets, frequently creating more accurate, sparser models than other architectures, including those for building sparse, nonlinear models. LCEN is robust against many issues typically present in datasets and modeling, including noise, multicollinearity, data scarcity, and hyperparameter variance. LCEN is also able to rediscover multiple physical laws from empirical data and, for processes with no known physical laws, LCEN achieves better results than many other dense and sparse methods -- including using 10.8-fold fewer features than dense methods and 8.1-fold fewer features than EN on one dataset, and is comparable to or better than ANNs on multiple datasets.
Despite the growing popularity of explainable and interpretable machine learning, there is still surprisingly limited work on inherently interpretable clustering methods. Recently, there has been a surge of interest in explaining the classic k-means algorithm, leading to efficient algorithms that approximate k-means clusters using axis-aligned decision trees. However, interpretable variants of k-means have limited applicability in practice, where more flexible clustering methods are often needed to obtain useful partitions of the data. In this work, we investigate interpretable kernel clustering, and propose algorithms that construct decision trees to approximate the partitions induced by kernel k-means, a nonlinear extension of k-means. We further build on previous work on explainable k-means and demonstrate how a suitable choice of features allows preserving interpretability without sacrificing approximation guarantees on the interpretable model.
The potential of Machine Learning Control (MLC) in HVAC systems is hindered by its opaque nature and inference mechanisms, which is challenging for users and modelers to fully comprehend, ultimately leading to a lack of trust in MLC-based decision-making. To address this challenge, this paper investigates and explores Interpretable Machine Learning (IML), a branch of Machine Learning (ML) that enhances transparency and understanding of models and their inferences, to improve the credibility of MLC and its industrial application in HVAC systems. Specifically, we developed an innovative framework that combines the principles of Shapley values and the in-context learning feature of Large Language Models (LLMs). While the Shapley values are instrumental in dissecting the contributions of various features in ML models, LLM provides an in-depth understanding of the non-data-driven or rule-based elements in MLC; combining them, LLM further packages these insights into a coherent, human-understandable narrative. The paper presents a case study to demonstrate the feasibility of the developed IML framework for model predictive control-based precooling under demand response events in a virtual testbed. The results indicate that the developed framework generates and explains the control signals in accordance with the rule-based rationale.
Variable importance plays a pivotal role in interpretable machine learning as it helps measure the impact of factors on the output of the prediction model. Model agnostic methods based on the generation of "null" features via permutation (or related approaches) can be applied. Such analysis is often utilized in pharmaceutical applications due to its ability to interpret black-box models, including tree-based ensembles. A major challenge and significant confounder in variable importance estimation however is the presence of between-feature correlation. Recently, several adjustments to marginal permutation utilizing feature knockoffs were proposed to address this issue, such as the variable importance measure known as conditional predictive impact (CPI). Assessment and evaluation of such approaches is the focus of our work. We first present a comprehensive simulation study investigating the impact of feature correlation on the assessment of variable importance. We then theoretically prove the limitation that highly correlated features pose for the CPI through the knockoff construction. While we expect that there is always no correlation between knockoff variables and its corresponding predictor variables, we prove that the correlation increases linearly beyond a certain correlation threshold between the predictor variables. Our findings emphasize the absence of free lunch when dealing with high feature correlation, as well as the necessity of understanding the utility and limitations behind methods in variable importance estimation.
Cooperative game theory has diverse applications in contemporary artificial intelligence, including domains like interpretable machine learning, resource allocation, and collaborative decision-making. However, specifying a cooperative game entails assigning values to exponentially many coalitions, and obtaining even a single value can be resource-intensive in practice. Yet simply leaving certain coalition values undisclosed introduces ambiguity regarding individual contributions to the collective grand coalition. This ambiguity often leads to players holding overly optimistic expectations, stemming from either inherent biases or strategic considerations, frequently resulting in collective claims exceeding the actual grand coalition value. In this paper, we present a framework aimed at optimizing the sequence for revealing coalition values, with the overarching goal of efficiently closing the gap between players' expectations and achievable outcomes in cooperative games. Our contributions are threefold: (i) we study the individual players' optimistic completions of games with missing coalition values along with the arising gap, and investigate its analytical characteristics that facilitate more efficient optimization; (ii) we develop methods to minimize this gap over classes of games with a known prior by disclosing values of additional coalitions in both offline and online fashion; and (iii) we empirically demonstrate the algorithms' performance in practical scenarios, together with an investigation into the typical order of revealing coalition values.
Interpretable machine learning has exploded as an area of interest over the last decade, sparked by the rise of increasingly large datasets and deep neural networks. Simultaneously, large language models (LLMs) have demonstrated remarkable capabilities across a wide array of tasks, offering a chance to rethink opportunities in interpretable machine learning. Notably, the capability to explain in natural language allows LLMs to expand the scale and complexity of patterns that can be given to a human. However, these new capabilities raise new challenges, such as hallucinated explanations and immense computational costs. In this position paper, we start by reviewing existing methods to evaluate the emerging field of LLM interpretation (both interpreting LLMs and using LLMs for explanation). We contend that, despite their limitations, LLMs hold the opportunity to redefine interpretability with a more ambitious scope across many applications, including in auditing LLMs themselves. We highlight two emerging research priorities for LLM interpretation: using LLMs to directly analyze new datasets and to generate interactive explanations.
Symbolic regression aims to derive interpretable symbolic expressions from data in order to better understand and interpret data. %which plays an important role in knowledge discovery and interpretable machine learning. In this study, a symbolic network called PruneSymNet is proposed for symbolic regression. This is a novel neural network whose activation function consists of common elementary functions and operators. The whole network is differentiable and can be trained by gradient descent method. Each subnetwork in the network corresponds to an expression, and our goal is to extract such subnetworks to get the desired symbolic expression. Therefore, a greedy pruning algorithm is proposed to prune the network into a subnetwork while ensuring the accuracy of data fitting. The proposed greedy pruning algorithm preserves the edge with the least loss in each pruning, but greedy algorithm often can not get the optimal solution. In order to alleviate this problem, we combine beam search during pruning to obtain multiple candidate expressions each time, and finally select the expression with the smallest loss as the final result. It was tested on the public data set and compared with the current popular algorithms. The results showed that the proposed algorithm had better accuracy.
Recently, interpretable machine learning has re-explored concept bottleneck models (CBM). An advantage of this model class is the user's ability to intervene on predicted concept values, affecting the downstream output. In this work, we introduce a method to perform such concept-based interventions on pretrained neural networks, which are not interpretable by design, only given a small validation set with concept labels. Furthermore, we formalise the notion of intervenability as a measure of the effectiveness of concept-based interventions and leverage this definition to fine-tune black boxes. Empirically, we explore the intervenability of black-box classifiers on synthetic tabular and natural image benchmarks. We focus on backbone architectures of varying complexity, from simple, fully connected neural nets to Stable Diffusion. We demonstrate that the proposed fine-tuning improves intervention effectiveness and often yields better-calibrated predictions. To showcase the practical utility of our techniques, we apply them to deep chest X-ray classifiers and show that fine-tuned black boxes are more intervenable than CBMs. Lastly, we establish that our methods are still effective under vision-language-model-based concept annotations, alleviating the need for a human-annotated validation set.
Explainable AI (XAI) and interpretable machine learning methods help to build trust in model predictions and derived insights, yet also present a perverse incentive for analysts to manipulate XAI metrics to support pre-specified conclusions. This paper introduces the concept of X-hacking, a form of p-hacking applied to XAI metrics such as Shap values. We show how an automated machine learning pipeline can be used to search for 'defensible' models that produce a desired explanation while maintaining superior predictive performance to a common baseline. We formulate the trade-off between explanation and accuracy as a multi-objective optimization problem and illustrate the feasibility and severity of X-hacking empirically on familiar real-world datasets. Finally, we suggest possible methods for detection and prevention, and discuss ethical implications for the credibility and reproducibility of XAI research.
We introduce a comprehensive data-driven framework aimed at enhancing the modeling of physical systems, employing inference techniques and machine learning enhancements. As a demonstrative application, we pursue the modeling of cathodic electrophoretic deposition (EPD), commonly known as e-coating. Our approach illustrates a systematic procedure for enhancing physical models by identifying their limitations through inference on experimental data and introducing adaptable model enhancements to address these shortcomings. We begin by tackling the issue of model parameter identifiability, which reveals aspects of the model that require improvement. To address generalizability , we introduce modifications which also enhance identifiability. However, these modifications do not fully capture essential experimental behaviors. To overcome this limitation, we incorporate interpretable yet flexible augmentations into the baseline model. These augmentations are parameterized by simple fully-connected neural networks (FNNs), and we leverage machine learning tools, particularly Neural Ordinary Differential Equations (Neural ODEs), to learn these augmentations. Our simulations demonstrate that the machine learning-augmented model more accurately captures observed behaviors and improves predictive accuracy. Nevertheless, we contend that while the model updates offer superior performance and capture the relevant physics, we can reduce off-line computational costs by eliminating certain dynamics without compromising accuracy or interpretability in downstream predictions of quantities of interest, particularly film thickness predictions. The entire process outlined here provides a structured approach to leverage data-driven methods. Firstly, it helps us comprehend the root causes of model inaccuracies, and secondly, it offers a principled method for enhancing model performance.
Air pollution stands as the fourth leading cause of death globally. While extensive research has been conducted in this domain, most approaches rely on large datasets when it comes to prediction. This limits their applicability in low-resource settings though more vulnerable. This study addresses this gap by proposing a novel machine learning approach for accurate air quality prediction using two months of air quality data. By leveraging the World Weather Repository, the meteorological, air pollutant, and Air Quality Index features from 197 capital cities were considered to predict air quality for the next day. The evaluation of several machine learning models demonstrates the effectiveness of the Random Forest algorithm in generating reliable predictions, particularly when applied to classification rather than regression, approach which enhances the model's generalizability by 42%, achieving a cross-validation score of 0.38 for regression and 0.89 for classification. To instill confidence in the predictions, interpretable machine learning was considered. Finally, a cost estimation comparing the implementation of this solution in high-resource and low-resource settings is presented including a tentative of technology licensing business model. This research highlights the potential for resource-limited countries to independently predict air quality while awaiting larger datasets to further refine their predictions.
Graph Neural Networks (GNNs) excel in delineating graph structures in diverse domains, including community analysis and recommendation systems. As the interpretation of GNNs becomes increasingly important, the demand for robust baselines and expansive graph datasets is accentuated, particularly in the context of Heterogeneous Information Networks (HIN). Addressing this, we introduce SynHING, a novel framework for Synthetic Heterogeneous Information Network Generation aimed at enhancing graph learning and explanation. SynHING systematically identifies major motifs in a target HIN and employs a bottom-up generation process with intra-cluster and inter-cluster merge modules. This process, supplemented by post-pruning techniques, ensures the synthetic HIN closely mirrors the original graph's structural and statistical properties. Crucially, SynHING provides ground-truth motifs for evaluating GNN explainer models, setting a new standard for explainable, synthetic HIN generation and contributing to the advancement of interpretable machine learning in complex networks.
This study presents an industry experience showcasing a vessel operational anomaly detection approach that utilizes semi-supervised deep learning models augmented with lightweight interpretable surrogate models, applied to an industrial sensorized vessel, called TUCANA. We leverage standard and Long Short-Term Memory (LSTM) autoencoders trained on normal operational data and tested with real anomaly-revealing data. We then provide a projection of the inference results on a lower-dimension data map generated by t-distributed stochastic neighbor embedding (t-SNE), which serves as an unsupervised baseline and shows the distribution of the identified anomalies. We also develop lightweight surrogate models using random forest and decision tree to promote transparency and interpretability for the inference results of the deep learning models and assist the engineer with an agile assessment of the flagged anomalies. The approach is empirically evaluated using real data from TUCANA. The empirical results show higher performance of the LSTM autoencoder -- as the anomaly detection module with effective capturing of temporal dependencies in the data -- and demonstrate the practicality of the lightweight surrogate models in providing helpful interpretability, which leads to higher efficiency for the engineer's decision-making.
Explanations in Computer Vision are often desired, but most Deep Neural Networks can only provide saliency maps with questionable faithfulness. Self-Explaining Neural Networks (SENN) extract interpretable concepts with fidelity, diversity, and grounding to combine them linearly for decision-making. While they can explain what was recognized, initial realizations lack accuracy and general applicability. We propose the Quantized-Self-Explaining Neural Network Q-SENN. Q-SENN satisfies or exceeds the desiderata of SENN while being applicable to more complex datasets and maintaining most or all of the accuracy of an uninterpretable baseline model, out-performing previous work in all considered metrics. Q-SENN describes the relationship between every class and feature as either positive, negative or neutral instead of an arbitrary number of possible relations, enforcing more binary human-friendly features. Since every class is assigned just 5 interpretable features on average, Q-SENN shows convincing local and global interpretability. Additionally, we propose a feature alignment method, capable of aligning learned features with human language-based concepts without additional supervision. Thus, what is learned can be more easily verbalized. The code is published: https://github.com/ThomasNorr/Q-SENN
In Federated Learning, clients train models on local data and send updates to a central server, which aggregates them into a global model using a fusion algorithm. This collaborative yet privacy-preserving training comes at a cost. FL developers face significant challenges in attributing global model predictions to specific clients. Localizing responsible clients is a crucial step towards (a) excluding clients primarily responsible for incorrect predictions and (b) encouraging clients who contributed high-quality models to continue participating in the future. Existing ML debugging approaches are inherently inapplicable as they are designed for single-model, centralized training. We introduce TraceFL, a fine-grained neuron provenance capturing mechanism that identifies clients responsible for a global model's prediction by tracking the flow of information from individual clients to the global model. Since inference on different inputs activates a different set of neurons of the global model, TraceFL dynamically quantifies the significance of the global model's neurons in a given prediction, identifying the most crucial neurons in the global model. It then maps them to the corresponding neurons in every participating client to determine each client's contribution, ultimately localizing the responsible client. We evaluate TraceFL on six datasets, including two real-world medical imaging datasets and four neural networks, including advanced models such as GPT. TraceFL achieves 99% accuracy in localizing the responsible client in FL tasks spanning both image and text classification tasks. At a time when state-of-the-artML debugging approaches are mostly domain-specific (e.g., image classification only), TraceFL is the first technique to enable highly accurate automated reasoning across a wide range of FL applications.
In the age of music streaming platforms, the task of automatically tagging music audio has garnered significant attention, driving researchers to devise methods aimed at enhancing performance metrics on standard datasets. Most recent approaches rely on deep neural networks, which, despite their impressive performance, possess opacity, making it challenging to elucidate their output for a given input. While the issue of interpretability has been emphasized in other fields like medicine, it has not received attention in music-related tasks. In this study, we explored the relevance of interpretability in the context of automatic music tagging. We constructed a workflow that incorporates three different information extraction techniques: a) leveraging symbolic knowledge, b) utilizing auxiliary deep neural networks, and c) employing signal processing to extract perceptual features from audio files. These features were subsequently used to train an interpretable machine-learning model for tag prediction. We conducted experiments on two datasets, namely the MTG-Jamendo dataset and the GTZAN dataset. Our method surpassed the performance of baseline models in both tasks and, in certain instances, demonstrated competitiveness with the current state-of-the-art. We conclude that there are use cases where the deterioration in performance is outweighed by the value of interpretability.
Controlling systems governed by partial differential equations is an inherently hard problem. Specifically, control of wave dynamics is challenging due to additional physical constraints and intrinsic properties of wave phenomena such as dissipation, attenuation, reflection, and scattering. In this work, we introduce an environment designed for the study of the control of acoustic waves by actuated metamaterial designs. We utilize this environment for the development of a novel machine-learning method, based on deep neural networks, for efficiently learning the dynamics of an acoustic PDE from samples. Our model is fully interpretable and maps physical constraints and intrinsic properties of the real acoustic environment into its latent representation of information. Within our model we use a trainable perfectly matched layer to explicitly learn the property of acoustic energy dissipation. Our model can be used to predict and control scattered wave energy. The capabilities of our model are demonstrated on an important problem in acoustics, which is the minimization of total scattered energy. Furthermore, we show that the prediction of scattered energy by our model generalizes in time and can be extended to long time horizons. We make our code repository publicly available.
Sparse linear models are one of several core tools for interpretable machine learning, a field of emerging importance as predictive models permeate decision-making in many domains. Unfortunately, sparse linear models are far less flexible as functions of their input features than black-box models like deep neural networks. With this capability gap in mind, we study a not-uncommon situation where the input features dichotomize into two groups: explanatory features, which are candidates for inclusion as variables in an interpretable model, and contextual features, which select from the candidate variables and determine their effects. This dichotomy leads us to the contextual lasso, a new statistical estimator that fits a sparse linear model to the explanatory features such that the sparsity pattern and coefficients vary as a function of the contextual features. The fitting process learns this function nonparametrically via a deep neural network. To attain sparse coefficients, we train the network with a novel lasso regularizer in the form of a projection layer that maps the network's output onto the space of $\ell_1$-constrained linear models. An extensive suite of experiments on real and synthetic data suggests that the learned models, which remain highly transparent, can be sparser than the regular lasso without sacrificing the predictive power of a standard deep neural network.
To address the issues of stability and fidelity in interpretable learning, a novel interpretable methodology, ensemble interpretation, is presented in this paper which integrates multi-perspective explanation of various interpretation methods. On one hand, we define a unified paradigm to describe the common mechanism of different interpretation methods, and then integrate the multiple interpretation results to achieve more stable explanation. On the other hand, a supervised evaluation method based on prior knowledge is proposed to evaluate the explaining performance of an interpretation method. The experiment results show that the ensemble interpretation is more stable and more consistent with human experience and cognition. As an application, we use the ensemble interpretation for feature selection, and then the generalization performance of the corresponding learning model is significantly improved.
Symbolic regression (SR) is an area of interpretable machine learning that aims to identify mathematical expressions, often composed of simple functions, that best fit in a given set of covariates $X$ and response $y$. In recent years, deep symbolic regression (DSR) has emerged as a popular method in the field by leveraging deep reinforcement learning to solve the complicated combinatorial search problem. In this work, we propose an alternative framework (GFN-SR) to approach SR with deep learning. We model the construction of an expression tree as traversing through a directed acyclic graph (DAG) so that GFlowNet can learn a stochastic policy to generate such trees sequentially. Enhanced with an adaptive reward baseline, our method is capable of generating a diverse set of best-fitting expressions. Notably, we observe that GFN-SR outperforms other SR algorithms in noisy data regimes, owing to its ability to learn a distribution of rewards over a space of candidate solutions.