The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. The research focus has mostly been on improving the accuracy and efficiency of classifiers, while their interpretability has been somewhat neglected. Classifier interpretability has become a critical constraint for many application domains and the introduction of the 'right to explanation' GDPR EU legislation in May 2018 is likely to further emphasize the importance of explainable learning algorithms. In this work we analyse the state-of-the-art for time series classification, and propose new algorithms that aim to maintain the classifier accuracy and efficiency, but keep interpretability as a key design constraint. We present new time series classification algorithms that advance the state-of-the-art by implementing the following three key ideas: (1) Multiple resolutions of symbolic approximations: we combine symbolic representations obtained using different parameters; (2) Multiple domain representations: we combine symbolic approximations in time (e.g., SAX) and frequency (e.g., SFA) domains; (3) Efficient navigation of a huge symbolic-words space: we adapt a symbolic sequence classifier named SEQL, to make it work with multiple domain representations (e.g., SAX-SEQL, SFA-SEQL), and use its greedy feature selection strategy to effectively filter the best features for each representation. We show that a multi-resolution multi-domain linear classifier, SAX-SFA-SEQL, achieves a similar accuracy to the state-of-the-art COTE ensemble, and to a recent deep learning method (FCN), but uses a fraction of the time required by either COTE or FCN. We discuss the accuracy, efficiency and interpretability of our proposed algorithms. To further analyse the interpretability aspect of our classifiers, we present a case study on an ecology benchmark.
Insight Centre for Data Analytics（洞察数据分析中心）；University College Dublin（都柏林大学学院）
The time series classification literature has expanded rapidly over the last decade, with many new classification approaches published each year. Prior research has mostly focused on improving the accuracy and efficiency of classifiers, with interpretability being somewhat neglected. This aspect of classifiers has become critical for many application domains and the introduction of the EU GDPR legislation in 2018 is likely to further emphasize the importance of interpretable learning algorithms. Currently, state-of-the-art classification accuracy is achieved with very complex models based on l…
Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学）
Subsequence-based time series classification algorithms provide accurate and interpretable models, but training these models is extremely computation intensive. The asymptotic time complexity of subsequence-based algorithms remains a higher-order polynomial, because these algorithms are based on exhaustive search for highly discriminative subsequences. Pattern sampling has been proposed as an effective alternative to mitigate the pattern explosion phenomenon. Therefore, we employ pattern sampling to extract discriminative features from discretized time series data. A weighted trie is created b…
Insight Centre for Data Analytics（洞察数据分析中心）；University College Dublin（都柏林大学）
Symbolic representations of time series have proven to be effective for time series classification, with many recent approaches including SAX-VSM, BOSS, WEASEL, and MrSEQL. The key idea is to transform numerical time series to symbolic representations in the time or frequency domain, i.e., sequences of symbols, and then extract features from these sequences. While achieving high accuracy, existing symbolic classifiers are computationally expensive. In this paper we present MrSQM, a new time series classifier which uses multiple symbolic representations and efficient sequence mining, to extract…
Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition
Federal University of ABC（ABC联邦大学）；Centrum Wiskunde & Informatica（荷兰数学与计算机科学研究院）；Boston Children’s Hospital（波士顿儿童医院）；Harvard Medical School（哈佛医学院）；University of Applied Sciences Upper Austria（上奥地利应用科学大学）；Flatiron Institute（熨斗研究所）；Princeton University（普林斯顿大学）；Universidade de Lisboa（里斯本大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；University of Utah（犹他大学）；Meta；Victoria University of Wellington（惠灵顿维多利亚大学）；University of otago（奥塔哥大学）；Universität Tübingen（图宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Abzu AI（Abzu人工智能公司）
One approach for interpreting black-box machine learning models is to find a global approximation of the model using simple interpretable functions, which is called a metamodel (a model of the model). Approximating the black-box with a metamodel can be used to 1) estimate instance-wise feature importance; 2) understand the functional form of the model; 3) analyze feature interactions. In this work, we propose a new method for finding interpretable metamodels. Our approach utilizes Kolmogorov superposition theorem, which expresses multivariate functions as a composition of univariate functions …
Facebook AI Research（脸书人工智能研究院）；Georgia Tech（佐治亚理工学院）
We propose a new class of probabilistic neural-symbolic models, that have symbolic functional programs as a latent, stochastic variable. Instantiated in the context of visual question answering, our probabilistic formulation offers two key conceptual advantages over prior neural-symbolic models for VQA. Firstly, the programs generated by our model are more understandable while requiring lesser number of teaching examples. Secondly, we show that one can pose counterfactual scenarios to the model, to probe its beliefs on the programs that could lead to a specified answer given an image. Our resu…
Trajectory classification tasks became more complex as large volumes of mobility data are being generated every day and enriched with new sources of information, such as social networks and IoT sensors. Fast classification algorithms are essential for discovering knowledge in trajectory data for real applications. In this work we propose a method for fast discovery of subtrajectories with the reduction of the search space and the optimization of the MASTERMovelets method, which has proven to be effective for discovering interpretable patterns in classification problems.
Rensselaer Polytechnic Institute（伦斯勒理工学院）；IBM T.J. Watson Research Center（IBM托马斯·J·沃森研究中心）；IBM Research（IBM研究院）
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 express…
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Singapore Eye Research Institute（新加坡眼科研究所）；Duke-NUS Medical School（杜克-新加坡国立大学医学院）；Institute for Molecular and Clinical Ophthalmology（分子与临床眼科研究所）；National University of Singapore（新加坡国立大学）
In this paper, we propose an explainable and interpretable diabetic retinopathy (ExplainDR) classification model based on neural-symbolic learning. To gain explainability, a highlevel symbolic representation should be considered in decision making. Specifically, we introduce a human-readable symbolic representation, which follows a taxonomy style of diabetic retinopathy characteristics related to eye health conditions to achieve explainability. We then include humanreadable features obtained from the symbolic representation in the disease prediction. Experimental results on a diabetic retinopa…
Deep neural networks based on layer-stacking architectures have historically suffered from poor inherent interpretability. Meanwhile, symbolic probabilistic models function with clear interpretability, but how to combine them with neural networks to enhance their performance remains to be explored. In this paper, we try to marry these two systems for text classification via a structured language model. We propose a Symbolic-Neural model that can learn to explicitly predict class labels of text spans from a constituency tree without requiring any access to span-level gold labels. As the structu…
IBM Research Europe（IBM欧洲研究院）；Imperial College London（伦敦帝国理工学院）；ILASP Limited（ILASP有限公司）；ICREA-Universitat Pompeu Fabra（ICREA-庞培法布拉大学）
Logic-based machine learning aims to learn general, interpretable knowledge in a data-efficient manner. However, labelled data must be specified in a structured logical form. To address this limitation, we propose a neural-symbolic learning framework, called Feed-Forward Neural-Symbolic Learner (FFNSL), that integrates a logic-based machine learning system capable of learning from noisy examples, with neural networks, in order to learn interpretable knowledge from labelled unstructured data. We demonstrate the generality of FFNSL on four neural-symbolic classification problems, where different…
Massive language models are the core of modern NLP modeling and have been shown to encode impressive amounts of commonsense and factual information. However, that knowledge exists only within the latent parameters of the model, inaccessible to inspection and interpretation, and even worse, factual information memorized from the training corpora is likely to become stale as the world changes. Knowledge stored as parameters will also inevitably exhibit all of the biases inherent in the source materials. To address these problems, we develop a neural language model that includes an explicit inter…
Towards symbolic regression for interpretable clinical decision scores
Federal University of ABC（ABC联邦大学）；University of Pennsylvania（宾夕法尼亚大学）；Institute for Biomedical Informatics, University of Pennsylvania（宾夕法尼亚大学生物医学信息学研究所）；Boston Children's Hospital, Harvard Medical School（哈佛医学院波士顿儿童医院）
Recently deep reinforcement learning has achieved tremendous success in wide ranges of applications. However, it notoriously lacks data-efficiency and interpretability. Data-efficiency is important as interacting with the environment is expensive. Further, interpretability can increase the transparency of the black-box-style deep RL models and hence gain trust from the users. In this work, we propose a new hierarchical framework via symbolic RL, leveraging a symbolic transition model to improve the data-efficiency and introduce the interpretability for learned policy. This framework consists o…
Turning Time Series into Algebraic Equations: Symbolic Machine Learning for Interpretable Modeling of Chaotic Time Series
SAFIR, Sorbonne University Abu Dhabi, UAE（SAFIR，索邦大学阿布扎赫德分校）；Sorbonne Center for Artificial Intelligence, Sorbonne University, Paris, France（索邦人工智能中心，索邦大学巴黎分校）
Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning
Energy \& Intelligence Lab, Department of Chemical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Imaging Institute, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah, 84112, USA；Department of Mechanical Engineering, School of Engineering, Urmia University of Technology, Urmia, Iran
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
We consider the problem of combining machine learning models to perform higher-level cognitive tasks with clear specifications. We propose the novel problem of Visual Discrimination Puzzles (VDP) that requires finding interpretable discriminators that classify images according to a logical specification. Humans can solve these puzzles with ease and they give robust, verifiable, and interpretable discriminators as answers. We propose a compositional neurosymbolic framework that combines a neural network to detect objects and relationships with a symbolic learner that finds interpretable discrim…
Interpretable and Explainable Logical Policies via Neurally Guided Symbolic Abstraction
Technical University of Darmstadt（达姆施塔特工业大学）；National Research Center for Applied Cybersecurity（国家应用网络安全研究中心）；Eindhoven University of Technology（埃因霍温理工大学）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）；German Research Center for AI (DFKI)（德国人工智能研究中心）
UIUC（伊利诺伊大学厄巴纳-香槟分校）；U of Oregon（俄勒冈大学）；MIT-IBM Watson AI Lab & IBM Research（MIT-IBM沃森人工智能实验室与IBM研究院）；Picsart AI Research (PAIR)（Picsart AI研究（PAIR））
We study the problem of concept induction in visual reasoning, i.e., identifying concepts and their hierarchical relationships from question-answer pairs associated with images; and achieve an interpretable model via working on the induced symbolic concept space. To this end, we first design a new framework named object-centric compositional attention model (OCCAM) to perform the visual reasoning task with object-level visual features. Then, we come up with a method to induce concepts of objects and relations using clues from the attention patterns between objects' visual features and question…
Interpretable Robotic Friction Learning via Symbolic Regression
Ludwig-Maximilians-Universität München（慕尼黑路易斯-马克西米利安大学）；German Aerospace Center（德国航空航天中心）；University of Tromsø（特罗姆瑟大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）
Centrum Wiskunde & Informatica（荷兰国家数学与计算机科学研究所）；University of Trieste（的里雅斯特大学）；IMT School for Advanced Studies Lucca（卢卡IMT高等研究院）
Many risk-sensitive applications require Machine Learning (ML) models to be interpretable. Attempts to obtain interpretable models typically rely on tuning, by trial-and-error, hyper-parameters of model complexity that are only loosely related to interpretability. We show that it is instead possible to take a meta-learning approach: an ML model of non-trivial Proxies of Human Interpretability (PHIs) can be learned from human feedback, then this model can be incorporated within an ML training process to directly optimize for interpretability. We show this for evolutionary symbolic regression. W…
Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics
Department of Industrial Systems Engineering and Management, National University of Singapore（工业系统工程与管理系，新加坡国立大学）；Department of Civil, Environmental and Geomatic Engineering, ETH Zürich（土木、环境与测绘工程系，苏黎世联邦理工学院）；Future Resilient Systems, Singapore-ETH Centre（未来韧性系统，新加坡-苏黎世中心）
University of Cambridge（剑桥大学）；Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；Inria（法国国家信息与自动化研究所）；University of Siena（锡耶纳大学）；INRA（法国国家农业食品与环境研究院）；Université Paris-Saclay（巴黎萨克雷大学）；KU Leuven（鲁汶大学）
National Aeronautics and Space Administration（美国国家航空航天局）；University of Utah（犹他大学）
Interpretability and uncertainty quantification in machine learning can provide justification for decisions, promote scientific discovery and lead to a better understanding of model behavior. Symbolic regression provides inherently interpretable machine learning, but relatively little work has focused on the use of symbolic regression on noisy data and the accompanying necessity to quantify uncertainty. A new Bayesian framework for genetic-programming-based symbolic regression (GPSR) is introduced that uses model evidence (i.e., marginal likelihood) to formulate replacement probability during …
Learning Interpretable Network Dynamics via Universal Neural Symbolic Regression
College of Computer Science and Technology, Jilin University（吉林大学计算机科学与技术学院）；Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, Jilin University（吉林大学符号计算与知识工程教育部重点实验室）
Mathematics & Statistics, University of Vermont（数学与统计学系，佛蒙特大学）；Vermont Complex Systems Center, University of Vermont（佛蒙特复杂系统中心，佛蒙特大学）；Computer Science, University of Vermont（计算机科学系，佛蒙特大学）
Insight Centre for Data Analytics, University College Dublin（都柏林大学学院洞察数据分析中心）；Accenture Labs（埃森哲实验室）；Inria（法国国家信息与自动化研究所）
Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such trade-off is often hard to achieve since we lack human-independent interpretability metrics. We introduce a novel sequence learning algorithm, that combines (i) linear classifiers - which are known to strike a good balance between predictive power and interpretability, and (ii) background knowledge embeddings. We extend the classic subsequence feature space with g…
Closing the Loop: PID Feedback Control for Interpretable Activation Steering in Symbolic Music Generation
Athens University of Economics and Business（雅典经济与商业大学）；Orfium Research（Orfium 研究）；Hellenic Mediterranean University（希腊地中海大学）；Archimedes / Athena Research Center（阿基米德/雅典娜研究中心）
