Supervised Feature Selection with Neuron Evolution in Sparse Neural Networks

Abstract: Feature selection that selects an informative subset of variables from data not only enhances the model interpretability and performance but also alleviates the resource demands. Recently, there has been growing attention on feature selection using neural networks. However, existing methods usually suffer from high computational costs when applied to high-dimensional datasets. In this paper, inspired by evolution processes, we propose a novel resource-efficient supervised feature selection method using sparse neural networks, named \enquote{NeuroFS}. By gradually pruning the uninformative features from the input layer of a sparse neural network trained from scratch, NeuroFS derives an informative subset of features efficiently. By performing several experiments on $11$ low and high-dimensional real-world benchmarks of different types, we demonstrate that NeuroFS achieves the highest ranking-based score among the considered state-of-the-art supervised feature selection models. The code is available on GitHub.

Zahra Atashgahi
Xuhao Zhang
Neil Kichler
Shiwei Liu
Lu Yin
Mykola Pechenizkiy
Raymond Veldhuis
Decebal Constantin Mocanu


Towards Interpretable Federated Learning

Abstract: Federated learning (FL) enables multiple data owners to build machine learning models collaboratively without exposing their private local data. In order for FL to achieve widespread adoption, it is important to balance the need for performance, privacy-preservation and interpretability, especially in mission critical applications such as finance and healthcare. Thus, interpretable federated learning (IFL) has become an emerging topic of research attracting significant interest from the academia and the industry alike. Its interdisciplinary nature can be challenging for new researchers to pick up. In this paper, we bridge this gap by providing (to the best of our knowledge) the first survey on IFL. We propose a unique IFL taxonomy which covers relevant works enabling FL models to explain the prediction results, support model debugging, and provide insights into the contributions made by individual data owners or data samples, which in turn, is crucial for allocating rewards fairly to motivate active and reliable participation in FL. We conduct comprehensive analysis of the representative IFL approaches, the commonly adopted performance evaluation metrics, and promising directions towards building versatile IFL techniques.

Anran Li
Rui Liu
Ming Hu
Yuanyuan Chen
Shipeng Wang
Lizhen Cui
Han Yu


Sparse, Geometric Autoencoder Models of V1

Abstract: The classical sparse coding model represents visual stimuli as a linear combination of a handful of learned basis functions that are Gabor-like when trained on natural image data. However, the Gabor-like filters learned by classical sparse coding far overpredict well-tuned simple cell receptive field (SCRF) profiles. A number of subsequent models have either discarded the sparse dictionary learning framework entirely or have yet to take advantage of the surge in unrolled, neural dictionary learning architectures. A key missing theme of these updates is a stronger notion of \emph{structured sparsity}. We propose an autoencoder architecture whose latent representations are implicitly, locally organized for spectral clustering, which begets artificial neurons better matched to observed primate data. The weighted-$\ell_1$ (WL) constraint in the autoencoder objective function maintains core ideas of the sparse coding framework, yet also offers a promising path to describe the differentiation of receptive fields in terms of a discriminative hierarchy in future work.


On marginal feature attributions of tree-based models

Abstract: Due to their power and ease of use, tree-based machine learning models, such as random forests and gradient-boosted tree ensembles, have become very popular. To interpret them, local feature attributions based on marginal expectations, e.g. marginal (interventional) Shapley, Owen or Banzhaf values, may be employed. Such methods are true to the model and implementation invariant, i.e. dependent only on the input-output function of the model. We contrast this with the popular TreeSHAP algorithm by presenting two (statistically similar) decision trees that compute the exact same function for which the "path-dependent" TreeSHAP yields different rankings of features, whereas the marginal Shapley values coincide. Furthermore, we discuss how the internal structure of tree-based models may be leveraged to help with computing their marginal feature attributions according to a linear game value. One important observation is that these are simple (piecewise-constant) functions with respect to a certain grid partition of the input space determined by the trained model. Another crucial observation, showcased by experiments with XGBoost, LightGBM and CatBoost libraries, is that only a portion of all features appears in a tree from the ensemble. Thus, the complexity of computing marginal Shapley (or Owen or Banzhaf) feature attributions may be reduced. This remains valid for a broader class of game values which we shall axiomatically characterize. A prime example is the case of CatBoost models where the trees are oblivious (symmetric) and the number of features in each of them is no larger than the depth. We exploit the symmetry to derive an explicit formula, with improved complexity and only in terms of the internal model parameters, for marginal Shapley (and Banzhaf and Owen) values of CatBoost models. This results in a fast, accurate algorithm for estimating these feature attributions.

Khashayar Filom
Alexey Miroshnikov
Konstandinos Kotsiopoulos
Arjun Ravi Kannan


Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learning

Abstract: The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes. This is accomplished here with the development of a novel graph neural network (GNN) autoencoding architecture with demonstrations on complex fluid flow applications. To address the first goal of interpretability, the GNN autoencoder achieves reduction in the number nodes in the encoding stage through an adaptive graph reduction procedure. This reduction procedure essentially amounts to flowfield-conditioned node sampling and sensor identification, and produces interpretable latent graph representations tailored to the flowfield reconstruction task in the form of so-called masked fields. These masked fields allow the user to (a) visualize where in physical space a given latent graph is active, and (b) interpret the time-evolution of the latent graph connectivity in accordance with the time-evolution of unsteady flow features (e.g. recirculation zones, shear layers) in the domain. To address the goal of unstructured mesh compatibility, the autoencoding architecture utilizes a series of multi-scale message passing (MMP) layers, each of which models information exchange among node neighborhoods at various lengthscales. The MMP layer, which augments standard single-scale message passing with learnable coarsening operations, allows the decoder to more efficiently reconstruct the flowfield from the identified regions in the masked fields. Analysis of latent graphs produced by the autoencoder for various model settings are conducted using using unstructured snapshot data sourced from large-eddy simulations in a backward-facing step (BFS) flow configuration with an OpenFOAM-based flow solver at high Reynolds numbers.

Shivam Barwey
Varun Shankar
Venkatasubramanian Viswanathan
Romit Maulik


Variational Autoencoder Learns Better Feature Representations for EEG-based Obesity Classification

Abstract: Obesity is a common issue in modern societies today that can lead to various diseases and significantly reduced quality of life. Currently, research has been conducted to investigate resting state EEG (electroencephalogram) signals with an aim to identify possible neurological characteristics associated with obesity. In this study, we propose a deep learning-based framework to extract the resting state EEG features for obese and lean subject classification. Specifically, a novel variational autoencoder framework is employed to extract subject-invariant features from the raw EEG signals, which are then classified by a 1-D convolutional neural network. Comparing with conventional machine learning and deep learning methods, we demonstrate the superiority of using VAE for feature extraction, as reflected by the significantly improved classification accuracies, better visualizations and reduced impurity measures in the feature representations. Future work can be directed to gaining an in-depth understanding regarding the spatial patterns that have been learned by the proposed model from a neurological view, as well as improving the interpretability of the proposed model by allowing it to uncover any temporal-related information.

Yuan Yue
Jeremiah D. Deng
Dirk De Ridder
Patrick Manning
Divya Adhia


Dictionary-based Manifold Learning

Abstract: We propose a paradigm for interpretable Manifold Learning for scientific data analysis, whereby we parametrize a manifold with $d$ smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a parametrization exists, we provide an algorithm for finding it based on sparse non-linear regression in the manifold tangent bundle, bypassing more standard manifold learning algorithms. We also discuss conditions for the existence of such parameterizations in function space and for successful recovery from finite samples. We demonstrate our method with experimental results from a real scientific domain.


CRC-RL: A Novel Visual Feature Representation Architecture for Unsupervised Reinforcement Learning

Abstract: This paper addresses the problem of visual feature representation learning with an aim to improve the performance of end-to-end reinforcement learning (RL) models. Specifically, a novel architecture is proposed that uses a heterogeneous loss function, called CRC loss, to learn improved visual features which can then be used for policy learning in RL. The CRC-loss function is a combination of three individual loss functions, namely, contrastive, reconstruction and consistency loss. The feature representation is learned in parallel to the policy learning while sharing the weight updates through a Siamese Twin encoder model. This encoder model is augmented with a decoder network and a feature projection network to facilitate computation of the above loss components. Through empirical analysis involving latent feature visualization, an attempt is made to provide an insight into the role played by this loss function in learning new action-dependent features and how they are linked to the complexity of the problems being solved. The proposed architecture, called CRC-RL, is shown to outperform the existing state-of-the-art methods on the challenging Deep mind control suite environments by a significant margin thereby creating a new benchmark in this field.

Darshita Jain
Anima Majumder
Samrat Dutta
Swagat Kumar


SparCA: Sparse Compressed Agglomeration for Feature Extraction and Dimensionality Reduction

Abstract: The most effective dimensionality reduction procedures produce interpretable features from the raw input space while also providing good performance for downstream supervised learning tasks. For many methods, this requires optimizing one or more hyperparameters for a specific task, which can limit generalizability. In this study we propose sparse compressed agglomeration (SparCA), a novel dimensionality reduction procedure that involves a multistep hierarchical feature grouping, compression, and feature selection process. We demonstrate the characteristics and performance of the SparCA method across heterogenous synthetic and real-world datasets, including images, natural language, and single cell gene expression data. Our results show that SparCA is applicable to a wide range of data types, produces highly interpretable features, and shows compelling performance on downstream supervised learning tasks without the need for hyperparameter tuning.

Leland Barnard
Farwa Ali
Hugo Botha
David T. Jones


A variational autoencoder-based nonnegative matrix factorisation model for deep dictionary learning

Abstract: Construction of dictionaries using nonnegative matrix factorisation (NMF) has extensive applications in signal processing and machine learning. With the advances in deep learning, training compact and robust dictionaries using deep neural networks, i.e., dictionaries of deep features, has been proposed. In this study, we propose a probabilistic generative model which employs a variational autoencoder (VAE) to perform nonnegative dictionary learning. In contrast to the existing VAE models, we cast the model under a statistical framework with latent variables obeying a Gamma distribution and design a new loss function to guarantee the nonnegative dictionaries. We adopt an acceptance-rejection sampling reparameterization trick to update the latent variables iteratively. We apply the dictionaries learned from VAE-NMF to two signal processing tasks, i.e., enhancement of speech and extraction of muscle synergies. Experimental results demonstrate that VAE-NMF performs better in learning the latent nonnegative dictionaries in comparison with state-of-the-art methods.

Hong-Bo Xie
Caoyuan Li
Shuliang Wang
Richard Yi Da Xu
Kerrie Mengersen


Causal Abstraction: A Theoretical Foundation for Mechanistic Interpretability

Abstract: Causal abstraction provides a theoretical foundation for mechanistic interpretability, the field concerned with providing intelligible algorithms that are faithful simplifications of the known, but opaque low-level details of black box AI models. Our contributions are (1) generalizing the theory of causal abstraction from mechanism replacement (i.e., hard and soft interventions) to arbitrary mechanism transformation (i.e., functionals from old mechanisms to new mechanisms), (2) providing a flexible, yet precise formalization for the core concepts of polysemantic neurons, the linear representation hypothesis, modular features, and graded faithfulness, and (3) unifying a variety of mechanistic interpretability methods in the common language of causal abstraction, namely, activation and path patching, causal mediation analysis, causal scrubbing, causal tracing, circuit analysis, concept erasure, sparse autoencoders, differential binary masking, distributed alignment search, and steering.

Atticus Geiger
Duligur Ibeling
Amir Zur
Maheep Chaudhary
Sonakshi Chauhan
Jing Huang
Aryaman Arora
Zhengxuan Wu
Noah Goodman
Christopher Potts
Thomas Icard


Semantic match: Debugging feature attribution methods in XAI for healthcare

Abstract: The recent spike in certified Artificial Intelligence (AI) tools for healthcare has renewed the debate around adoption of this technology. One thread of such debate concerns Explainable AI (XAI) and its promise to render AI devices more transparent and trustworthy. A few voices active in the medical AI space have expressed concerns on the reliability of Explainable AI techniques and especially feature attribution methods, questioning their use and inclusion in guidelines and standards. Despite valid concerns, we argue that existing criticism on the viability of post-hoc local explainability methods throws away the baby with the bathwater by generalizing a problem that is specific to image data. We begin by characterizing the problem as a lack of semantic match between explanations and human understanding. To understand when feature importance can be used reliably, we introduce a distinction between feature importance of low- and high-level features. We argue that for data types where low-level features come endowed with a clear semantics, such as tabular data like Electronic Health Records (EHRs), semantic match can be obtained, and thus feature attribution methods can still be employed in a meaningful and useful way. Finally, we sketch a procedure to test whether semantic match has been achieved.

Giovanni Cinà
Tabea E. Röber
Rob Goedhart
Ş. İlker Birbil

ACM Conference on Health, Inference, and Learning


Mechanism of feature learning in deep fully connected networks and kernel machines that recursively learn features

Abstract: In recent years neural networks have achieved impressive results on many technological and scientific tasks. Yet, the mechanism through which these models automatically select features, or patterns in data, for prediction remains unclear. Identifying such a mechanism is key to advancing performance and interpretability of neural networks and promoting reliable adoption of these models in scientific applications. In this paper, we identify and characterize the mechanism through which deep fully connected neural networks learn features. We posit the Deep Neural Feature Ansatz, which states that neural feature learning occurs by implementing the average gradient outer product to up-weight features strongly related to model output. Our ansatz sheds light on various deep learning phenomena including emergence of spurious features and simplicity biases and how pruning networks can increase performance, the "lottery ticket hypothesis." Moreover, the mechanism identified in our work leads to a backpropagation-free method for feature learning with any machine learning model. To demonstrate the effectiveness of this feature learning mechanism, we use it to enable feature learning in classical, non-feature learning models known as kernel machines and show that the resulting models, which we refer to as Recursive Feature Machines, achieve state-of-the-art performance on tabular data.

Adityanarayanan Radhakrishnan
Daniel Beaglehole
Parthe Pandit
Mikhail Belkin


Rank-LIME: Local Model-Agnostic Feature Attribution for Learning to Rank

Abstract: Understanding why a model makes certain predictions is crucial when adapting it for real world decision making. LIME is a popular model-agnostic feature attribution method for the tasks of classification and regression. However, the task of learning to rank in information retrieval is more complex in comparison with either classification or regression. In this work, we extend LIME to propose Rank-LIME, a model-agnostic, local, post-hoc linear feature attribution method for the task of learning to rank that generates explanations for ranked lists. We employ novel correlation-based perturbations, differentiable ranking loss functions and introduce new metrics to evaluate ranking based additive feature attribution models. We compare Rank-LIME with a variety of competing systems, with models trained on the MS MARCO datasets and observe that Rank-LIME outperforms existing explanation algorithms in terms of Model Fidelity and Explain-NDCG. With this we propose one of the first algorithms to generate additive feature attributions for explaining ranked lists.

Tanya Chowdhury
Razieh Rahimi
James Allan

International Conference on the Theory of Information Retrieval


Impossibility Theorems for Feature Attribution

Abstract: Despite a sea of interpretability methods that can produce plausible explanations, the field has also empirically seen many failure cases of such methods. In light of these results, it remains unclear for practitioners how to use these methods and choose between them in a principled way. In this paper, we show that for moderately rich model classes (easily satisfied by neural networks), any feature attribution method that is complete and linear -- for example, Integrated Gradients and SHAP -- can provably fail to improve on random guessing for inferring model behaviour. Our results apply to common end-tasks such as characterizing local model behaviour, identifying spurious features, and algorithmic recourse. One takeaway from our work is the importance of concretely defining end-tasks: once such an end-task is defined, a simple and direct approach of repeated model evaluations can outperform many other complex feature attribution methods.

Blair Bilodeau
Natasha Jaques
Pang Wei Koh
Been Kim

Proceedings of the National Academy of Sciences of the United States of America


Learning Invariant Subspaces of Koopman Operators--Part 1: A Methodology for Demonstrating a Dictionary's Approximate Subspace Invariance

Abstract: Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary. In a widely used algorithm, Extended Dynamic Mode Decomposition, the dictionary functions are drawn from a fixed class of functions. Recently, deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Our results provide a hypothesis to explain the success of deep neural networks in learning numerical approximations to Koopman operators. Part 2 of this paper will extend this explanation by demonstrating the subspace invariant of heterogeneous dictionaries and presenting a head-to-head numerical comparison of deepDMD and low-parameter heterogeneous dictionary learning.

Charles A. Johnson
Shara Balakrishnan
Enoch Yeung


Data Leakage via Access Patterns of Sparse Features in Deep Learning-based Recommendation Systems

Abstract: Online personalized recommendation services are generally hosted in the cloud where users query the cloud-based model to receive recommended input such as merchandise of interest or news feed. State-of-the-art recommendation models rely on sparse and dense features to represent users' profile information and the items they interact with. Although sparse features account for 99% of the total model size, there was not enough attention paid to the potential information leakage through sparse features. These sparse features are employed to track users' behavior, e.g., their click history, object interactions, etc., potentially carrying each user's private information. Sparse features are represented as learned embedding vectors that are stored in large tables, and personalized recommendation is performed by using a specific user's sparse feature to index through the tables. Even with recently-proposed methods that hides the computation happening in the cloud, an attacker in the cloud may be able to still track the access patterns to the embedding tables. This paper explores the private information that may be learned by tracking a recommendation model's sparse feature access patterns. We first characterize the types of attacks that can be carried out on sparse features in recommendation models in an untrusted cloud, followed by a demonstration of how each of these attacks leads to extracting users' private information or tracking users by their behavior over time.

Hanieh Hashemi
Wenjie Xiong
Liu Ke
Kiwan Maeng
Murali Annavaram
G. Edward Suh
Hsien-Hsin S. Lee


Interpretable Node Representation with Attribute Decoding

Abstract: Variational Graph Autoencoders (VGAEs) are powerful models for unsupervised learning of node representations from graph data. In this work, we systematically analyze modeling node attributes in VGAEs and show that attribute decoding is important for node representation learning. We further propose a new learning model, interpretable NOde Representation with Attribute Decoding (NORAD). The model encodes node representations in an interpretable approach: node representations capture community structures in the graph and the relationship between communities and node attributes. We further propose a rectifying procedure to refine node representations of isolated notes, improving the quality of these nodes' representations. Our empirical results demonstrate the advantage of the proposed model when learning graph data in an interpretable approach.


Interpretability with full complexity by constraining feature information

Abstract: Interpretability is a pressing issue for machine learning. Common approaches to interpretable machine learning constrain interactions between features of the input, rendering the effects of those features on a model's output comprehensible but at the expense of model complexity. We approach interpretability from a new angle: constrain the information about the features without restricting the complexity of the model. Borrowing from information theory, we use the Distributed Information Bottleneck to find optimal compressions of each feature that maximally preserve information about the output. The learned information allocation, by feature and by feature value, provides rich opportunities for interpretation, particularly in problems with many features and complex feature interactions. The central object of analysis is not a single trained model, but rather a spectrum of models serving as approximations that leverage variable amounts of information about the inputs. Information is allocated to features by their relevance to the output, thereby solving the problem of feature selection by constructing a learned continuum of feature inclusion-to-exclusion. The optimal compression of each feature -- at every stage of approximation -- allows fine-grained inspection of the distinctions among feature values that are most impactful for prediction. We develop a framework for extracting insight from the spectrum of approximate models and demonstrate its utility on a range of tabular datasets.

International Conference on Learning Representations


Where to Pay Attention in Sparse Training for Feature Selection?

Abstract: A new line of research for feature selection based on neural networks has recently emerged. Despite its superiority to classical methods, it requires many training iterations to converge and detect informative features. The computational time becomes prohibitively long for datasets with a large number of samples or a very high dimensional feature space. In this paper, we present a new efficient unsupervised method for feature selection based on sparse autoencoders. In particular, we propose a new sparse training algorithm that optimizes a model's sparse topology during training to pay attention to informative features quickly. The attention-based adaptation of the sparse topology enables fast detection of informative features after a few training iterations. We performed extensive experiments on 10 datasets of different types, including image, speech, text, artificial, and biological. They cover a wide range of characteristics, such as low and high-dimensional feature spaces, and few and large training samples. Our proposed approach outperforms the state-of-the-art methods in terms of selecting informative features while reducing training iterations and computational costs substantially. Moreover, the experiments show the robustness of our method in extremely noisy environments.

Ghada Sokar
Zahra Atashgahi
Mykola Pechenizkiy
Decebal Constantin Mocanu


Mixture of Decision Trees for Interpretable Machine Learning

Abstract: This work introduces a novel interpretable machine learning method called Mixture of Decision Trees (MoDT). It constitutes a special case of the Mixture of Experts ensemble architecture, which utilizes a linear model as gating function and decision trees as experts. Our proposed method is ideally suited for problems that cannot be satisfactorily learned by a single decision tree, but which can alternatively be divided into subproblems. Each subproblem can then be learned well from a single decision tree. Therefore, MoDT can be considered as a method that improves performance while maintaining interpretability by making each of its decisions understandable and traceable to humans. Our work is accompanied by a Python implementation, which uses an interpretable gating function, a fast learning algorithm, and a direct interface to fine-tuned interpretable visualization methods. The experiments confirm that the implementation works and, more importantly, show the superiority of our approach compared to single decision trees and random forests of similar complexity.

Simeon Brüggenjürgen
Nina Schaaf
Pascal Kerschke
Marco F. Huber

International Conference on Machine Learning and Applications


Evaluating Feature Attribution Methods for Electrocardiogram

Abstract: The performance of cardiac arrhythmia detection with electrocardiograms(ECGs) has been considerably improved since the introduction of deep learning models. In practice, the high performance alone is not sufficient and a proper explanation is also required. Recently, researchers have started adopting feature attribution methods to address this requirement, but it has been unclear which of the methods are appropriate for ECG. In this work, we identify and customize three evaluation metrics for feature attribution methods based on the characteristics of ECG: localization score, pointing game, and degradation score. Using the three evaluation metrics, we evaluate and analyze eleven widely-used feature attribution methods. We find that some of the feature attribution methods are much more adequate for explaining ECG, where Grad-CAM outperforms the second-best method by a large margin.

Jangwon Suh
Jimyeong Kim
Euna Jung
Wonjong Rhee


Understanding Sparse Feature Updates in Deep Networks using Iterative Linearisation

Abstract: Larger and deeper networks generalise well despite their increased capacity to overfit. Understanding why this happens is theoretically and practically important. One recent approach looks at the infinitely wide limits of such networks and their corresponding kernels. However, these theoretical tools cannot fully explain finite networks as the empirical kernel changes significantly during gradient-descent-based training in contrast to infinite networks. In this work, we derive an iterative linearised training method as a novel empirical tool to further investigate this distinction, allowing us to control for sparse (i.e. infrequent) feature updates and quantify the frequency of feature learning needed to achieve comparable performance. We justify iterative linearisation as an interpolation between a finite analog of the infinite width regime, which does not learn features, and standard gradient descent training, which does. Informally, we also show that it is analogous to a damped version of the Gauss-Newton algorithm -- a second-order method. We show that in a variety of cases, iterative linearised training surprisingly performs on par with standard training, noting in particular how much less frequent feature learning is required to achieve comparable performance. We also show that feature learning is essential for good performance. Since such feature learning inevitably causes changes in the NTK kernel, we provide direct negative evidence for the NTK theory, which states the NTK kernel remains constant during training.


Interpretable Few-shot Learning with Online Attribute Selection

Abstract: Few-shot learning (FSL) presents a challenging learning problem in which only a few samples are available for each class. Decision interpretation is more important in few-shot classification due to a greater chance of error compared to traditional classification. However, the majority of the previous FSL methods are black-box models. In this paper, we propose an inherently interpretable model for FSL based on human-friendly attributes. Previously, human-friendly attributes have been utilized to train models with the potential for human interaction and interpretability. However, such approaches are not directly extendible to the few-shot classification scenario. Moreover, we propose an online attribute selection mechanism to effectively filter out irrelevant attributes in each episode. The attribute selection mechanism improves accuracy and helps with interpretability by reducing the number of attributes that participate in each episode. We further propose a mechanism that automatically detects the episodes where the pool of available human-friendly attributes is insufficient, and subsequently augments it by engaging some learned unknown attributes. We demonstrate that the proposed method achieves results on par with black-box few-shot learning models on four widely used datasets. We also empirically evaluate the level of decision alignment between different models and human understanding and show that our model outperforms the comparison methods based on this criterion.


Generalization Beyond Feature Alignment: Concept Activation-Guided Contrastive Learning

Abstract: Learning invariant representations via contrastive learning has seen state-of-the-art performance in domain generalization (DG). Despite such success, in this paper, we find that its core learning strategy -- feature alignment -- could heavily hinder model generalization. Drawing insights in neuron interpretability, we characterize this problem from a neuron activation view. Specifically, by treating feature elements as neuron activation states, we show that conventional alignment methods tend to deteriorate the diversity of learned invariant features, as they indiscriminately minimize all neuron activation differences. This instead ignores rich relations among neurons -- many of them often identify the same visual concepts despite differing activation patterns. With this finding, we present a simple yet effective approach, Concept Contrast (CoCo), which relaxes element-wise feature alignments by contrasting high-level concepts encoded in neurons. Our CoCo performs in a plug-and-play fashion, thus it can be integrated into any contrastive method in DG. We evaluate CoCo over four canonical contrastive methods, showing that CoCo promotes the diversity of feature representations and consistently improves model generalization capability. By decoupling this success through neuron coverage analysis, we further find that CoCo potentially invokes more meaningful neurons during training, thereby improving model learning.

Yibing Liu
Chris Xing Tian
Haoliang Li
Shiqi Wang


New Interpretable Patterns and Discriminative Features from Brain Functional Network Connectivity Using Dictionary Learning

Abstract: Independent component analysis (ICA) of multi-subject functional magnetic resonance imaging (fMRI) data has proven useful in providing a fully multivariate summary that can be used for multiple purposes. ICA can identify patterns that can discriminate between healthy controls (HC) and patients with various mental disorders such as schizophrenia (Sz). Temporal functional network connectivity (tFNC) obtained from ICA can effectively explain the interactions between brain networks. On the other hand, dictionary learning (DL) enables the discovery of hidden information in data using learnable basis signals through the use of sparsity. In this paper, we present a new method that leverages ICA and DL for the identification of directly interpretable patterns to discriminate between the HC and Sz groups. We use multi-subject resting-state fMRI data from $358$ subjects and form subject-specific tFNC feature vectors from ICA results. Then, we learn sparse representations of the tFNCs and introduce a new set of sparse features as well as new interpretable patterns from the learned atoms. Our experimental results show that the new representation not only leads to effective classification between HC and Sz groups using sparse features, but can also identify new interpretable patterns from the learned atoms that can help understand the complexities of mental diseases such as schizophrenia.

Fateme Ghayem
Hanlu Yang
Furkan Kantar
Seung-Jun Kim
Vince D. Calhoun
Tulay Adali

IEEE International Conference on Acoustics, Speech, and Signal Processing


Individualized and Global Feature Attributions for Gradient Boosted Trees in the Presence of $\ell_2$ Regularization

Abstract: While $\ell_2$ regularization is widely used in training gradient boosted trees, popular individualized feature attribution methods for trees such as Saabas and TreeSHAP overlook the training procedure. We propose Prediction Decomposition Attribution (PreDecomp), a novel individualized feature attribution for gradient boosted trees when they are trained with $\ell_2$ regularization. Theoretical analysis shows that the inner product between PreDecomp and labels on in-sample data is essentially the total gain of a tree, and that it can faithfully recover additive models in the population case when features are independent. Inspired by the connection between PreDecomp and total gain, we also propose TreeInner, a family of debiased global feature attributions defined in terms of the inner product between any individualized feature attribution and labels on out-sample data for each tree. Numerical experiments on a simulated dataset and a genomic ChIP dataset show that TreeInner has state-of-the-art feature selection performance. Code reproducing experiments is available at https://github.com/nalzok/TreeInner .


A robust estimator of mutual information for deep learning interpretability

Abstract: We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced $``$Jimmie$"$), an algorithm based on Gaussian mixture models that can be applied to both discrete and continuous settings. GMM-MI is computationally efficient, robust to the choice of hyperparameters and provides the uncertainty on the MI estimate due to the finite sample size. We extensively validate GMM-MI on toy data for which the ground truth MI is known, comparing its performance against established mutual information estimators. We then demonstrate the use of our MI estimator in the context of representation learning, working with synthetic data and physical datasets describing highly non-linear processes. We train deep learning models to encode high-dimensional data within a meaningful compressed (latent) representation, and use GMM-MI to quantify both the level of disentanglement between the latent variables, and their association with relevant physical quantities, thus unlocking the interpretability of the latent representation. We make GMM-MI publicly available.

Davide Piras
Hiranya V. Peiris
Andrew Pontzen
Luisa Lucie-Smith
Ningyuan Guo
Brian Nord

Machine Learning: Science and Technology, Volume 4, Number 2, 025006, April 2023


Abstract Interpretation-Based Feature Importance for SVMs

Abstract: We propose a symbolic representation for support vector machines (SVMs) by means of abstract interpretation, a well-known and successful technique for designing and implementing static program analyses. We leverage this abstraction in two ways: (1) to enhance the interpretability of SVMs by deriving a novel feature importance measure, called abstract feature importance (AFI), that does not depend in any way on a given dataset of the accuracy of the SVM and is very fast to compute, and (2) for verifying stability, notably individual fairness, of SVMs and producing concrete counterexamples when the verification fails. We implemented our approach and we empirically demonstrated its effectiveness on SVMs based on linear and non-linear (polynomial and radial basis function) kernels. Our experimental results show that, independently of the accuracy of the SVM, our AFI measure correlates much more strongly with the stability of the SVM to feature perturbations than feature importance measures widely available in machine learning software such as permutation feature importance. It thus gives better insight into the trustworthiness of SVMs.

Abhinandan Pal
Francesco Ranzato
Caterina Urban
Marco Zanella


Gradient Backpropagation based Feature Attribution to Enable Explainable-AI on the Edge

Abstract: There has been a recent surge in the field of Explainable AI (XAI) which tackles the problem of providing insights into the behavior of black-box machine learning models. Within this field, \textit{feature attribution} encompasses methods which assign relevance scores to input features and visualize them as a heatmap. Designing flexible accelerators for multiple such algorithms is challenging since the hardware mapping of these algorithms has not been studied yet. In this work, we first analyze the dataflow of gradient backpropagation based feature attribution algorithms to determine the resource overhead required over inference. The gradient computation is optimized to minimize the memory overhead. Second, we develop a High-Level Synthesis (HLS) based configurable FPGA design that is targeted for edge devices and supports three feature attribution algorithms. Tile based computation is employed to maximally use on-chip resources while adhering to the resource constraints. Representative CNNs are trained on CIFAR-10 dataset and implemented on multiple Xilinx FPGAs using 16-bit fixed-point precision demonstrating flexibility of our library. Finally, through efficient reuse of allocated hardware resources, our design methodology demonstrates a pathway to repurpose inference accelerators to support feature attribution with minimal overhead, thereby enabling real-time XAI on the edge.

Ashwin Bhat
Adou Sangbone Assoa
Arijit Raychowdhury

IEEE/IFIP International Conference on Very Large Scale Integration of System-on-Chip


Dictionary Learning for the Almost-Linear Sparsity Regime

Abstract: Dictionary learning, the problem of recovering a sparsely used matrix $\mathbf{D} \in \mathbb{R}^{M \times K}$ and $N$ $s$-sparse vectors $\mathbf{x}_i \in \mathbb{R}^{K}$ from samples of the form $\mathbf{y}_i = \mathbf{D}\mathbf{x}_i$, is of increasing importance to applications in signal processing and data science. When the dictionary is known, recovery of $\mathbf{x}_i$ is possible even for sparsity linear in dimension $M$, yet to date, the only algorithms which provably succeed in the linear sparsity regime are Riemannian trust-region methods, which are limited to orthogonal dictionaries, and methods based on the sum-of-squares hierarchy, which requires super-polynomial time in order to obtain an error which decays in $M$. In this work, we introduce SPORADIC (SPectral ORAcle DICtionary Learning), an efficient spectral method on family of reweighted covariance matrices. We prove that in high enough dimensions, SPORADIC can recover overcomplete ($K > M$) dictionaries satisfying the well-known restricted isometry property (RIP) even when sparsity is linear in dimension up to logarithmic factors. Moreover, these accuracy guarantees have an ``oracle property" that the support and signs of the unknown sparse vectors $\mathbf{x}_i$ can be recovered exactly with high probability, allowing for arbitrarily close estimation of $\mathbf{D}$ with enough samples in polynomial time. To the author's knowledge, SPORADIC is the first polynomial-time algorithm which provably enjoys such convergence guarantees for overcomplete RIP matrices in the near-linear sparsity regime.

Computer Science
Engineering
Mathematics

International Conference on Algorithmic Learning Theory


Interpreting County Level COVID-19 Infection and Feature Sensitivity using Deep Learning Time Series Models

Abstract: 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.

Md Khairul Islam
Di Zhu
Yingzheng Liu
Andrej Erkelens
Nick Daniello
Judy Fox


Minimalistic Unsupervised Learning with the Sparse Manifold Transform

Abstract: We describe a minimalistic and interpretable method for unsupervised learning, without resorting to data augmentation, hyperparameter tuning, or other engineering designs, that achieves performance close to the SOTA SSL methods. Our approach leverages the sparse manifold transform, which unifies sparse coding, manifold learning, and slow feature analysis. With a one-layer deterministic sparse manifold transform, one can achieve 99.3% KNN top-1 accuracy on MNIST, 81.1% KNN top-1 accuracy on CIFAR-10 and 53.2% on CIFAR-100. With a simple gray-scale augmentation, the model gets 83.2% KNN top-1 accuracy on CIFAR-10 and 57% on CIFAR-100. These results significantly close the gap between simplistic "white-box" methods and the SOTA methods. Additionally, we provide visualization to explain how an unsupervised representation transform is formed. The proposed method is closely connected to latent-embedding self-supervised methods and can be treated as the simplest form of VICReg. Though there remains a small performance gap between our simple constructive model and SOTA methods, the evidence points to this as a promising direction for achieving a principled and white-box approach to unsupervised learning.

Yubei Chen
Zeyu Yun
Yi Ma
Bruno Olshausen
Yann LeCun


Higher-order Neural Additive Models: An Interpretable Machine Learning Model with Feature Interactions

Abstract: Neural Additive Models (NAMs) have recently demonstrated promising predictive performance while maintaining interpretability. However, their capacity is limited to capturing only first-order feature interactions, which restricts their effectiveness on real-world datasets. To address this limitation, we propose Higher-order Neural Additive Models (HONAMs), an interpretable machine learning model that effectively and efficiently captures feature interactions of arbitrary orders. HONAMs improve predictive accuracy without compromising interpretability, an essential requirement in high-stakes applications. This advantage of HONAM can help analyze and extract high-order interactions present in datasets. The source code for HONAM is publicly available at https://github.com/gim4855744/HONAM/.


WeightedSHAP: analyzing and improving Shapley based feature attributions

Abstract: Shapley value is a popular approach for measuring the influence of individual features. While Shapley feature attribution is built upon desiderata from game theory, some of its constraints may be less natural in certain machine learning settings, leading to unintuitive model interpretation. In particular, the Shapley value uses the same weight for all marginal contributions -- i.e. it gives the same importance when a large number of other features are given versus when a small number of other features are given. This property can be problematic if larger feature sets are more or less informative than smaller feature sets. Our work performs a rigorous analysis of the potential limitations of Shapley feature attribution. We identify simple settings where the Shapley value is mathematically suboptimal by assigning larger attributions for less influential features. Motivated by this observation, we propose WeightedSHAP, which generalizes the Shapley value and learns which marginal contributions to focus directly from data. On several real-world datasets, we demonstrate that the influential features identified by WeightedSHAP are better able to recapitulate the model's predictions compared to the features identified by the Shapley value.


In-context Learning and Induction Heads

Abstract: "Induction heads" are attention heads that implement a simple algorithm to complete token sequences like [A][B] ... [A] -> [B]. In this work, we present preliminary and indirect evidence for a hypothesis that induction heads might constitute the mechanism for the majority of all "in-context learning" in large transformer models (i.e. decreasing loss at increasing token indices). We find that induction heads develop at precisely the same point as a sudden sharp increase in in-context learning ability, visible as a bump in the training loss. We present six complementary lines of evidence, arguing that induction heads may be the mechanistic source of general in-context learning in transformer models of any size. For small attention-only models, we present strong, causal evidence; for larger models with MLPs, we present correlational evidence.

Catherine Olsson
Nelson Elhage
Neel Nanda
Nicholas Joseph
Nova DasSarma
Tom Henighan
Ben Mann
Amanda Askell
Yuntao Bai
Anna Chen
Tom Conerly
Dawn Drain
Deep Ganguli
Zac Hatfield-Dodds
Danny Hernandez
Scott Johnston
Andy Jones
Jackson Kernion
Liane Lovitt
Kamal Ndousse
Dario Amodei
Tom Brown
Jack Clark
Jared Kaplan
Sam McCandlish
Chris Olah


Sparse Interaction Additive Networks via Feature Interaction Detection and Sparse Selection

Abstract: There is currently a large gap in performance between the statistically rigorous methods like linear regression or additive splines and the powerful deep methods using neural networks. Previous works attempting to close this gap have failed to fully investigate the exponentially growing number of feature combinations which deep networks consider automatically during training. In this work, we develop a tractable selection algorithm to efficiently identify the necessary feature combinations by leveraging techniques in feature interaction detection. Our proposed Sparse Interaction Additive Networks (SIAN) construct a bridge from these simple and interpretable models to fully connected neural networks. SIAN achieves competitive performance against state-of-the-art methods across multiple large-scale tabular datasets and consistently finds an optimal tradeoff between the modeling capacity of neural networks and the generalizability of simpler methods.


Error Controlled Feature Selection for Ultrahigh Dimensional and Highly Correlated Feature Space Using Deep Learning

Abstract: In recent years, deep learning has been at the center of analytics due to its impressive empirical success in analyzing complex data objects. Despite this success, most of the existing tools behave like black-box machines, thus the increasing interest in interpretable, reliable, and robust deep learning models applicable to a broad class of applications. Feature-selected deep learning has emerged as a promising tool in this realm. However, the recent developments do not accommodate ultra-high dimensional and highly correlated features, in addition to the high noise level. In this article, we propose a novel screening and cleaning method with the aid of deep learning for a data-adaptive multi-resolutional discovery of highly correlated predictors with a controlled error rate. Extensive empirical evaluations over a wide range of simulated scenarios and several real datasets demonstrate the effectiveness of the proposed method in achieving high power while keeping the false discovery rate at a minimum.

Arkaprabha Ganguli
David Todem
Tapabrata Maiti


"Is your explanation stable?": A Robustness Evaluation Framework for Feature Attribution

Abstract: Understanding the decision process of neural networks is hard. One vital method for explanation is to attribute its decision to pivotal features. Although many algorithms are proposed, most of them solely improve the faithfulness to the model. However, the real environment contains many random noises, which may leads to great fluctuations in the explanations. More seriously, recent works show that explanation algorithms are vulnerable to adversarial attacks. All of these make the explanation hard to trust in real scenarios. To bridge this gap, we propose a model-agnostic method \emph{Median Test for Feature Attribution} (MeTFA) to quantify the uncertainty and increase the stability of explanation algorithms with theoretical guarantees. MeTFA has the following two functions: (1) examine whether one feature is significantly important or unimportant and generate a MeTFA-significant map to visualize the results; (2) compute the confidence interval of a feature attribution score and generate a MeTFA-smoothed map to increase the stability of the explanation. Experiments show that MeTFA improves the visual quality of explanations and significantly reduces the instability while maintaining the faithfulness. To quantitatively evaluate the faithfulness of an explanation under different noise settings, we further propose several robust faithfulness metrics. Experiment results show that the MeTFA-smoothed explanation can significantly increase the robust faithfulness. In addition, we use two scenarios to show MeTFA's potential in the applications. First, when applied to the SOTA explanation method to locate context bias for semantic segmentation models, MeTFA-significant explanations use far smaller regions to maintain 99\%+ faithfulness. Second, when tested with different explanation-oriented attacks, MeTFA can help defend vanilla, as well as adaptive, adversarial attacks against explanations.

Yuyou Gan
Yuhao Mao
Xuhong Zhang
Shouling Ji
Yuwen Pu
Meng Han
Jianwei Yin
Ting Wang

Conference on Computer and Communications Security


EFI: A Toolbox for Feature Importance Fusion and Interpretation in Python

Abstract: This paper presents an open-source Python toolbox called Ensemble Feature Importance (EFI) to provide machine learning (ML) researchers, domain experts, and decision makers with robust and accurate feature importance quantification and more reliable mechanistic interpretation of feature importance for prediction problems using fuzzy sets. The toolkit was developed to address uncertainties in feature importance quantification and lack of trustworthy feature importance interpretation due to the diverse availability of machine learning algorithms, feature importance calculation methods, and dataset dependencies. EFI merges results from multiple machine learning models with different feature importance calculation approaches using data bootstrapping and decision fusion techniques, such as mean, majority voting and fuzzy logic. The main attributes of the EFI toolbox are: (i) automatic optimisation of ML algorithms, (ii) automatic computation of a set of feature importance coefficients from optimised ML algorithms and feature importance calculation techniques, (iii) automatic aggregation of importance coefficients using multiple decision fusion techniques, and (iv) fuzzy membership functions that show the importance of each feature to the prediction task. The key modules and functions of the toolbox are described, and a simple example of their application is presented using the popular Iris dataset.

Aayush Kumar
Jimiama Mafeni Mase
Divish Rengasamy
Benjamin Rothwell
Mercedes Torres Torres
David A. Winkler
Grazziela P. Figueredo

International Conference on Machine Learning, Optimization, and Data Science


Algorithms to estimate Shapley value feature attributions

Abstract: Feature attributions based on the Shapley value are popular for explaining machine learning models; however, their estimation is complex from both a theoretical and computational standpoint. We disentangle this complexity into two factors: (1)~the approach to removing feature information, and (2)~the tractable estimation strategy. These two factors provide a natural lens through which we can better understand and compare 24 distinct algorithms. Based on the various feature removal approaches, we describe the multiple types of Shapley value feature attributions and methods to calculate each one. Then, based on the tractable estimation strategies, we characterize two distinct families of approaches: model-agnostic and model-specific approximations. For the model-agnostic approximations, we benchmark a wide class of estimation approaches and tie them to alternative yet equivalent characterizations of the Shapley value. For the model-specific approximations, we clarify the assumptions crucial to each method's tractability for linear, tree, and deep models. Finally, we identify gaps in the literature and promising future research directions.

Hugh Chen
Ian C. Covert
Scott M. Lundberg
Su-In Lee


ControlBurn: Nonlinear Feature Selection with Sparse Tree Ensembles

Abstract: ControlBurn is a Python package to construct feature-sparse tree ensembles that support nonlinear feature selection and interpretable machine learning. The algorithms in this package first build large tree ensembles that prioritize basis functions with few features and then select a feature-sparse subset of these basis functions using a weighted lasso optimization criterion. The package includes visualizations to analyze the features selected by the ensemble and their impact on predictions. Hence ControlBurn offers the accuracy and flexibility of tree-ensemble models and the interpretability of sparse generalized additive models. ControlBurn is scalable and flexible: for example, it can use warm-start continuation to compute the regularization path (prediction error for any number of selected features) for a dataset with tens of thousands of samples and hundreds of features in seconds. For larger datasets, the runtime scales linearly in the number of samples and features (up to a log factor), and the package support acceleration using sketching. Moreover, the ControlBurn framework accommodates feature costs, feature groupings, and $\ell_0$-based regularizers. The package is user-friendly and open-source: its documentation and source code appear on https://pypi.org/project/ControlBurn/ and https://github.com/udellgroup/controlburn/.

Brian Liu
Miaolan Xie
Haoyue Yang
Madeleine Udell


Comparing Feature Importance and Rule Extraction for Interpretability on Text Data

Abstract: Complex machine learning algorithms are used more and more often in critical tasks involving text data, leading to the development of interpretability methods. Among local methods, two families have emerged: those computing importance scores for each feature and those extracting simple logical rules. In this paper we show that using different methods can lead to unexpectedly different explanations, even when applied to simple models for which we would expect qualitative coincidence. To quantify this effect, we propose a new approach to compare explanations produced by different methods.

2nd Workshop on Explainable and Ethical AI, 26th International Conference on Pattern Recognition (ICPR 2022)


Learning sparse features can lead to overfitting in neural networks

Abstract: It is widely believed that the success of deep networks lies in their ability to learn a meaningful representation of the features of the data. Yet, understanding when and how this feature learning improves performance remains a challenge: for example, it is beneficial for modern architectures trained to classify images, whereas it is detrimental for fully-connected networks trained for the same task on the same data. Here we propose an explanation for this puzzle, by showing that feature learning can perform worse than lazy training (via random feature kernel or the NTK) as the former can lead to a sparser neural representation. Although sparsity is known to be essential for learning anisotropic data, it is detrimental when the target function is constant or smooth along certain directions of input space. We illustrate this phenomenon in two settings: (i) regression of Gaussian random functions on the d-dimensional unit sphere and (ii) classification of benchmark datasets of images. For (i), we compute the scaling of the generalization error with number of training points, and show that methods that do not learn features generalize better, even when the dimension of the input space is large. For (ii), we show empirically that learning features can indeed lead to sparse and thereby less smooth representations of the image predictors. This fact is plausibly responsible for deteriorating the performance, which is known to be correlated with smoothness along diffeomorphisms.

Leonardo Petrini
Francesco Cagnetta
Eric Vanden-Eijnden
Matthieu Wyart


Multi-Omic Data Integration and Feature Selection for Survival-based Patient Stratification via Supervised Concrete Autoencoders

Abstract: Cancer is a complex disease with significant social and economic impact. Advancements in high-throughput molecular assays and the reduced cost for performing high-quality multi-omics measurements have fuelled insights through machine learning . Previous studies have shown promise on using multiple omic layers to predict survival and stratify cancer patients. In this paper, we developed a Supervised Autoencoder (SAE) model for survival-based multi-omic integration which improves upon previous work, and report a Concrete Supervised Autoencoder model (CSAE), which uses feature selection to jointly reconstruct the input features as well as predict survival. Our experiments show that our models outperform or are on par with some of the most commonly used baselines, while either providing a better survival separation (SAE) or being more interpretable (CSAE). We also perform a feature selection stability analysis on our models and notice that there is a power-law relationship with features which are commonly associated with survival. The code for this project is available at: https://github.com/phcavelar/coxae

Pedro Henrique da Costa Avelar
Roman Laddach
Sophia Karagiannis
Min Wu
Sophia Tsoka


Supervised Dictionary Learning with Auxiliary Covariates

Abstract: Supervised dictionary learning (SDL) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. The goal of SDL is to learn a class-discriminative dictionary, which is a set of latent feature vectors that can well-explain both the features as well as labels of observed data. In this paper, we provide a systematic study of SDL, including the theory, algorithm, and applications of SDL. First, we provide a novel framework that `lifts' SDL as a convex problem in a combined factor space and propose a low-rank projected gradient descent algorithm that converges exponentially to the global minimizer of the objective. We also formulate generative models of SDL and provide global estimation guarantees of the true parameters depending on the hyperparameter regime. Second, viewed as a nonconvex constrained optimization problem, we provided an efficient block coordinate descent algorithm for SDL that is guaranteed to find an $\varepsilon$-stationary point of the objective in $O(\varepsilon^{-1}(\log \varepsilon^{-1})^{2})$ iterations. For the corresponding generative model, we establish a novel non-asymptotic local consistency result for constrained and regularized maximum likelihood estimation problems, which may be of independent interest. Third, we apply SDL for imbalanced document classification by supervised topic modeling and also for pneumonia detection from chest X-ray images. We also provide simulation studies to demonstrate that SDL becomes more effective when there is a discrepancy between the best reconstructive and the best discriminative dictionaries.


Pruning for Feature-Preserving Circuits in CNNs

Abstract: Deep convolutional neural networks are a powerful model class for a range of computer vision problems, but it is difficult to interpret the image filtering process they implement, given their sheer size. In this work, we introduce a method for extracting 'feature-preserving circuits' from deep CNNs, leveraging methods from saliency-based neural network pruning. These circuits are modular sub-functions, embedded within the network, containing only a subset of convolutional kernels relevant to a target feature. We compare the efficacy of 3 saliency-criteria for extracting these sparse circuits. Further, we show how 'sub-feature' circuits can be extracted, that preserve a feature's responses to particular images, dividing the feature into even sparser filtering processes. We also develop a tool for visualizing 'circuit diagrams', which render the entire image filtering process implemented by circuits in a parsable format.

Chris Hamblin
Talia Konkle
George Alvarez


Interpretable Feature Engineering for Time Series Predictors using Attention Networks

Abstract: Regression problems with time-series predictors are common in banking and many other areas of application. In this paper, we use multi-head attention networks to develop interpretable features and use them to achieve good predictive performance. The customized attention layer explicitly uses multiplicative interactions and builds feature-engineering heads that capture temporal dynamics in a parsimonious manner. Convolutional layers are used to combine multivariate time series. We also discuss methods for handling static covariates in the modeling process. Visualization and explanation tools are used to interpret the results and explain the relationship between the inputs and the extracted features. Both simulation and real dataset are used to illustrate the usefulness of the methodology. Keyword: Attention heads, Deep neural networks, Interpretable feature engineering

Tianjie Wang
Jie Chen
Joel Vaughan
Vijayan N. Nair


Constructive Interpretability with CoLabel: Corroborative Integration, Complementary Features, and Collaborative Learning

Abstract: Machine learning models with explainable predictions are increasingly sought after, especially for real-world, mission-critical applications that require bias detection and risk mitigation. Inherent interpretability, where a model is designed from the ground-up for interpretability, provides intuitive insights and transparent explanations on model prediction and performance. In this paper, we present CoLabel, an approach to build interpretable models with explanations rooted in the ground truth. We demonstrate CoLabel in a vehicle feature extraction application in the context of vehicle make-model recognition (VMMR). CoLabel performs VMMR with a composite of interpretable features such as vehicle color, type, and make, all based on interpretable annotations of the ground truth labels. First, CoLabel performs corroborative integration to join multiple datasets that each have a subset of desired annotations of color, type, and make. Then, CoLabel uses decomposable branches to extract complementary features corresponding to desired annotations. Finally, CoLabel fuses them together for final predictions. During feature fusion, CoLabel harmonizes complementary branches so that VMMR features are compatible with each other and can be projected to the same semantic space for classification. With inherent interpretability, CoLabel achieves superior performance to the state-of-the-art black-box models, with accuracy of 0.98, 0.95, and 0.94 on CompCars, Cars196, and BoxCars116K, respectively. CoLabel provides intuitive explanations due to constructive interpretability, and subsequently achieves high accuracy and usability in mission-critical situations.

Abhijit Suprem
Sanjyot Vaidya
Suma Cherkadi
Purva Singh
Joao Eduardo Ferreira
Calton Pu

International Conference on Cognitive Machine Intelligence


Locally Aggregated Feature Attribution on Natural Language Model Understanding

Abstract: With the growing popularity of deep-learning models, model understanding becomes more important. Much effort has been devoted to demystify deep neural networks for better interpretability. Some feature attribution methods have shown promising results in computer vision, especially the gradient-based methods where effectively smoothing the gradients with reference data is key to a robust and faithful result. However, direct application of these gradient-based methods to NLP tasks is not trivial due to the fact that the input consists of discrete tokens and the "reference" tokens are not explicitly defined. In this work, we propose Locally Aggregated Feature Attribution (LAFA), a novel gradient-based feature attribution method for NLP models. Instead of relying on obscure reference tokens, it smooths gradients by aggregating similar reference texts derived from language model embeddings. For evaluation purpose, we also design experiments on different NLP tasks including Entity Recognition and Sentiment Analysis on public datasets as well as key feature detection on a constructed Amazon catalogue dataset. The superior performance of the proposed method is demonstrated through experiments.

Sheng Zhang
Jin Wang
Haitao Jiang
Rui Song

North American Chapter of the Association for Computational Linguistics


Physically Interpretable Feature Learning and Inverse Design of Supercritical Airfoils

Abstract: Machine-learning models have demonstrated a great ability to learn complex patterns and make predictions. In high-dimensional nonlinear problems of fluid dynamics, data representation often greatly affects the performance and interpretability of machine learning algorithms. With the increasing application of machine learning in fluid dynamics studies, the need for physically explainable models continues to grow. This paper proposes a feature learning algorithm based on variational autoencoders, which is able to assign physical features to some latent variables of the variational autoencoder. In addition, it is theoretically proved that the remaining latent variables are independent of the physical features. The proposed algorithm is trained to include shock wave features in its latent variables for the reconstruction of supercritical pressure distributions. The reconstruction accuracy and physical interpretability are also compared with those of other variational autoencoders. Then, the proposed algorithm is used for the inverse design of supercritical airfoils, which enables the generation of airfoil geometries based on physical features rather than the complete pressure distributions. It also demonstrates the ability to manipulate certain pressure distribution features of the airfoil without changing the others.


Geometric Deep Learning to Identify the Critical 3D Structural Features of the Optic Nerve Head for Glaucoma Diagnosis

Abstract: Purpose: The optic nerve head (ONH) undergoes complex and deep 3D morphological changes during the development and progression of glaucoma. Optical coherence tomography (OCT) is the current gold standard to visualize and quantify these changes, however the resulting 3D deep-tissue information has not yet been fully exploited for the diagnosis and prognosis of glaucoma. To this end, we aimed: (1) To compare the performance of two relatively recent geometric deep learning techniques in diagnosing glaucoma from a single OCT scan of the ONH; and (2) To identify the 3D structural features of the ONH that are critical for the diagnosis of glaucoma. Methods: In this study, we included a total of 2,247 non-glaucoma and 2,259 glaucoma scans from 1,725 subjects. All subjects had their ONHs imaged in 3D with Spectralis OCT. All OCT scans were automatically segmented using deep learning to identify major neural and connective tissues. Each ONH was then represented as a 3D point cloud. We used PointNet and dynamic graph convolutional neural network (DGCNN) to diagnose glaucoma from such 3D ONH point clouds and to identify the critical 3D structural features of the ONH for glaucoma diagnosis. Results: Both the DGCNN (AUC: 0.97$\pm$0.01) and PointNet (AUC: 0.95$\pm$0.02) were able to accurately detect glaucoma from 3D ONH point clouds. The critical points formed an hourglass pattern with most of them located in the inferior and superior quadrant of the ONH. Discussion: The diagnostic accuracy of both geometric deep learning approaches was excellent. Moreover, we were able to identify the critical 3D structural features of the ONH for glaucoma diagnosis that tremendously improved the transparency and interpretability of our method. Consequently, our approach may have strong potential to be used in clinical applications for the diagnosis and prognosis of a wide range of ophthalmic disorders.

Fabian A. Braeu
Alexandre H. Thiéry
Tin A. Tun
Aiste Kadziauskiene
George Barbastathis
Tin Aung
Michaël J. A. Girard

American journal of ophthalmology-glaucoma


Interpretability of Machine Learning Methods Applied to Neuroimaging

Abstract: Deep learning methods have become very popular for the processing of natural images, and were then successfully adapted to the neuroimaging field. As these methods are non-transparent, interpretability methods are needed to validate them and ensure their reliability. Indeed, it has been shown that deep learning models may obtain high performance even when using irrelevant features, by exploiting biases in the training set. Such undesirable situations can potentially be detected by using interpretability methods. Recently, many methods have been proposed to interpret neural networks. However, this domain is not mature yet. Machine learning users face two major issues when aiming to interpret their models: which method to choose, and how to assess its reliability? Here, we aim at providing answers to these questions by presenting the most common interpretability methods and metrics developed to assess their reliability, as well as their applications and benchmarks in the neuroimaging context. Note that this is not an exhaustive survey: we aimed to focus on the studies which we found to be the most representative and relevant.

Elina Thibeau-Sutre
Sasha Collin
Ninon Burgos
Olivier Colliot


Attributable Visual Similarity Learning

Abstract: This paper proposes an attributable visual similarity learning (AVSL) framework for a more accurate and explainable similarity measure between images. Most existing similarity learning methods exacerbate the unexplainability by mapping each sample to a single point in the embedding space with a distance metric (e.g., Mahalanobis distance, Euclidean distance). Motivated by the human semantic similarity cognition, we propose a generalized similarity learning paradigm to represent the similarity between two images with a graph and then infer the overall similarity accordingly. Furthermore, we establish a bottom-up similarity construction and top-down similarity inference framework to infer the similarity based on semantic hierarchy consistency. We first identify unreliable higher-level similarity nodes and then correct them using the most coherent adjacent lower-level similarity nodes, which simultaneously preserve traces for similarity attribution. Extensive experiments on the CUB-200-2011, Cars196, and Stanford Online Products datasets demonstrate significant improvements over existing deep similarity learning methods and verify the interpretability of our framework. Code is available at https://github.com/zbr17/AVSL.

Borui Zhang
Wenzhao Zheng
Jie Zhou
Jiwen Lu


Feature visualization for convolutional neural network models trained on neuroimaging data

Abstract: A major prerequisite for the application of machine learning models in clinical decision making is trust and interpretability. Current explainability studies in the neuroimaging community have mostly focused on explaining individual decisions of trained models, e.g. obtained by a convolutional neural network (CNN). Using attribution methods such as layer-wise relevance propagation or SHAP heatmaps can be created that highlight which regions of an input are more relevant for the decision than others. While this allows the detection of potential data set biases and can be used as a guide for a human expert, it does not allow an understanding of the underlying principles the model has learned. In this study, we instead show, to the best of our knowledge, for the first time results using feature visualization of neuroimaging CNNs. Particularly, we have trained CNNs for different tasks including sex classification and artificial lesion classification based on structural magnetic resonance imaging (MRI) data. We have then iteratively generated images that maximally activate specific neurons, in order to visualize the patterns they respond to. To improve the visualizations we compared several regularization strategies. The resulting images reveal the learned concepts of the artificial lesions, including their shapes, but remain hard to interpret for abstract features in the sex classification task.

Fabian Eitel
Anna Melkonyan
Kerstin Ritter


On Understanding the Influence of Controllable Factors with a Feature Attribution Algorithm: a Medical Case Study

Abstract: Feature attribution XAI algorithms enable their users to gain insight into the underlying patterns of large datasets through their feature importance calculation. Existing feature attribution algorithms treat all features in a dataset homogeneously, which may lead to misinterpretation of consequences of changing feature values. In this work, we consider partitioning features into controllable and uncontrollable parts and propose the Controllable fActor Feature Attribution (CAFA) approach to compute the relative importance of controllable features. We carried out experiments applying CAFA to two existing datasets and our own COVID-19 non-pharmaceutical control measures dataset. Experimental results show that with CAFA, we are able to exclude influences from uncontrollable features in our explanation while keeping the full dataset for prediction.

Veera Raghava Reddy Kovvuri
Siyuan Liu
Monika Seisenberger
Berndt Müller
Xiuyi Fan

International Symposium on INnovations in Intelligent SysTems and Applications


Attri-VAE: attribute-based interpretable representations of medical images with variational autoencoders

Abstract: Deep learning (DL) methods where interpretability is intrinsically considered as part of the model are required to better understand the relationship of clinical and imaging-based attributes with DL outcomes, thus facilitating their use in the reasoning behind medical decisions. Latent space representations built with variational autoencoders (VAE) do not ensure individual control of data attributes. Attribute-based methods enforcing attribute disentanglement have been proposed in the literature for classical computer vision tasks in benchmark data. In this paper, we propose a VAE approach, the Attri-VAE, that includes an attribute regularization term to associate clinical and medical imaging attributes with different regularized dimensions in the generated latent space, enabling a better-disentangled interpretation of the attributes. Furthermore, the generated attention maps explained the attribute encoding in the regularized latent space dimensions. Using the Attri-VAE approach we analyzed healthy and myocardial infarction patients with clinical, cardiac morphology, and radiomics attributes. The proposed model provided an excellent trade-off between reconstruction fidelity, disentanglement, and interpretability, outperforming state-of-the-art VAE approaches according to several quantitative metrics. The resulting latent space allowed the generation of realistic synthetic data in the trajectory between two distinct input samples or along a specific attribute dimension to better interpret changes between different cardiac conditions.

Irem Cetin
Maialen Stephens
Oscar Camara
Miguel Angel Gonzalez Ballester


Sparse Neural Additive Model: Interpretable Deep Learning with Feature Selection via Group Sparsity

Abstract: Interpretable machine learning has demonstrated impressive performance while preserving explainability. In particular, neural additive models (NAM) offer the interpretability to the black-box deep learning and achieve state-of-the-art accuracy among the large family of generalized additive models. In order to empower NAM with feature selection and improve the generalization, we propose the sparse neural additive models (SNAM) that employ the group sparsity regularization (e.g. Group LASSO), where each feature is learned by a sub-network whose trainable parameters are clustered as a group. We study the theoretical properties for SNAM with novel techniques to tackle the non-parametric truth, thus extending from classical sparse linear models such as the LASSO, which only works on the parametric truth. Specifically, we show that SNAM with subgradient and proximal gradient descents provably converges to zero training loss as $t\to\infty$, and that the estimation error of SNAM vanishes asymptotically as $n\to\infty$. We also prove that SNAM, similar to LASSO, can have exact support recovery, i.e. perfect feature selection, with appropriate regularization. Moreover, we show that the SNAM can generalize well and preserve the `identifiability', recovering each feature's effect. We validate our theories via extensive experiments and further testify to the good accuracy and efficiency of SNAM.

Shiyun Xu
Zhiqi Bu
Pratik Chaudhari
Ian J. Barnett


The Need for Interpretable Features: Motivation and Taxonomy

Abstract: Through extensive experience developing and explaining machine learning (ML) applications for real-world domains, we have learned that ML models are only as interpretable as their features. Even simple, highly interpretable model types such as regression models can be difficult or impossible to understand if they use uninterpretable features. Different users, especially those using ML models for decision-making in their domains, may require different levels and types of feature interpretability. Furthermore, based on our experiences, we claim that the term "interpretable feature" is not specific nor detailed enough to capture the full extent to which features impact the usefulness of ML explanations. In this paper, we motivate and discuss three key lessons: 1) more attention should be given to what we refer to as the interpretable feature space, or the state of features that are useful to domain experts taking real-world actions, 2) a formal taxonomy is needed of the feature properties that may be required by these domain experts (we propose a partial taxonomy in this paper), and 3) transforms that take data from the model-ready state to an interpretable form are just as essential as traditional ML transforms that prepare features for the model.

Alexandra Zytek
Ignacio Arnaldo
Dongyu Liu
Laure Berti-Equille
Kalyan Veeramachaneni


Evaluating Feature Attribution Methods in the Image Domain

Abstract: Feature attribution maps are a popular approach to highlight the most important pixels in an image for a given prediction of a model. Despite a recent growth in popularity and available methods, little attention is given to the objective evaluation of such attribution maps. Building on previous work in this domain, we investigate existing metrics and propose new variants of metrics for the evaluation of attribution maps. We confirm a recent finding that different attribution metrics seem to measure different underlying concepts of attribution maps, and extend this finding to a larger selection of attribution metrics. We also find that metric results on one dataset do not necessarily generalize to other datasets, and methods with desirable theoretical properties such as DeepSHAP do not necessarily outperform computationally cheaper alternatives. Based on these findings, we propose a general benchmarking approach to identify the ideal feature attribution method for a given use case. Implementations of attribution metrics and our experiments are available online.

Arne Gevaert
Axel-Jan Rousseau
Thijs Becker
Dirk Valkenborg
Tijl De Bie
Yvan Saeys


Dictionary learning for clustering on hyperspectral images

Abstract: Dictionary learning and sparse coding have been widely studied as mechanisms for unsupervised feature learning. Unsupervised learning could bring enormous benefit to the processing of hyperspectral images and to other remote sensing data analysis because labelled data are often scarce in this field. We propose a method for clustering the pixels of hyperspectral images using sparse coefficients computed from a representative dictionary as features. We show empirically that the proposed method works more effectively than clustering on the original pixels. We also demonstrate that our approach, in certain circumstances, outperforms the clustering results of features extracted using principal component analysis and non-negative matrix factorisation. Furthermore, our method is suitable for applications in repetitively clustering an ever-growing amount of high-dimensional data, which is the case when working with hyperspectral satellite imagery.


Visualizing the Diversity of Representations Learned by Bayesian Neural Networks

Abstract: Explainable Artificial Intelligence (XAI) aims to make learning machines less opaque, and offers researchers and practitioners various tools to reveal the decision-making strategies of neural networks. In this work, we investigate how XAI methods can be used for exploring and visualizing the diversity of feature representations learned by Bayesian Neural Networks (BNNs). Our goal is to provide a global understanding of BNNs by making their decision-making strategies a) visible and tangible through feature visualizations and b) quantitatively measurable with a distance measure learned by contrastive learning. Our work provides new insights into the \emph{posterior} distribution in terms of human-understandable feature information with regard to the underlying decision making strategies. The main findings of our work are the following: 1) global XAI methods can be applied to explain the diversity of decision-making strategies of BNN instances, 2) Monte Carlo dropout with commonly used Dropout rates exhibit increased diversity in feature representations compared to the multimodal posterior approximation of MultiSWAG, 3) the diversity of learned feature representations highly correlates with the uncertainty estimate for the output and 4) the inter-mode diversity of the multimodal posterior decreases as the network width increases, while the intra mode diversity increases. These findings are consistent with the recent Deep Neural Networks theory, providing additional intuitions about what the theory implies in terms of humanly understandable concepts.

Dennis Grinwald
Kirill Bykov
Shinichi Nakajima
Marina M. -C. Höhne

Published in Transactions on Machine Learning Research (11/2023)


Differentiable Rule Induction with Learned Relational Features

Abstract: Rule-based decision models are attractive due to their interpretability. However, existing rule induction methods often result in long and consequently less interpretable rule models. This problem can often be attributed to the lack of appropriately expressive vocabulary, i.e., relevant predicates used as literals in the decision model. Most existing rule induction algorithms presume pre-defined literals, naturally decoupling the definition of the literals from the rule learning phase. In contrast, we propose the Relational Rule Network (R2N), a neural architecture that learns literals that represent a linear relationship among numerical input features along with the rules that use them. This approach opens the door to increasing the expressiveness of induced decision models by coupling literal learning directly with rule learning in an end-to-end differentiable fashion. On benchmark tasks, we show that these learned literals are simple enough to retain interpretability, yet improve prediction accuracy and provide sets of rules that are more concise compared to state-of-the-art rule induction algorithms.

Remy Kusters
Yusik Kim
Marine Collery
Christian de Sainte Marie
Shubham Gupta

International Workshop on Neural-Symbolic Learning and Reasoning


Dictionary Learning with Uniform Sparse Representations for Anomaly Detection

Abstract: Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data and the smallest approximation error is a hard problem approached by dictionary learning (DL). We study how DL performs in detecting abnormal samples in a dataset of signals. In this paper we use a particular DL formulation that seeks uniform sparse representations model to detect the underlying subspace of the majority of samples in a dataset, using a K-SVD-type algorithm. Numerical simulations show that one can efficiently use this resulted subspace to discriminate the anomalies over the regular data points.

Paul Irofti
Cristian Rusu
Andrei Pătraşcu