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Different prediction models might perform equally well (Rashomon set) in the same task, but offer conflicting interpretations and conclusions about the data. The Rashomon effect in the context of Explainable AI (XAI) has been recognized as a critical factor. Although the Rashomon set has been introduced and studied in various contexts, its practical application is at its infancy stage and lacks adequate guidance and evaluation. We study the problem of the Rashomon set sampling from a practical viewpoint and identify two fundamental axioms - generalizability and implementation sparsity that exploring methods ought to satisfy in practical usage. These two axioms are not satisfied by most known attribution methods, which we consider to be a fundamental weakness. We use the norms to guide the design of an $\epsilon$-subgradient-based sampling method. We apply this method to a fundamental mathematical problem as a proof of concept and to a set of practical datasets to demonstrate its ability compared with existing sampling methods.

Explanations of machine learning models are important, especially in scientific areas such as chemistry, biology, and physics, where they guide future laboratory experiments and resource requirements. These explanations can be derived from well-trained machine learning models (data-driven perspective) or specific domain knowledge (domain-driven perspective). However, there exist inconsistencies between these perspectives due to accurate yet misleading machine learning models and various stakeholders with specific needs, wants, or aims. This paper calls attention to these inconsistencies and suggests a way to find an accurate model with expected explanations that reinforce physical laws and meet stakeholders' requirements from a set of equally-good models, also known as Rashomon sets. Our goal is to foster a comprehensive understanding of these inconsistencies and ultimately contribute to the integration of eXplainable Artificial Intelligence (XAI) into scientific domains.

The fractal dimension of a surface allows its degree of roughness to be characterized quantitatively. However, limited effort is attempted to calculate the fractal dimension of surfaces computed from precisely known atomic coordinates from computational biomolecular and nanomaterial studies. This work proposes methods to estimate the fractal dimension of the surface of any 3D object composed of spheres, by representing the surface as either a voxelized point cloud or a mathematically exact surface, and computing its box-counting dimension. Sphractal is published as a Python package that provides these functionalities, and its utility is demonstrated on a set of simulated palladium nanoparticle data., Comment: 18 pages, 13 figures

In this paper, we introduce the idea of decomposing the residuals of regression with respect to the data instances instead of features. This allows us to determine the effects of each individual instance on the model and each other, and in doing so makes for a model-agnostic method of identifying instances of interest. In doing so, we can also determine the appropriateness of the model and data in the wider context of a given study. The paper focuses on the possible applications that such a framework brings to the relatively unexplored field of instance analysis in the context of Explainable AI tasks., Comment: Accepted, 40th International Conference on Machine Learning

Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.

Black box models only provide results for deep learning tasks, and lack informative details about how these results were obtained. Knowing how input variables are related to outputs, in addition to why they are related, can be critical to translating predictions into laboratory experiments, or defending a model prediction under scrutiny. In this paper, we propose a general theory that defines a variance tolerance factor (VTF) inspired by influence function, to interpret features in the context of black box neural networks by ranking the importance of features, and construct a novel architecture consisting of a base model and feature model to explore the feature importance in a Rashomon set that contains all well-performing neural networks. Two feature importance ranking methods in the Rashomon set and a feature selection method based on the VTF are created and explored. A thorough evaluation on synthetic and benchmark datasets is provided, and the method is applied to two real world examples predicting the formation of noncrystalline gold nanoparticles and the chemical toxicity 1793 aromatic compounds exposed to a protozoan ciliate for 40 hours.

Iron oxides and oxyhydroxides are challenging to model computationally as competing phases may differ in formation energies by only several kJ/mol, they undergo magnetization transitions with temperature, their structures may contain partially occupied sites or long-range ordering of vacancies, and some loose structures require proper description of weak interactions such as hydrogen bonding and dispersive forces. If structures and transformations are to be reliably predicted under different chemical conditions, each of these challenges must be overcome simultaneously, while preserving a high level of numerical accuracy and physical sophistication. Here we present comparative studies of structure, magnetization, and elasticity properties of iron oxides and oxyhydroxides using density functional theory calculations with plane-wave and locally-confined-atomic-orbital basis sets, which are implemented in VASP and SIESTA packages, respectively. We have selected hematite, maghemite, goethite, lepidocrocite, and magnetite as model systems from a total of 13 known iron oxides and oxyhydroxides; and use same convergence criteria and almost equivalent settings in order to make consistent comparisons. Our results show both basis sets can reproduce the energetic stability and magnetic ordering, and are in agreement with experimental observations. There are advantages to choosing one basis set over the other, depending on the intended focus. In our case, we find the method using PW basis set most appropriate, and combine our results to construct the first phase diagram of iron oxides and oxyhydroxides in the space of competing chemical potentials, generated entirely from first principles, Comment: 46 pages - Accepted for publication in PRB (19 journal pages), January 2011

A reliable explanation for the underlying mechanism responsible for the persistent aggregation and self-assembly of colloidal 5 nm diamond nanoparticles is critical to the development of nanodiamond-based technologies. Although a number of mechanisms have been proposed, validation has been hindered by the inherent difficulty associated with the identification and characterisation of the inter-particle interfaces. In this paper we present results of high resolution aberration corrected electron microscopy and complementary computer simulations to explicate the features involved, and confirm the electrostatic interaction mechanism as the most probable cause for the formation of agglutinates and agglomerates of primary particles., Comment: 9 pages (including Supplementary Information), accepted for publication by Nanoscale

Fluorescent defects in non-cytotoxic diamond nanoparticles are candidates for qubits in quantum computing, optical labels in biomedical imaging and sensors in magnetometry. For each application these defects need to be optically and thermodynamically stable, and included in individual particles at suitable concentrations (singly or in large numbers). In this letter, we combine simulations, theory and experiment to provide the first comprehensive and generic prediction of the size, temperature and nitrogen-concentration dependent stability of optically active NV defects in nanodiamonds., Comment: Published in Nano Letters August 2009 24 pages, 6 figures