Growing complexity of closed box image classifiers has heightened the demand for explainable artificial intelligence (XAI) to offer transparency and trust for model decisions. Model-agnostic approaches have gained attention, as they provide explanations without accessing the closed box's internals, making them ideal for scenarios requiring data privacy and security. However, existing methods relying on superpixels face four challenges: (1) limited scalability, as superpixel-based features are coupled to specific image and cannot generalize; (2) low comprehensibility, due to the high dimensionality of superpixels and absence of clear semantic meaning; (3) lack of robustness, since uncertainty modeling is absent in explanation methods; (4) poor transferability, as integrating knowledge from human and explanations remains challenging. To alleviate these challenges, general type-2 hierarchical fuzzy model-agnostic explanation of image classification (GT2-HFMAE-I) is proposed to explain decisions of any closed box image classifier. Our innovations and contributions include the proposal of the framework, the algorithm, and the interface of GT2-HFMAE-I. First, the biaxial hierarchical framework is presented to formulate explanations with scalability along the spatial axis with local, domain and universe levels and the semantic axis with different segmentation granularity. Second, the model-agnostic algorithm is developed to identify explanatory features of image with semantic comprehensibility in low-dimensional space by combining superpixels and semantic segmentation, and train a general type-2 fuzzy logic system to approximate the closed box model with robustness to handle uncertainty in explanations. Third, a user interface, with feature salience to highlight image segments as the decision basis and semantic inference to present the decision logic via IF-THEN rules, is designed to deliver explanations to users with transferability. Finally, experiments with explanatory metrics show the competitive explanation quality of our method compared to mainstream model-agnostic methods on multiple datasets.

Instrumental variables (IVs) are widely used to estimate causal effects in the presence of unobserved confounding between an exposure $X$ and outcome $Y$. An IV must affect $Y$ exclusively through $X$ and be unconfounded with $Y$. We present a framework for relaxing these assumptions with tuneable and interpretable "budget constraints". Our algorithm returns a feasible set of causal effects that can be identified exactly given perfect knowledge of observable covariance statistics. This feasible set might contain disconnected sets of possible solutions for the causal effect. We discuss conditions under which this set is sharp, i.e., contains all and only effects consistent with the background assumptions and the joint distribution of observable variables. Our method applies to a wide class of semiparametric models, and we demonstrate how its ability to select specific subsets of instruments confers an advantage over convex relaxations in both linear and nonlinear settings. We adapt our algorithm to form confidence sets that are asymptotically valid under a common statistical assumption from the Mendelian randomization literature. An accompanying R package, budgetIVr, is available from CRAN.

We propose a principled method for autoencoding with random forests. Our strategy builds on foundational results from nonparametric statistics and spectral graph theory to learn a low-dimensional embedding of the model that optimally represents relationships in the data. We provide exact and approximate solutions to the decoding problem via constrained optimization, split relabeling, and nearest neighbors regression. These methods effectively invert the compression pipeline, establishing a map from the embedding space back to the input space using splits learned by the ensemble's constituent trees. The resulting decoders are universally consistent under common regularity assumptions. The procedure works with supervised or unsupervised models, providing a window into conditional or joint distributions. We demonstrate various applications of this autoencoder, including powerful new tools for visualization, compression, clustering, and denoising. Experiments illustrate the ease and utility of our method in a wide range of settings, including tabular, image, and genomic data.

Artificial intelligence (AI) has made remarkable achievements in extensive fields, whereas its closed boxnature limited applications in many critical areas. Against this drawback, explainable AI (XAI), has emerged as a focal point of current research. Recently, fuzzy logic systems (FLSs) attract increasing attention in XAI because of their linguistic representation, which can be naturally understood by humans. However, the focus of these works is limited by simply relying on inherent rule-based structures for explanation. Motivated by further exploring, the potential of FLS to overcome the challenges of XAI in terms of comprehensibility, scalability, and transferability, in this work, we propose fuzzy model-agnostic explanation (FMAE) as a post-hoc paradigm to explain the behavior of closed boxmodels. The innovations and contributions of this work provide a unified framework offering four levels of explanation, develop the associated algorithms to present the hidden knowledge behind the closed boxmodel in human-understandable form at different levels of granularity, and create the interface to deliver explanations to users. First, we introduce the hierarchical FMAE framework to formulate explanations into four levels including sample, local, domain, and universe. Second, the learning and explaining algorithms are developed to systematically construct FLS to model the behavior of closed boxmodels in the four levels where downscaling is performed by simplification to facilitate explanations with concise rules and upscaling is performed by the aggregation to integrate explanations at a higher level. Third, the proposed explanation interface unifies two typical forms of expression in XAI by fuzzy rules: the semantic inference explanation revealing the decision mechanism of the closed boxmodel and the feature salience explanation reflecting the attribution and interaction of input features. Simulated user experiments are designed on the comprehensive explanatory metrics. Compared with mainstream methods, the result shows outstanding explanation performance on real-world datasets for both regression and classification tasks.

Instrumental variables (IVs) are a popular and powerful tool for estimating causal effects in the presence of unobserved confounding. However, classical approaches rely on strong assumptions such as the exclusion criterion, which states that instrumental effects must be entirely mediated by treatments. This assumption often fails in practice. When IV methods are improperly applied to data that do not meet the exclusion criterion, estimated causal effects may be badly biased. In this work, we propose a novel solution that provides partial identification in linear systems given a set of leaky instruments, which are allowed to violate the exclusion criterion to some limited degree. We derive a convex optimization objective that provides provably sharp bounds on the average treatment effect under some common forms of information leakage, and implement inference procedures to quantify the uncertainty of resulting estimates. We demonstrate our method in a set of experiments with simulated data, where it performs favorably against the state of the art. An accompanying $\texttt{R}$ package, $\texttt{leakyIV}$, is available from $\texttt{CRAN}$.

We propose methods for density estimation and data synthesis using a novel form of unsupervised random forests. Inspired by generative adversarial networks, we implement a recursive procedure in which trees gradually learn structural properties of the data through alternating rounds of generation and discrimination. The method is provably consistent under minimal assumptions. Unlike classic tree-based alternatives, our approach provides smooth (un)conditional densities and allows for fully synthetic data generation. We achieve comparable or superior performance to state-of-the-art probabilistic circuits and deep learning models on various tabular data benchmarks while executing about two orders of magnitude faster on average. An accompanying $R$ package, $arf$, is available on $CRAN$.

One of the goals of causal inference is to generalize from past experiments and observational data to novel conditions. While it is in principle possible to eventually learn a mapping from a novel experimental condition to an outcome of interest, provided a sufficient variety of experiments is available in the training data, coping with a large combinatorial space of possible interventions is hard. Under a typical sparse experimental design, this mapping is ill-posed without relying on heavy regularization or prior distributions. Such assumptions may or may not be reliable, and can be hard to defend or test. In this paper, we take a close look at how to warrant a leap from past experiments to novel conditions based on minimal assumptions about the factorization of the distribution of the manipulated system, communicated in the well-understood language of factor graph models. A postulated interventional factor model (IFM) may not always be informative, but it conveniently abstracts away a need for explicitly modeling unmeasured confounding and feedback mechanisms, leading to directly testable claims. Given an IFM and datasets from a collection of experimental regimes, we derive conditions for identifiability of the expected outcomes of new regimes never observed in these training data. We implement our framework using several efficient algorithms, and apply them on a range of semi-synthetic experiments.

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has received relatively little attention. We adapt the popular Shapley value framework to explain various types of predictive uncertainty, quantifying each feature's contribution to the conditional entropy of individual model outputs. We consider games with modified characteristic functions and find deep connections between the resulting Shapley values and fundamental quantities from information theory and conditional independence testing. We outline inference procedures for finite sample error rate control with provable guarantees, and implement efficient algorithms that perform well in a range of experiments on real and simulated data. Our method has applications to covariate shift detection, active learning, feature selection, and active feature-value acquisition.

Inferring causal relationships from observational data is rarely straightforward, but the problem is especially difficult in high dimensions. For these applications, causal discovery algorithms typically require parametric restrictions or extreme sparsity constraints. We relax these assumptions and focus on an important but more specialized problem, namely recovering the causal order among a subgraph of variables known to descend from some (possibly large) set of confounding covariates, i.e. a $\textit{confounder blanket}$. This is useful in many settings, for example when studying a dynamic biomolecular subsystem with genetic data providing background information. Under a structural assumption called the $\textit{confounder blanket principle}$, which we argue is essential for tractable causal discovery in high dimensions, our method accommodates graphs of low or high sparsity while maintaining polynomial time complexity. We present a structure learning algorithm that is provably sound and complete with respect to a so-called $\textit{lazy oracle}$. We design inference procedures with finite sample error control for linear and nonlinear systems, and demonstrate our approach on a range of simulated and real-world datasets. An accompanying $\texttt{R}$ package, $\texttt{cbl}$, is available from $\texttt{CRAN}$.

We examine the problem of causal response estimation for complex objects (e.g., text, images, genomics). In this setting, classical \emph{atomic} interventions are often not available (e.g., changes to characters, pixels, DNA base-pairs). Instead, we only have access to indirect or \emph{crude} interventions (e.g., enrolling in a writing program, modifying a scene, applying a gene therapy). In this work, we formalize this problem and provide an initial solution. Given a collection of candidate mediators, we propose (a) a two-step method for predicting the causal responses of crude interventions; and (b) a testing procedure to identify mediators of crude interventions. We demonstrate, on a range of simulated and real-world-inspired examples, that our approach allows us to efficiently estimate the effect of crude interventions with limited data from new treatment regimes.

Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence (XAI), a fast-growing research area that is so far lacking in firm theoretical foundations. Building on work in logic, probability, and causality, we establish the central role of necessity and sufficiency in XAI, unifying seemingly disparate methods in a single formal framework. We provide a sound and complete algorithm for computing explanatory factors with respect to a given context, and demonstrate its flexibility and competitive performance against state of the art alternatives on various tasks.

Abstract We propose the conditional predictive impact (CPI), a consistent and unbiased estimator of the association between one or several features and a given outcome, conditional on a reduced feature set. Building on the knockoff framework of Candès et al. (J R Stat Soc Ser B 80:551–577, 2018), we develop a novel testing procedure that works in conjunction with any valid knockoff sampler, supervised learning algorithm, and loss function. The CPI can be efficiently computed for high-dimensional data without any sparsity constraints. We demonstrate convergence criteria for the CPI and develop statistical inference procedures for evaluating its magnitude, significance, and precision. These tests aid in feature and model selection, extending traditional frequentist and Bayesian techniques to general supervised learning tasks. The CPI may also be applied in causal discovery to identify underlying multivariate graph structures. We test our method using various algorithms, including linear regression, neural networks, random forests, and support vector machines. Empirical results show that the CPI compares favorably to alternative variable importance measures and other nonparametric tests of conditional independence on a diverse array of real and synthetic datasets. Simulations confirm that our inference procedures successfully control Type I error with competitive power in a range of settings. Our method has been implemented in an package, , which can be downloaded from https://github.com/dswatson/cpi .

MOTIVATION: Clustering patient omic data is integral to developing precision medicine because it allows the identification of disease subtypes. A current major challenge is the integration multi-omic data to identify a shared structure and reduce noise. Cluster analysis is also increasingly applied on single-omic data, for example, in single cell RNA-seq analysis for clustering the transcriptomes of individual cells. This technology has clinical implications. Our motivation was therefore to develop a flexible and effective spectral clustering tool for both single and multi-omic data. RESULTS: We present Spectrum, a new spectral clustering method for complex omic data. Spectrum uses a self-tuning density-aware kernel we developed that enhances the similarity between points that share common nearest neighbours. It uses a tensor product graph data integration and diffusion procedure to reduce noise and reveal underlying structures. Spectrum contains a new method for finding the optimal number of clusters (K) involving eigenvector distribution analysis. Spectrum can automatically find K for both Gaussian and non-Gaussian structures. We demonstrate across 21 real expression datasets that Spectrum gives improved runtimes and better clustering results relative to other methods. AVAILABILITY AND IMPLEMENTATION: Spectrum is available as an R software package from CRAN https://cran.r-project.org/web/packages/Spectrum/index.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.