Kenneth L. McMillan
The notion of Craig interpolant, used as a form of explanation in automated reasoning, is adapted from logical inference to statistical inference and used to explain inferences made by neural networks. The method produces explanations that are at the same time concise, understandable and precise.
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Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs
本文提出了一种基于Langevin采样器和概率流ODE的方法，用于高效采样复杂分布并提升贝叶斯推断性能。
We introduce a method, KL-LIME, for explaining predictions of Bayesian predictive models by projecting the information in the predictive distribution locally to a simpler, interpretable explanation model. The proposed approach combines the recent Local Interpretable Model-agnostic Explanations (LIME) method with ideas from Bayesian projection predictive variable selection methods. The information theoretic basis helps in navigating the trade-off between explanation fidelity and complexity. We demonstrate the method in explaining MNIST digit classifications made by a Bayesian deep convolutional…
We consider the problem of the stability of saliency-based explanations of Neural Network predictions under adversarial attacks in a classification task. Saliency interpretations of deterministic Neural Networks are remarkably brittle even when the attacks fail, i.e. for attacks that do not change the classification label. We empirically show that interpretations provided by Bayesian Neural Networks are considerably more stable under adversarial perturbations of the inputs and even under direct attacks to the explanations. By leveraging recent results, we also provide a theoretical explanation…
This paper aims to improve the explainability of Autoencoder's (AE) predictions by proposing two explanation methods based on the mean and epistemic uncertainty of log-likelihood estimate, which naturally arise from the probabilistic formulation of the AE called Bayesian Autoencoders (BAE). To quantitatively evaluate the performance of explanation methods, we test them in sensor network applications, and propose three metrics based on covariate shift of sensors : (1) G-mean of Spearman drift coefficients, (2) G-mean of sensitivity-specificity of explanation ranking and (3) sensor explanation q…
A Bayesian explanation of machine learning models based on modes and functional ANOVA
本文提出一种基于贝叶斯框架和函数ANOVA分解的逆解释方法，通过特征距离排序解释标签偏差，相比SHAP更直观稳健，且额外成本与维度无关。
Explaining Bayesian Neural Networks
本文研究如何将局部归因方法扩展到贝叶斯神经网络，通过从近似后验中采样多个局部解释并分析其分布与可变性，从而为预测解释引入不确定性信息，并在多个数据集上验证了该框架的有效性。
EBLIME: Enhanced Bayesian Local Interpretable Model-agnostic Explanations
本研究提出增强型贝叶斯局部可解释模型无关解释方法EBLIME，通过贝叶斯岭回归获取特征重要性分布并给出相关理论结果，在基准数据集和工业缺陷定位应用中表现优于现有方法，不确定性量化能力更优。
Recent work in cognitive science has uncovered a diversity of explanatory values, or dimensions along which we judge explanations as better or worse. We propose a Bayesian account of how these values fit together to guide explanation. The resulting taxonomy provides a set of predictors for which explanations people prefer and shows how core values from psychology, statistics, and the philosophy of science emerge from a common mathematical framework. In addition to operationalizing the explanatory virtues associated with, for example, scientific argument-making, this framework also enables us t…
We introduce a simple and intuitive framework that provides quantitative explanations of statistical models through the probabilistic assessment of input feature importance. The core idea comes from utilizing the Dirichlet distribution to define the importance of input features and learning it via approximate Bayesian inference. The learned importance has probabilistic interpretation and provides the relative significance of each input feature to a model's output, additionally assessing confidence about its importance quantification. As a consequence of using the Dirichlet distribution over th…
Bayesian Networks and Machine Learning for COVID-19 Severity Explanation and Demographic Symptom Classification
针对COVID-19传播与重症相关的不确定性，研究提出结合贝叶斯网络与机器学习的三阶段方法，在CDC数据集上实现99.99%的测试准确率，助力理解症状关联与患者分层。
We seek to achieve the Holy Grail of Bayesian inference for gravitational-wave astronomy: using deep-learning techniques to instantly produce the posterior $p(θ|D)$ for the source parameters $θ$, given the detector data $D$. To do so, we train a deep neural network to take as input a signal + noise data set (drawn from the astrophysical source-parameter prior and the sampling distribution of detector noise), and to output a parametrized approximation of the corresponding posterior. We rely on a compact representation of the data based on reduced-order modeling, which we generate efficiently us…
Explainable AI (XAI) aims to provide interpretations for predictions made by learning machines, such as deep neural networks, in order to make the machines more transparent for the user and furthermore trustworthy also for applications in e.g. safety-critical areas. So far, however, no methods for quantifying uncertainties of explanations have been conceived, which is problematic in domains where a high confidence in explanations is a prerequisite. We therefore contribute by proposing a new framework that allows to convert any arbitrary explanation method for neural networks into an explanatio…
As black box explanations are increasingly being employed to establish model credibility in high-stakes settings, it is important to ensure that these explanations are accurate and reliable. However, prior work demonstrates that explanations generated by state-of-the-art techniques are inconsistent, unstable, and provide very little insight into their correctness and reliability. In addition, these methods are also computationally inefficient, and require significant hyper-parameter tuning. In this paper, we address the aforementioned challenges by developing a novel Bayesian framework for gen…
Prediction can be safely used as a proxy for explanation in causally consistent Bayesian generalized linear models
本文通过大规模模拟贝叶斯广义线性模型，研究模型选择中预测作为解释代理的有效性，发现仅当模型与真实因果结构一致时，该代理才安全有效。
Deep neural networks are complex and opaque. As they enter application in a variety of important and safety critical domains, users seek methods to explain their output predictions. We develop an approach to explaining deep neural networks by constructing causal models on salient concepts contained in a CNN. We develop methods to extract salient concepts throughout a target network by using autoencoders trained to extract human-understandable representations of network activations. We then build a bayesian causal model using these extracted concepts as variables in order to explain image class…
As we move away from the data, the predictive uncertainty should increase, since a great variety of explanations are consistent with the little available information. We introduce Distance-Aware Prior (DAP) calibration, a method to correct overconfidence of Bayesian deep learning models outside of the training domain. We define DAPs as prior distributions over the model parameters that depend on the inputs through a measure of their distance from the training set. DAP calibration is agnostic to the posterior inference method, and it can be performed as a post-processing step. We demonstrate it…
Despite all the benefits of automated hyperparameter optimization (HPO), most modern HPO algorithms are black-boxes themselves. This makes it difficult to understand the decision process which leads to the selected configuration, reduces trust in HPO, and thus hinders its broad adoption. Here, we study the combination of HPO with interpretable machine learning (IML) methods such as partial dependence plots. These techniques are more and more used to explain the marginal effect of hyperparameters on the black-box cost function or to quantify the importance of hyperparameters. However, if such m…
We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanation to the Bayesian Occam's razor criteria, under the assumption that the data is generated by an i.i.d distribution. Moreover, as the negative log-likelihood is an unbounded loss function, we motivate and propose a PAC-Bayesian theorem tailored for the sub-gamma loss family, and w…
It has recently been established that the numerical solution of ordinary differential equations can be posed as a nonlinear Bayesian inference problem, which can be approximately solved via Gaussian filtering and smoothing, whenever a Gauss--Markov prior is used. In this paper the class of $ν$ times differentiable linear time invariant Gauss--Markov priors is considered. A taxonomy of Gaussian estimators is established, with the maximum a posteriori estimate at the top of the hierarchy, which can be computed with the iterated extended Kalman smoother. The remaining three classes are termed exp…
Comparing Bayesian neural networks (BNNs) with different widths is challenging because, as the width increases, multiple model properties change simultaneously, and, inference in the finite-width case is intractable. In this work, we empirically compare finite- and infinite-width BNNs, and provide quantitative and qualitative explanations for their performance difference. We find that when the model is mis-specified, increasing width can hurt BNN performance. In these cases, we provide evidence that finite-width BNNs generalize better partially due to the properties of their frequency spectrum…
Explainable components in XAI algorithms often come from a familiar set of models, such as linear models or decision trees. We formulate an approach where the type of explanation produced is guided by a specification. Specifications are elicited from the user, possibly using interaction with the user and contributions from other areas. Areas where a specification could be obtained include forensic, medical, and scientific applications. Providing a menu of possible types of specifications in an area is an exploratory knowledge representation and reasoning task for the algorithm designer, aiming…
We consider representation learning (hypothesis class $\mathcal{H} = \mathcal{F}\circ\mathcal{G}$) where training and test distributions can be different. Recent studies provide hints and failure examples for domain invariant representation learning, a common approach for this problem, but the explanations provided are somewhat different and do not provide a unified picture. In this paper, we provide new decompositions of risk which give finer-grained explanations and clarify potential generalization issues. For Single-Source Domain Adaptation, we give an exact decomposition (an equality) of t…
The Epistemic Value of Novel Predictive Success in Scientific and Criminal Investigations: A Bayesian Explanation
本文通过贝叶斯网络分析，在刑事案件背景下探讨新颖预测成功的认知价值，论证“新证据”与“旧证据”的强度分析可普遍应用于科学理论评估，以解决预测与容纳的哲学争议。
We present the Bayesian Case Model (BCM), a general framework for Bayesian case-based reasoning (CBR) and prototype classification and clustering. BCM brings the intuitive power of CBR to a Bayesian generative framework. The BCM learns prototypes, the "quintessential" observations that best represent clusters in a dataset, by performing joint inference on cluster labels, prototypes and important features. Simultaneously, BCM pursues sparsity by learning subspaces, the sets of features that play important roles in the characterization of the prototypes. The prototype and subspace representation…
To construct interpretable explanations that are consistent with the original ML model, counterfactual examples---showing how the model's output changes with small perturbations to the input---have been proposed. This paper extends the work in counterfactual explanations by addressing the challenge of feasibility of such examples. For explanations of ML models in critical domains such as healthcare and finance, counterfactual examples are useful for an end-user only to the extent that perturbation of feature inputs is feasible in the real world. We formulate the problem of feasibility as prese…
Deep Ensembles Secretly Perform Empirical Bayes
本研究揭示了深度集成实际上通过隐式学习数据依赖的先验来执行精确的贝叶斯平均，即实现经验贝叶斯程序，从而在理论上证明其合理性并解释其优越的经验性能。
Extracting Explanations, Justification, and Uncertainty from Black-Box Deep Neural Networks
本文提出一种贝叶斯方法，无需重训练即可从黑盒深度神经网络中提取解释、理由与不确定性，并在CIFAR-10上验证，显著提升可解释性与可靠性。
We show that a neural network with arbitrary depth and non-linearities, with dropout applied before every weight layer, is mathematically equivalent to an approximation to a well known Bayesian model. This interpretation might offer an explanation to some of dropout's key properties, such as its robustness to over-fitting. Our interpretation allows us to reason about uncertainty in deep learning, and allows the introduction of the Bayesian machinery into existing deep learning frameworks in a principled way. This document is an appendix for the main paper "Dropout as a Bayesian Approximation: …
Doctors often rely on their past experience in order to diagnose patients. For a doctor with enough experience, almost every patient would have similarities to key cases seen in the past, and each new patient could be viewed as a mixture of these key past cases. Because doctors often tend to reason this way, an efficient computationally aided diagnostic tool that thinks in the same way might be helpful in locating key past cases of interest that could assist with diagnosis. This article develops a novel mathematical model to mimic the type of logical thinking that physicians use when consideri…
Monografía de Estadística Bayesiana
本文是贝叶斯统计导论的课程笔记，前三章详细阐述贝叶斯范式，第四章介绍决策论基础，进而在第五章将参数化贝叶斯推断作为决策问题引入。
BDeu marginal likelihood score is a popular model selection criterion for selecting a Bayesian network structure based on sample data. This non-informative scoring criterion assigns same score for network structures that encode same independence statements. However, before applying the BDeu score, one must determine a single parameter, the equivalent sample size alpha. Unfortunately no generally accepted rule for determining the alpha parameter has been suggested. This is disturbing, since in this paper we show through a series of concrete experiments that the solution of the network structure…
ACE: Adapting sampling for Counterfactual Explanations
针对现有反事实解释方法样本效率低、黑盒模型评估成本高的问题，提出结合贝叶斯估计与随机优化的ACE算法，通过优先选择高信息量点减少查询次数，在保证反事实解释准确可行的同时提升了评估效率。
Walk the Talk? Measuring the Faithfulness of Large Language Model Explanations
针对大语言模型解释可能不忠实的问题，提出基于概念差异的忠实度定义，结合辅助LLM生成反事实与贝叶斯层次模型的估算方法，可量化并发现不忠实模式。
Probabilistic Conceptual Explainers: Trustworthy Conceptual Explanations for Vision Foundation Models
针对视觉Transformer事后可信解释方法不足的问题，提出含五项评判标准的变分贝叶斯解释框架PACE，通过建模图像块嵌入分布提供多层级概念解释，实验表明其性能优于现有最优方法。
The motivations for using variational inference (VI) in neural networks differ significantly from those in latent variable models. This has a counter-intuitive consequence; more expressive variational approximations can provide significantly worse predictions as compared to those with less expressive families. In this work we make two contributions. First, we identify a cause of this performance gap, variational over-pruning. Second, we introduce a theoretically grounded explanation for this phenomenon. Our perspective sheds light on several related published results and provides intuition int…
Post-hoc explanation methods are gaining popularity for interpreting, understanding, and debugging neural networks. Most analyses using such methods explain decisions in response to inputs drawn from the test set. However, the test set may have few examples that trigger some model behaviors, such as high-confidence failures or ambiguous classifications. To address these challenges, we introduce a flexible model inspection framework: Bayes-TrEx. Given a data distribution, Bayes-TrEx finds in-distribution examples with a specified prediction confidence. We demonstrate several use cases of Bayes-…
Machine learning techniques have been successfully applied to super-resolution tasks on natural images where visually pleasing results are sufficient. However in many scientific domains this is not adequate and estimations of errors and uncertainties are crucial. To address this issue we propose a Bayesian framework that decomposes uncertainties into epistemic and aleatoric uncertainties. We test the validity of our approach by super-resolving images of the Sun's magnetic field and by generating maps measuring the range of possible high resolution explanations compatible with a given low resol…
Few-Shot Multimodal Medical Imaging: A Theoretical Framework
本文提出少样本多模态医学影像的理论框架，通过样本复杂性、不确定性量化和可解释性分析，为低资源环境下的高效、可靠诊断模型设计提供理论基础。
We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to score-based structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and is given by the probability that a conditional independence test correctly shows that an edge cannot exist. What really distinguishes this new scoring function from earlier work is that it has the property of becoming computationally easier to maximize as the amount of data increases. We prove a polynomial sample complexity result, showing that maximizing …
Deep ensembles have been empirically shown to be a promising approach for improving accuracy, uncertainty and out-of-distribution robustness of deep learning models. While deep ensembles were theoretically motivated by the bootstrap, non-bootstrap ensembles trained with just random initialization also perform well in practice, which suggests that there could be other explanations for why deep ensembles work well. Bayesian neural networks, which learn distributions over the parameters of the network, are theoretically well-motivated by Bayesian principles, but do not perform as well as deep ens…
Training deep graph neural networks (GNNs) poses a challenging task, as the performance of GNNs may suffer from the number of hidden message-passing layers. The literature has focused on the proposals of {over-smoothing} and {under-reaching} to explain the performance deterioration of deep GNNs. In this paper, we propose a new explanation for such deteriorated performance phenomenon, {mis-simplification}, that is, mistakenly simplifying graphs by preventing self-loops and forcing edges to be unweighted. We show that such simplifying can reduce the potential of message-passing layers to capture…
This paper describes the Bayesian SIR modeling of the 3 waves of Covid-19 in two contrasting US states during 2020-2021. A variety of models are evaluated at the county level for goodness-of-fit and an assessment of confounding predictors is also made. It is found that models with three deprivation predictors and neighborhood effects are important. In addition the work index from Google mobility was also found to provide increased explanation of the transmission dynamic.
Long-tailed classification poses a challenge due to its heavy imbalance in class probabilities and tail-sensitivity risks with asymmetric misprediction costs. Recent attempts have used re-balancing loss and ensemble methods, but they are largely heuristic and depend heavily on empirical results, lacking theoretical explanation. Furthermore, existing methods overlook the decision loss, which characterizes different costs associated with tailed classes. This paper presents a general and principled framework from a Bayesian-decision-theory perspective, which unifies existing techniques including …
A salient approach to interpretable machine learning is to restrict modeling to simple models. In the Bayesian framework, this can be pursued by restricting the model structure and prior to favor interpretable models. Fundamentally, however, interpretability is about users' preferences, not the data generation mechanism; it is more natural to formulate interpretability as a utility function. In this work, we propose an interpretability utility, which explicates the trade-off between explanation fidelity and interpretability in the Bayesian framework. The method consists of two steps. First, a …
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this topic and a comprehensive experimental analysis of the most-known algorithms. We start by describing the distance metric learning problem and its main mathematical foundations, divided into three main blocks: convex analysis, matrix analysis and information theory. Then, we will describe a representative set of the most popular distance metric learning methods u…
Explainable Bayesian deep learning through input-skip Latent Binary Bayesian Neural Networks
研究用人工神经网络建模自然现象的问题，核心方法是提出输入跳跃潜在二元贝叶斯神经网络。主要贡献是简化网络、量化不确定性、识别协变量、调整非线性，还引入活跃路径增强解释。
BioBO: Biology-informed Bayesian Optimization for Perturbation Design
BioBO结合多模态基因嵌入和富集分析，提升代理建模和获取策略，提高标签效率25-40%，并提供路径级解释，链接设计与生物调控电路。
Income, education, and other poverty-related variables: a journey through Bayesian hierarchical models
本研究提出使用贝叶斯分层模型分析泰国多分辨率治理结构中的贫困相关变量，发现其优于完全池化和无池化模型，并揭示教育在地区与家庭收入间起中介作用。
General bounds on the quality of Bayesian coresets
本文提出了贝叶斯核心集近似的KL散度通用上下界，适用于广泛的模型范围，并利用下界解释了重要性采样方法性能差的原因，利用上界分析了子样本优化方法的表现。
An important aspect of Bayesian model selection is how to deal with huge model spaces, since exhaustive enumeration of all the models entertained is unfeasible and inferences have to be based on the very small proportion of models visited. This is the case for the variable selection problem, with a moderate to large number of possible explanatory variables being considered in this paper. We review some of the strategies proposed in the literature and argue that inferences based on empirical frequencies via Markov Chain Monte Carlo sampling of the posterior distribution outperforms recently pro…
Inverse decision-making using neural amortized Bayesian actors
针对连续动作任务中贝叶斯决策模型逆向推断的计算难题，提出用无监督预训练神经网络摊销贝叶斯执行者，实现高效基于梯度的参数推断，有效解释个体行为模式并支持模型比较。
Product risk assessment is the overall process of determining whether a product, which could be anything from a type of washing machine to a type of teddy bear, is judged safe for consumers to use. There are several methods used for product risk assessment, including RAPEX, which is the primary method used by regulators in the UK and EU. However, despite its widespread use, we identify several limitations of RAPEX including a limited approach to handling uncertainty and the inability to incorporate causal explanations for using and interpreting test data. In contrast, Bayesian Networks (BNs) a…
Witnessing Quantum Bayesian Inference beyond Classical Learning
本文证明量子贝叶斯逆推可产生与任何经典贝叶斯学习不相容的预测，且五结果测量即突破经典界限，展示其更强的表达力。
Robust Domain Generalisation with Causal Invariant Bayesian Neural Networks
针对训练域与目标域不一致时深度神经网络性能骤降的问题，提出解耦数据分布学习与推理机制的因果不变贝叶斯神经网络，经理论和实验验证可近似因果干预推理，在分布外图像识别任务上优于点估计同类模型。
Explaining predictions from Bayesian networks, for example to physicians, is non-trivial. Various explanation methods for Bayesian network inference have appeared in literature, focusing on different aspects of the underlying reasoning. While there has been a lot of technical research, there is very little known about how well humans actually understand these explanations. In this paper, we present ongoing research in which four different explanation approaches were compared through a survey by asking a group of human participants to interpret the explanations.
Provably Robust Bayesian Counterfactual Explanations under Model Changes
本文提出PSCE方法，通过概率安全和鲁棒性保证，在模型变化下生成更可靠且具有判别性的反事实解释。
Bayesian Belief Networks have been largely overlooked by Expert Systems practitioners on the grounds that they do not correspond to the human inference mechanism. In this paper, we introduce an explanation mechanism designed to generate intuitive yet probabilistically sound explanations of inferences drawn by a Bayesian Belief Network. In particular, our mechanism accounts for the results obtained due to changes in the causal and the evidential support of a node.
Sparse Bayesian Multidimensional Item Response Theory
本文提出一种可扩展的贝叶斯EM算法，用于从混合数据中估计稀疏因子载荷并自动确定潜在因子维度，有效解决了传统MCMC方法在MIRT模型中速度慢且难以实现精确稀疏恢复的问题。
Regularizing Explanations in Bayesian Convolutional Neural Networks
针对贝叶斯神经网络无法通过权重分布注入领域知识、难纠正虚假特征关注的问题，提出兼容贝叶斯推理的解释正则化方法，提升模型在虚假特征场景下的预测性能且优于数据增强方法。
Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we explicate the desiderata of an explanation and confront them with the concept of explanation proposed by existing methods. The necessity of taking into account causal approaches when a causal graph is available is discussed. We then introduce causal explanation trees, based on the construction of explanation trees using the measure of causal information ow (Ay and Polani, 2006). This approach is compared to several other methods on known networks.
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