Papers

Representation learners that disentangle factors of variation have already proven to be important in addressing various real world concerns such as fairness and interpretability. Initially consisting of unsupervised models with independence assumptions, more recently, weak supervision and correlated features have been explored, but without a causal view of the generative process. In contrast, we work under the regime of a causal generative process where generative factors are either independent or can be potentially confounded by a set of observed or unobserved confounders. We present an analysis of disentangled representations through the notion of disentangled causal process. We motivate the need for new metrics and datasets to study causal disentanglement and propose two evaluation metrics and a dataset. We show that our metrics capture the desiderata of disentangled causal process. Finally we perform an empirical study on state of the art disentangled representation learners using our metrics and dataset to evaluate them from causal perspective.

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Neural networks have a bias towards low frequency functions. This spectral bias has been the subject of several previous studies, both empirical and theoretical. Here we present a computable definition of the spectral bias based on a decomposition of the reconstruction error into a low and a high frequency component. The distinction between low and high frequencies is made in a way that allows for easy interpretation of the spectral bias. Furthermore, we present two methods for estimating the spectral bias. Method 1 relies on the use of the discrete Fourier transform to explicitly estimate the Fourier spectrum of the prediction residual, and Method 2 uses convolution to extract the low frequency components, where the convolution integral is estimated by Monte Carlo methods. The spectral bias depends on the distribution of the data, which is approximated with kernel density estimation when unknown. We devise a set of numerical experiments that confirm that low frequencies are learned first, a behavior quantified by our definition.

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The success of deep neural nets heavily relies on their ability to encode complex relations between their input and their output. While this property serves to fit the training data well, it also obscures the mechanism that drives prediction. This study aims to reveal hidden concepts by employing an intervention mechanism that shifts the predicted class based on discrete variational autoencoders. An explanatory model then visualizes the encoded information from any hidden layer and its corresponding intervened representation. By the assessment of differences between the original representation and the intervened representation, one can determine the concepts that can alter the class, hence providing interpretability. We demonstrate the effectiveness of our approach on CelebA, where we show various visualizations for bias in the data and suggest different interventions to reveal and change bias.

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The need to understand the inner workings of opaque Machine Learning models has prompted researchers to devise various types of post-hoc explanations. A large class of such explainers proceed in two phases: first perturb an input instance whose explanation is sought, and then generate an interpretable artifact to explain the prediction of the opaque model on that instance. Recently, Deutch and Frost proposed to use an additional input from the user: a set of constraints over the input space to guide the perturbation phase. While this approach affords the user the ability to tailor the explanation to their needs, striking a balance between flexibility, theoretical rigor and computational cost has remained an open challenge. We propose a novel constraint-driven explanation generation approach which simultaneously addresses these issues in a modular fashion. Our framework supports the use of expressive Boolean constraints giving the user more flexibility to specify the subspace to generate perturbations from. Leveraging advances in Formal Methods, we can theoretically guarantee strict adherence of the samples to the desired distribution. This also allows us to compute fidelity in a rigorous way, while scaling much better in practice. Our empirical study demonstrates concrete uses of our tool CLIME in obtaining more meaningful explanations with high fidelity.

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Explainable artificial intelligence has rapidly emerged since lawmakers have started requiring interpretable models for safety-critical domains. Concept-based neural networks have arisen as explainable-by-design methods as they leverage human-understandable symbols (i.e. concepts) to predict class memberships. However, most of these approaches focus on the identification of the most relevant concepts but do not provide concise, formal explanations of how such concepts are leveraged by the classifier to make predictions. In this paper, we propose a novel end-to-end differentiable approach enabling the extraction of logic explanations from neural networks using the formalism of First-Order Logic. The method relies on an entropy-based criterion which automatically identifies the most relevant concepts. We consider four different case studies to demonstrate that: (i) this entropy-based criterion enables the distillation of concise logic explanations in safety-critical domains from clinical data to computer vision; (ii) the proposed approach outperforms state-of-the-art white-box models in terms of classification accuracy.

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With Artificial Intelligence on the rise, human interaction with autonomous agents becomes more frequent. Effective human-agent collaboration requires users to understand the agent's behavior, as failing to do so may cause reduced productiveness, misuse or frustration. Agent strategy summarization methods are used to describe the strategy of an agent to its destined user through demonstration. A summary's objective is to maximize the user's understanding of the agent's aptitude by showcasing its behaviour in a selected set of world states. While shown to be useful, we show that current methods are limited when tasked with comparing between agents, as each summary is independently generated for a specific agent. In this paper, we propose a novel method for generating dependent and contrastive summaries that emphasize the differences between agent policies by identifying states in which the agents disagree on the best course of action. We conduct user studies to assess both the affect of our method on an agent selection task and on an agent understanding task. Our results show that the novel disagreement-based summaries lead to improved user performance compared to summaries generated using HIGHLIGHTS, the most common strategy summarization algorithm.

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To interpret uncertainty estimates from differentiable probabilistic models, recent work has proposed generating a single Counterfactual Latent Uncertainty Explanation (CLUE) for a given data point where the model is uncertain. We broaden the exploration to examine δ-CLUE, the set of potential CLUEs within a δ ball of the original input in latent space. We study the diversity of such sets and find that many CLUEs are redundant; as such, we propose DIVerse CLUE (∇-CLUE), a set of CLUEs which each propose a distinct explanation as to how one can decrease the uncertainty associated with an input. We then further propose GLobal AMortised CLUE (GLAM-CLUE), a distinct, novel method which learns amortised mappings that apply to specific groups of uncertain inputs, taking them and efficiently transforming them in a single function call into inputs for which a model will be certain. Our experiments show that δ-CLUE, ∇-CLUE, and GLAM-CLUE all address shortcomings of CLUE and provide beneficial explanations of uncertainty estimates to practitioners.

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Inferring the causal structure of a set of random variables is a crucial problem in many disciplines of science. Over the past two decades, various approaches have been pro- posed for causal discovery from observational data. How- ever, most of the existing methods are designed for either purely discrete or continuous data, which limit their practical usage. In this paper, we target the problem of causal structure learning from observational mixed-type data. Although there are a few methods that are able to handle mixed-type data, they suffer from restrictions, such as linear assumption and poor scalability. To overcome these weaknesses, we formulate the causal mechanisms via mixed structure equation model and prove its identifiability under mild conditions. A novel locally consistent score, named CVMIC, is proposed for causal directed acyclic graph (DAG) structure learning. Moreover, we propose an efficient conditional independence test, named MRCIT, for mixed-type data, which is used in causal skeleton learning and final pruning to further improve the computational efficiency and precision of our model. Experimental results on both synthetic and real-world data demonstrate that our proposed hybrid model outperforms the other state-of-the-art methods. Our source code is available at https://github.com/DAMO-DI-ML/AAAI2022-HCM.

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Algorithmic fairness is typically studied from the perspective of predictions. Instead, here we investigate fairness from the perspective of recourse actions suggested to individuals to remedy an unfavourable classification. We propose two new fair-ness criteria at the group and individual level, which—unlike prior work on equalising the average group-wise distance from the decision boundary—explicitly account for causal relationships between features, thereby capturing downstream effects of recourse actions performed in the physical world. We explore how our criteria relate to others, such as counterfactual fairness, and show that fairness of recourse is complementary to fairness of prediction. We study theoretically and empirically how to enforce fair causal recourse by altering the classifier and perform a case study on the Adult dataset. Finally, we discuss whether fairness violations in the data generating process revealed by our criteria may be better addressed by societal interventions as opposed to constraints on the classifier.

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We consider the problem of acquiring causal representations and concepts in a reinforcement learning setting. Our approach defines a causal variable as being both manipulable by a policy, and able to predict the outcome. We thereby obtain a parsimonious causal graph in which interventions occur at the level of policies. The approach avoids defining a generative model of the data, prior pre-processing, or learning the transition kernel of the Markov decision process. Instead, causal variables and policies are determined by maximizing a new optimization target inspired by mediation analysis, which differs from the expected return. The maximization is accomplished using a generalization of Bellman's equation which is shown to converge, and the method finds meaningful causal representations in a simulated environment.

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Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence network among the dimensions of multi-dimensional temporal processes is of high importance in disciplines where a high-frequency data is to model, e.g. in financial data or in seismological data. This paper approaches the problem of learning Granger-causal network in multi-dimensional Hawkes processes. We formulate this problem as a model selection task in which we follow the minimum description length (MDL) principle. Moreover, we propose a general algorithm for MDL-based inference using a Monte-Carlo method and we use it for our causal discovery problem. We compare our algorithm with the state-of-the-art baseline methods on synthetic and real-world financial data. The synthetic experiments demonstrate superiority of our method in causal graph discovery compared to the baseline methods with respect to the size of the data. The results of experiments with the G-7 bonds price data are consistent with the experts’ knowledge.

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Providing model explanations has gained significant popularity recently. In contrast with the traditional feature-level model explanations, concept-based explanations can provide explanations in the form of high-level human concepts. However, existing concept-based explanation methods implicitly follow a two-step procedure that involves human intervention. Specifically, they first need the human to be involved to define (or extract) the high-level concepts, and then manually compute the importance scores of these identified concepts in a post-hoc way. This laborious process requires significant human effort and resource expenditure due to manual work, which hinders their large-scale deployability. In practice, it is challenging to automatically generate the concept-based explanations without human intervention due to the subjectivity of defining the units of concept-based interpretability. In addition, due to its data-driven nature, the interpretability itself is also potentially susceptible to malicious manipulations. Hence, our goal in this paper is to free human from this tedious process, while ensuring that the generated explanations are provably robust to adversarial perturbations. We propose a novel concept-based interpretation method, which can not only automatically provide the prototype-based concept explanations but also provide certified robustness guarantees for the generated prototype-based explanations. We also conduct extensive experiments on real-world datasets to verify the desirable properties of the proposed method.

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Recently, many regression based conditional independence (CI) test methods have been proposed to solve the problem of causal discovery. These methods provide alternatives to test CI of $x,y$ given $Z$ by first removing the information of controlling set $Z$ from $x$ and $y$, and then testing the independence between two residuals $R_{x,Z}$ and $R_{y,Z}$. When these residuals are linearly uncorrelated, the independence test between residuals is nontrivial. With the ability to calculate inner product in high-dimensional space, kernel-based methods are usually used to achieve this goal, but still consume considerable time. In this paper, we investigate the independence between two linear combinations under linear non-Gaussian structural equation model. We show that the dependence between two residuals $R_{x,Z}$ and $R_{y,Z}$ can be captured by the difference between the similarity of $(R_{x,Z},R_{y,Z})$ and that of $(R_{x,Z},R_{r})$ ($R_{r}$ is an independent copy of $R_{y,Z}$) in high-dimensional space. With this result, we design a new method called SCIT for CI test, where permutation test is performed to control Type I error rate. The proposed method is simpler yet more efficient and effective than the existing ones. When applied to causal discovery, the proposed method outperforms the counterparts in terms of both speed and Type II error rate, especially in the case of small sample size, which is validated by our extensive experiments on both synthetic and real-world datasets.

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This paper considers the problem of expected loss minimization given a data distribution that is dependent on the decision-maker's action and evolves dynamically in time according to a geometric decay process. Motivated by practice, empirical information settings are considered: namely, the decision-maker either has oracle access, for a fixed batch size, to the empirical gradient of the loss (first order setting), or the empirical loss function (zero order setting). Novel algorithms for each of these settings are introduced, both of which operate on the same underlying principle: the decision-maker repeatedly deploys a fixed decision over a fixed length epoch, thereby allowing the dynamically changing environment to sufficiently mix before updating the decision. The proposed algorithms are shown to converge to the optimal point. Specifically, high-probability sample complexity guarantees are given, which depend exponentially on the epoch length and logarithmically on the batch size. The algorithms are evaluated on a ``semi-synthetic" example using real world data from the SFpark dynamic pricing pilot study; it is shown that the announced prices result in an improvement for the institution's objective (target occupancy), while achieving an overall reduction in parking rates.

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Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for achieving acceleration, based on the recently introduced notion of fixed-time stability of dynamical systems. The method presents itself as a generalization of simple gradient-based methods suitably scaled to achieve convergence to the optimizer in a fixed-time, independent of the initialization. We achieve this by first leveraging a continuous-time framework for designing fixed-time stable dynamical systems, and later providing a consistent discretization strategy, such that the equivalent discrete-time algorithm tracks the optimizer in a practically fixed number of iterations. We also provide a theoretical analysis of the convergence behavior of the proposed gradient flows, and their robustness to additive disturbances for a range of functions obeying strong convexity, strict convexity, and possibly nonconvexity but satisfying the Polyak-Łojasiewicz inequality. We also show that the regret bound on the convergence rate is constant by virtue of the fixed-time convergence. The hyperparameters have intuitive interpretations and can be tuned to fit the requirements on the desired convergence rates. We validate the accelerated convergence properties of the proposed schemes on a range of numerical examples against the state-of-the-art optimization algorithms. Our work provides insights on developing novel optimization algorithms via discretization of continuous-time flows.

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Model transparency is a prerequisite in many domains and an increasingly popular area in machine learning research. In the medical domain, for instance, unveiling the mechanisms behind a disease often has higher priority than the diagnostic itself since it might dictate or guide potential treatments and research directions. One of the most popular approaches to explain model global predictions is the permutation importance where the performance on permuted data is benchmarked against the baseline. However, this method and other related approaches will undervalue the importance of a feature in the presence of covariates since these cover part of its provided information. To address this issue, we propose Covered Information Disentanglement CID, a framework that considers all feature information overlap to correct the values provided by permutation importance. We further show how to compute \CID efficiently when coupled with Markov random fields. We demonstrate its efficacy in adjusting permutation importance first on a controlled toy dataset and discuss its effect on real-world medical data.

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Random forests have long been considered as powerful model ensembles in machine learning. By training multiple decision trees, whose diversity is fostered through data and feature subsampling, the resulting random forest can lead to more stable and reliable predictions than a single decision tree. This however comes at the cost of decreased interpretability: while decision trees are often easily interpretable, the predictions made by random forests are much more difficult to understand, as they involve a majority vote over multiple decision trees. In this paper, we examine different types of reasons that explain “why” an input instance is classified as positive or negative by a Boolean random forest. Notably, as an alternative to prime-implicant explanations taking the form of subset-minimal implicants of the random forest, we introduce majoritary reasons which are subset-minimal implicants of a strict majority of decision trees. For these abductive explanations, the tractability of the generation problem (finding one reason) and the optimization problem (finding one shortest reason) are investigated. Experiments conducted on various datasets reveal the existence of a trade-off between runtime complexity and sparsity. In practice, prime-implicant explanations - for which the identification problem is DP-complete - are slightly larger than majoritary reasons that can be generated using a simple linear-time greedy algorithm. They are also significantly larger than minimum-size majoritary reasons which can be approached using an anytime PARTIAL MAXSAT algorithm.

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Many efforts have been made for revealing the decision-making process of black-box learning machines such as deep neural networks, resulting in useful local and global explanation methods. For local explanation, stochasticity is known to help: a simple method, called SmoothGrad, has improved the visual quality of gradient-based attribution by adding noise to the input space and averaging the explanations of the noisy inputs. In this paper, we extend this idea and propose NoiseGrad that enhances both local and global explanation methods. Specifically, NoiseGrad introduces stochasticity in the weight parameter space, such that the decision boundary is perturbed. NoiseGrad is expected to enhance the local explanation, similarly to SmoothGrad, due to the dual relationship between the input perturbation and the decision boundary perturbation. We evaluate NoiseGrad and its fusion with SmoothGrad -FusionGrad- qualitatively and quantitatively with several evaluation criteria, and show that our novel approach significantly outperforms the baseline methods. Both NoiseGrad and FusionGrad are method-agnostic and as handy as SmoothGrad using a simple heuristic for the choice of the hyperparameter setting without the need of fine-tuning.

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Optimization is often cast as a deterministic problem, where the solution is found through some iterative procedure such as gradient descent. However, when training neural networks the loss function changes over (iteration) time due to the randomized selection of a subset of the samples. This randomization turns the optimization problem into a stochastic one. We propose to consider the loss as a noisy observation with respect to some reference optimum. This interpretation of the loss allows us to adopt Kalman filtering as an optimizer, as its recursive formulation is designed to estimate unknown parameters from noisy measurements. Moreover, we show that the Kalman Filter dynamical model for the evolution of the unknown parameters can be used to capture the gradient dynamics of advanced methods such as Momentum and Adam. We call this stochastic optimization method KOALA, which is short for Kalman Optimization Algorithm with Loss Adaptivity. KOALA is an easy to implement, scalable, and efficient method to train neural networks. We provide convergence analysis and show experimentally that it yields parameter estimates that are on par with or better than existing state of the art optimization algorithms across several neural network architectures and machine learning tasks, such as computer vision and language modeling.

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Understanding the black-box prediction for neural networks is challenging. To achieve this, early studies have designed influence function (IF) to measure the effect of removing a single training point on neural networks. However, the classic implicit Hessian-vector product (IHVP) method for calculating IF is fragile, and theoretical analysis of IF in the context of neural networks is still lacking. To this end, we utilize the neural tangent kernel (NTK) theory to calculate IF for the neural network trained with regularized mean-square loss, and prove that the approximation error can be arbitrarily small when the width is sufficiently large for two-layer ReLU networks. We analyze the error bound for the classic IHVP method in the over-parameterized regime to understand when and why it fails or not. In detail, our theoretical analysis reveals that (1) the accuracy of IHVP depends on the regularization term, and is pretty low under weak regularization; (2) the accuracy of IHVP has a significant correlation with the probability density of corresponding training points. We further borrow the theory from NTK to understand the IFs better, including quantifying the complexity for influential samples and depicting the variation of IFs during the training dynamics. Numerical experiments on real-world data confirm our theoretical results and demonstrate our findings.

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Unlike traditional supervised learning, in many settings only partial feedback is available. We may only observe outcomes for the chosen actions, but not the counterfactual outcomes associated with other alternatives. Such settings encompass a wide variety of applications including pricing, online marketing and precision medicine. A key challenge is that observational data are influenced by historical policies deployed in the system, yielding a biased data distribution. We approach this task as a domain adaptation problem and propose a self-training algorithm which imputes outcomes with \textit{categorical} values for \textit{finite} unseen actions in the observational data to simulate a randomized trial through pseudolabelling, which we refer to as Counterfactual Self-Training (CST). CST iteratively imputes pseudolabels and retrains the model. In addition, we show input consistency loss can further improve CST performance which is shown in recent theoretical analysis of pseudolabelling. We demonstrate the effectiveness of the proposed algorithms on both synthetic and real datasets.

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We address the poor scalability of learning algorithms for orthogonal recurrent neural networks via the use of stochastic coordinate descent on the orthogonal group, leading to a cost per iteration that increases linearly with the number of recurrent states. This contrasts with the cubic dependency of typical feasible algorithms such as stochastic Riemannian gradient descent, which prohibits the use of big network architectures. Coordinate descent rotates successively two columns of the recurrent matrix. When the coordinate (i.e., indices of rotated columns) is selected uniformly at random at each iteration, we prove convergence of the algorithm under standard assumptions on the loss function, stepsize and minibatch noise. In addition, we numerically show that the Riemannian gradient has an approximately sparse structure. Leveraging this observation, we propose a variant of our proposed algorithm that relies on the Gauss-Southwell coordinate selection rule. Experiments on a benchmark recurrent neural network training problem show that the proposed approach is a very promising step towards the training of orthogonal recurrent neural networks with big architectures.

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In black-box optimization problems, we aim to maximize an unknown objective function, where the function is only accessible through feedbacks of an evaluation or simulation oracle. In real-life, the feedbacks of such oracles are often noisy and available after some unknown delay that may depend on the computation time of the oracle. Additionally, if the exact evaluations are expensive but coarse approximations are available at a lower cost, the feedbacks can have multi-fidelity. In order to address this problem, we propose a generic extension of hierarchical optimistic tree search (HOO), called ProCrastinated Tree Search (PCTS), that flexibly accommodates a delay and noise-tolerant bandit algorithm. We provide a generic proof technique to quantify regret of PCTS under delayed, noisy, and multi-fidelity feedbacks. Specifically, we derive regret bounds of PCTS enabled with delayed-UCB1 (DUCB1) and delayed-UCB-V (DUCBV) algorithms. Given a horizon T, PCTS retains the regret bound of non-delayed HOO for expected delay of O(log T), and worsens by T^{(1-\alpha)/(d+2)} for expected delays of O(T^{1-\alpha}) for \alpha \in (0,1]. We experimentally validate on multiple synthetic functions and hyperparameter tuning problems that PCTS outperforms the state-of-the-art black-box optimization methods for feedbacks with different noise levels, delays, and fidelity.

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We consider the problem of reducing the false discovery rate in multiple high-dimensional interventional datasets under unknown intervention targets when the time efficiency is acceptable. Traditional algorithms merged directly multiple causal DAGs learned, which ignores the contradictions of different datasets, leading to lots of contradictory directions of edges. For reducing the contradictory information, we propose a new algorithm, which first learns an intervention Markov equivalence class (I-MEC) before merging multiple causal DAGs. It utilizes the full power of the constraints available in interventional data and combines ideas from local learning, intervention, and search-and-score techniques in a principled and effective way in different intervention experiments. Specifically, local learning on multiple datasets is used to build a causal skeleton. Perfect intervention destroys some possible triangles and obtains more V-structures, getting a theoretically correct I-MEC. Search and scoring techniques based on the learned I-MEC further identify the remaining unoriented edges. Experiments on benchmark Bayesian networks with the number of variables from 20 to 724 validate that the effectiveness of our algorithm in reducing the false discovery rate in high-dimensional interventional data.

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