The task of geometry problem solving has been a long-standing focus in the automated mathematics community and draws growing attention due to its complexity for both symbolic and neural models. Although prior studies have explored various effective approaches for enhancing problem solving performances, two fundamental challenges remain unaddressed, which are essential to the application in practical scenarios. First, the multi-step reasoning gap between the initial geometric conditions and ultimate problem goal leads to a great search space for solution exploration. Second, obtaining multiple interpretable and shorter solutions remains an open problem. In this work, we introduce the Causal-Reasoning Geometry Problem Solver to overcome these challenges.

Suppose we are considering a multivariate event sequence. What caused a specific event to happen? Which variables are causes of each other?

Suppose we are considering a multivariate event sequence. What caused a specific event to happen? Which variables are causes of each other?

Causal discovery from time-series data aims to capture both intra-slice (contemporaneous) and inter-slice (time-lagged) causality between variables within the temporal chain, which is crucial for various scientific disciplines. Compared to causal discovery from non-time-series data, causal discovery from time-series data necessitates more serialized samples with a larger amount of observed time steps. To address the challenges, we propose a novel gradient-based causal discovery approach STIC, which focuses on \textbf{S}hort-\textbf{T}erm \textbf{I}nvariance using \textbf{C}onvolutional neural networks to uncover the causal relationships from time-series data. Specifically, STIC leverages both the short-term time and mechanism invariance of causality within each window observation, which possesses the property of independence, to enhance sample efficiency. Furthermore, we construct two causal convolution kernels, which correspond to the short-term time and mechanism invariance respectively, to estimate the window causal graph. To demonstrate the necessity of convolutional neural networks for causal discovery from time-series data, we theoretically derive the equivalence between convolution and the underlying generative principle of time-series data under the assumption that the additive noise model is identifiable. Experimental evaluations conducted on both synthetic and FMRI benchmark datasets demonstrate that our STIC outperforms baselines significantly and achieves the state-of-the-art performance, particularly when the datasets contain a limited number of observed time steps. Code is available at \url{https://github.com/HITshenrj/STIC}.

Causal discovery with latent variables is a crucial but challenging task. Despite the emergence of numerous methods aimed at addressing this challenge, they are not fully identified to the structure that two observed variables are influenced by one latent variable and there might be a directed edge in between. Interestingly, we notice that this structure can be identified through the utilization of higher-order cumulants. By leveraging the higher-order cumulants of non-Gaussian data, we provide an analytical solution for estimating the causal coefficients or their ratios. With the estimated (ratios of) causal coefficients, we propose a novel approach to identify the existence of a causal edge between two observed variables subject to latent variable influence. In case when such a causal edge exits, we introduce an asymmetry criterion to determine the causal direction. The experimental results demonstrate the effectiveness of our proposed method.

Time series data are found in many areas of healthcare such as medical time series, electronic health records (EHR), measurements of vitals, and wearable devices. Causal discovery, which involves estimating causal relationships from observational data, holds the potential to play a significant role in extracting actionable insights about human health. In this study, we present a novel constraint-based causal discovery approach for autocorrelated and non-stationary time series data (CDANs). Our proposed method addresses several limitations of existing causal discovery methods for autocorrelated and non-stationary time series data, such as high dimensionality, the inability to identify lagged causal relationships, and overlooking changing modules. Our approach identifies lagged and instantaneous/contemporaneous causal relationships along with changing modules that vary over time. The method optimizes the conditioning sets in a constraint-based search by considering lagged parents instead of conditioning on the entire past that addresses high dimensionality. The changing modules are detected by considering both contemporaneous and lagged parents. The approach first detects the lagged adjacencies, then identifies the changing modules and contemporaneous adjacencies, and finally determines the causal direction. We extensively evaluated our proposed method on synthetic and real-world clinical datasets, and compared its performance with several baseline approaches. The experimental results demonstrate the effectiveness of the proposed method in detecting causal relationships and changing modules for autocorrelated and non-stationary time series data.

With the rise of AI, algorithms have become better at learning underlying patterns from the training data including ingrained social biases based on gender, race, etc. Deployment of such algorithms to domains such as hiring, healthcare, law enforcement, etc. has raised serious concerns about fairness, accountability, trust and interpretability in machine learning algorithms. To alleviate this problem, we propose D-BIAS, a visual interactive tool that embodies human-in-the-loop AI approach for auditing and mitigating social biases from tabular datasets. It uses a graphical causal model to represent causal relationships among different features in the dataset and as a medium to inject domain knowledge. A user can detect the presence of bias against a group, say females, or a subgroup, say black females, by identifying unfair causal relationships in the causal network and using an array of fairness metrics. Thereafter, the user can mitigate bias by acting on the unfair causal edges. For each interaction, say weakening/deleting a biased causal edge, the system uses a novel method to simulate a new (debiased) dataset based on the current causal model. Users can visually assess the impact of their interactions on different fairness metrics, utility metrics, data distortion, and the underlying data distribution. Once satisfied, they can download the debiased dataset and use it for any downstream application for fairer predictions. We evaluate D-BIAS by conducting experiments on 3 datasets and also a formal user study. We found that D-BIAS helps reduce bias significantly compared to the baseline debiasing approach across different fairness metrics while incurring little data distortion and a small loss in utility. Moreover, our human-in-the-loop based approach significantly outperforms an automated approach on trust, interpretability and accountability.

Fuzzy cognitive maps (FCMs) model feedback causal relations in interwoven webs of causality and policy variables. FCMs are fuzzy signed directed graphs that allow degrees of causal influence and event occurrence. Such causal models can simulate a wide range of policy scenarios and decision processes. Their directed loops or cycles directly model causal feedback. Their nonlinear dynamics permit forward-chaining inference from input causes and policy options to output effects. Users can add detailed dynamics and feedback links directly to the causal model or infer them with statistical learning laws. Users can fuse or combine FCMs from multiple experts by weighting and adding the underlying fuzzy edge matrices and do so recursively if needed. The combined FCM tends to better represent domain knowledge as the expert sample size increases if the expert sample approximates a random sample. Many causal models use more restrictive directed acyclic graphs (DAGs) and Bayesian probabilities. DAGs do not model causal feedback because they do not contain closed loops. Combining DAGs also tends to produce cycles and thus tends not to produce a new DAG. Combining DAGs tends to produce a FCM. FCM causal influence is also transitive whereas probabilistic causal influence is not transitive in general. Overall: FCMs trade the numerical precision of probabilistic DAGs for pattern prediction, faster and scalable computation, ease of combination, and richer feedback representation. We show how FCMs can apply to problems of public support for insurgency and terrorism and to US-China conflict relations in Graham Allison's Thucydides-trap framework. The appendix gives the textual justification of the Thucydides-trap FCM. It also extends our earlier theorem [Osoba-Kosko2017] to a more general result that shows the transitive and total causal influence that upstream concept nodes exert on downstream nodes.