Topological Residual Asymmetry for Bivariate Causal Direction

Inferring causal direction from purely observational bivariate data is fragile: many methods commit to a direction even in ambiguous or near non-identifiable regimes. We propose Topological Residual Asymmetry (TRA), a geometry-based criterion for additive-noise models. TRA compares the shapes of two cross-fitted regressor-residual clouds after rank-based copula standardization: in the correct direction, residuals are approximately independent, producing a two-dimensional bulk, while in the reverse direction -- especially under low noise -- the cloud concentrates near a one-dimensional tube. We quantify this bulk-tube contrast using a 0D persistent-homology functional, computed efficiently from Euclidean MST edge-length profiles. We prove consistency in a triangular-array small-noise regime, extend the method to fixed noise via a binned variant (TRA-s), and introduce TRA-C, a confounding-aware abstention rule calibrated by a Gaussian-copula plug-in bootstrap. Extensive experiments across many challenging synthetic and real-data scenarios demonstrate the method's superiority.

Meta-Learning and representation learner: A short theoretical note

Meta-learning, or "learning to learn," is a subfield of machine learning where the goal is to develop models and algorithms that can learn from various tasks and improve their learning process over time. Unlike traditional machine learning methods focusing on learning a specific task, meta-learning aims to leverage experience from previous tasks to enhance future learning. This approach is particularly beneficial in scenarios where the available data for a new task is limited, but there exists abundant data from related tasks. By extracting and utilizing the underlying structure and patterns across these tasks, meta-learning algorithms can achieve faster convergence and better performance with fewer data. The following notes are mainly inspired from \cite{vanschoren2018meta}, \cite{baxter2019learning}, and \cite{maurer2005algorithmic}.

Causal Contrastive Learning for Counterfactual Regression Over Time

Estimating treatment effects over time holds significance in various domains, including precision medicine, epidemiology, economy, and marketing. This paper introduces a unique approach to counterfactual regression over time, emphasizing long-term predictions. Distinguishing itself from existing models like Causal Transformer, our approach highlights the efficacy of employing RNNs for long-term forecasting, complemented by Contrastive Predictive Coding (CPC) and Information Maximization (InfoMax). Emphasizing efficiency, we avoid the need for computationally expensive transformers. Leveraging CPC, our method captures long-term dependencies in the presence of time-varying confounders. Notably, recent models have disregarded the importance of invertible representation, compromising identification assumptions. To remedy this, we employ the InfoMax principle, maximizing a lower bound of mutual information between sequence data and its representation. Our method achieves state-of-the-art counterfactual estimation results using both synthetic and real-world data, marking the pioneering incorporation of Contrastive Predictive Encoding in causal inference.

Causal Dynamic Variational Autoencoder for Counterfactual Regression in Longitudinal Data

Estimating treatment effects over time is relevant in many real-world applications, such as precision medicine, epidemiology, economy, and marketing. Many state-of-the-art methods either assume the observations of all confounders or seek to infer the unobserved ones. We take a different perspective by assuming unobserved risk factors, i.e., adjustment variables that affect only the sequence of outcomes. Under unconfoundedness, we target the Individual Treatment Effect (ITE) estimation with unobserved heterogeneity in the treatment response due to missing risk factors. We address the challenges posed by time-varying effects and unobserved adjustment variables. Led by theoretical results over the validity of the learned adjustment variables and generalization bounds over the treatment effect, we devise Causal DVAE (CDVAE). This model combines a Dynamic Variational Autoencoder (DVAE) framework with a weighting strategy using propensity scores to estimate counterfactual responses. The CDVAE model allows for accurate estimation of ITE and captures the underlying heterogeneity in longitudinal data. Evaluations of our model show superior performance over state-of-the-art models.