Causal discovery seeks to uncover the causal dependencies among variables. For this purpose, we propose an algorithm called Tensor-based Second-order Causal Discovery (TSCD). Its input is a tensor obtained from the covariance matrices of observational and interventional data. Assuming the causal dependencies follow a linear structural equation model on a directed acyclic graph (DAG), TSCD outputs the DAG and the functions on its edges, requiring only that the noise variables are uncorrelated. We also implement a version of the approach for nonlinear models. Our focus on second-order statistics (via the covariance matrices) is motivated by their statistical and computational efficiency relative to higher-order moments, their identifiability relative to first-order statistics, and that they work regardless of whether the variables are Gaussian. We show that TSCD has identifiable causal order and parameters from a number of interventions that is logarithmic in the number of variables. Experiments show that TSCD is robust to noise, competitive with existing methods, and scales to hundreds of variables.

Similarly to [6], we consider that all environments have the same underlying Structural Causal Model (SCM) and that the different environments correspond to different interventions on the SCM. We provide here the formal definition for SCMs and interventions. We say that Xi causes Xj if Xi 2Pa(Xj). Definition A.2. (Intervention) [6]: Consider a SCMC =( S,N). An intervention e on C consists of replacing one or several of its structural equations to obtain an intervened SCMCe =( Se,N e) with structural equations: Sej: Xej fj(Pa(Xej),N ej), for j =1,...m (11) The variable Xe is intervened on if Si 6= Sei or Ni 6= Nei .

Ourmethodologyincorporates a certain amount of backtracking when needed, allowing changes in causally preceding variables tominimize deviations from realistic scenarios. Specifically, we introduce a novel optimization framework that permits but also controls the extent of backtracking with a "naturalness" criterion. Empirical experiments demonstrate the effectiveness of our method.

Random Forest ensembles are a strong baseline for tabular prediction tasks, but their reliance on hundreds of deep trees often results in high inference latency and memory demands, limiting deployment in latency-sensitive or resource-constrained environments. We introduce DiNo (Distance with Nodes) and RanBu (Random Bushes), two shallow-forest methods that convert a small set of depth-limited trees into efficient, distance-weighted predictors. DiNo measures cophenetic distances via the most recent common ancestor of observation pairs, while RanBu applies kernel smoothing to Breiman's classical proximity measure. Both approaches operate entirely after forest training: no additional trees are grown, and tuning of the single bandwidth parameter $h$ requires only lightweight matrix-vector operations. Across three synthetic benchmarks and 25 public datasets, RanBu matches or exceeds the accuracy of full-depth random forests-particularly in high-noise settings-while reducing training plus inference time by up to 95\%. DiNo achieves the best bias-variance trade-off in low-noise regimes at a modest computational cost. Both methods extend directly to quantile regression, maintaining accuracy with substantial speed gains. The implementation is available as an open-source R/C++ package at https://github.com/tiagomendonca/dirf. We focus on structured tabular random samples (i.i.d.), leaving extensions to other modalities for future work.