Contemporary machine learning optimizes for predictive accuracy, yet systems that achieve state of the art performance remain causally opaque: their internal representations provide no principled handle for intervention. We can retrain such models, but we cannot surgically edit specific mechanisms while holding others fixed, because learned latent variables lack causal semantics. We argue for a conceptual reorientation: intelligence is the ability to build and refine explanations, falsifiable claims about manipulable structure that specify what changes and what remains invariant under intervention. Explanations subsume prediction but demand more: causal commitments that can be independently tested and corrected at the level of mechanisms. We introduce computational explanations, mappings from observations to intervention ready causal accounts. We instantiate these explanations with Energy Structured Causal Models (ESCMs), in which mechanisms are expressed as constraints (energy functions or vector fields) rather than explicit input output maps, and interventions act by local surgery on those constraints. This shift makes internal structure manipulable at the level where explanations live: which relations must hold, which can change, and what follows when they do. We provide concrete instantiations of the structural-causal principles LAP and ICM in the ESCM context, and also argue that empirical risk minimization systematically produces fractured, entangled representations, a failure we analyze as gauge ambiguity in encoder energy pairs. Finally, we show that under mild conditions, ESCMs recover standard SCM semantics. Building on Part I's principles (LAP, ICM, CAP) and its definition of intelligence as explanation-building under criticism, this paper offers a formal language for causal reasoning in systems that aspire to understand, not merely to predict.

We evaluate the performance of targeted maximum likelihood estimation (TMLE) for estimating the average treatment effect in missing data scenarios under varying levels of positivity violations. We employ model- and design-based simulations, with the latter using undersmoothed highly adaptive lasso on the 'WASH Benefits Bangladesh' dataset to mimic real-world complexities. Five missingness-directed acyclic graphs are considered, capturing common missing data mechanisms in epidemiological research, particularly in one-point exposure studies. These mechanisms include also not-at-random missingness in the exposure, outcome, and confounders. We compare eight missing data methods in conjunction with TMLE as the analysis method, distinguishing between non-multiple imputation (non-MI) and multiple imputation (MI) approaches. The MI approaches use both parametric and machine-learning models. Results show that non-MI methods, particularly complete cases with TMLE incorporating an outcome-missingness model, exhibit lower bias compared to all other evaluated missing data methods and greater robustness against positivity violations across. In Comparison MI with classification and regression trees (CART) achieve lower root mean squared error, while often maintaining nominal coverage rates. Our findings highlight the trade-offs between bias and coverage, and we recommend using complete cases with TMLE incorporating an outcome-missingness model for bias reduction and MI CART when accurate confidence intervals are the priority.

Predictive benchmarking, the evaluation of machine learning models based on predictive performance and competitive ranking, is a central epistemic practice in machine learning research and an increasingly prominent method for scientific inquiry. Yet, benchmark scores alone provide at best measurements of model performance relative to an evaluation dataset and a concrete learning problem. Drawing substantial scientific inferences from the results, say about theoretical tasks like image classification, requires additional assumptions about the theoretical structure of the learning problems, evaluation functions, and data distributions. We make these assumptions explicit by developing conditions of construct validity inspired by psychological measurement theory. We examine these assumptions in practice through three case studies, each exemplifying a typical intended inference: measuring engineering progress in computer vision with ImageNet; evaluating policy-relevant weather predictions with WeatherBench; and examining limitations of the predictability of life events with the Fragile Families Challenge. Our framework clarifies the conditions under which benchmark scores can support diverse scientific claims, bringing predictive benchmarking into perspective as an epistemological practice and a key site of conceptual and theoretical reasoning in machine learning.

Semi-supervised learning (SSL) aims to train a machine learning model using both labelled and unlabelled data. While the unlabelled data have been used in various ways to improve the prediction accuracy, the reason why unlabelled data could help is not fully understood. One interesting and promising direction is to understand SSL from a causal perspective. In light of the independent causal mechanisms principle, the unlabelled data can be helpful when the label causes the features but not vice versa. However, the causal relations between the features and labels can be complex in real world applications. In this paper, we propose a SSL framework that works with general causal models in which the variables have flexible causal relations. More specifically, we explore the causal graph structures and design corresponding causal generative models which can be learned with the help of unlabelled data. The learned causal generative model can generate synthetic labelled data for training a more accurate predictive model. We verify the effectiveness of our proposed method by empirical studies on both simulated and real data.

We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging, as the true underlying dataset is unobserved. To address this, we investigate coreset construction using surrogate error metrics that are tractable and provably related to the true clustering cost. We analyze a traditional metric from prior work and introduce a new error metric that more closely aligns with the true cost. Although our metric is defined independently of the noise distribution, it enables approximation guarantees that scale with the noise level. We design a coreset construction algorithm based on this metric and show that, under mild assumptions on the data and noise, enforcing an $\varepsilon$-bound under our metric yields smaller coresets and tighter guarantees on the true clustering cost than those obtained via classical metrics. In particular, we prove that the coreset size can improve by a factor of up to $\mathrm{poly}(k)$, where $n$ is the dataset size. Experiments on real-world datasets support our theoretical findings and demonstrate the practical advantages of our approach.

Random Forests (RF) and Extreme Gradient Boosting (XGBoost) are two of the most widely used and highly performing classification and regression models. They aggregate equally weighted CART trees, generated randomly in RF or sequentially in XGBoost. In this paper, we propose Adaptive Forests (AF), a novel approach that adaptively selects the weights of the underlying CART models. AF combines (a) the Optimal Predictive-Policy Trees (OP2T) framework to prescribe tailored, input-dependent unequal weights to trees and (b) Mixed Integer Optimization (MIO) to refine weight candidates dynamically, enhancing overall performance. We demonstrate that AF consistently outperforms RF, XGBoost, and other weighted RF in binary and multi-class classification problems over 20+ real-world datasets.

The estimation of unknown parameters in nonlinear partial differential equations (PDEs) offers valuable insights across a wide range of scientific domains. In this work, we focus on estimating plant root parameters in the Richards equation, which is essential for understanding the soil-plant system in agricultural studies. Since conventional methods are computationally intensive and often yield unstable estimates, we develop a new Gaussian process collocation method for efficient Bayesian inference. Unlike existing Gaussian process-based approaches, our method constructs an approximate posterior distribution using samples drawn from a Gaussian process model fitted to the observed data, which does not require any structural assumption about the underlying PDE. Further, we propose to use an importance sampling procedure to correct for the discrepancy between the approximate and true posterior distributions. As an alternative, we also devise a prior-guided Bayesian optimization algorithm leveraging the approximate posterior. Simulation studies demonstrate that our method yields robust estimates under various settings. Finally, we apply our method on a real agricultural data set and estimate the plant root parameters with uncertainty quantification.

Uncovering the underlying causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the joint discovery of a causal graph and unknown interventions as a meta-learning problem. MetaCaDI is a Bayesian framework that learns a shared causal graph structure across multiple experiments and is optimized to rapidly adapt to new, few-shot intervention target prediction tasks. A key innovation is our model's analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at both causal graph recovery and identifying intervention targets from as few as 10 data instances, proving its robustness in data-scarce scenarios.

Risk assessment tools in healthcare commonly employ point-based scoring systems that map patients to ordinal risk categories via thresholds. While electronic health record (EHR) data presents opportunities for data-driven optimization of these tools, two fundamental challenges impede standard supervised learning: (1) partial supervision arising from intervention-censored outcomes, where only extreme categories can be reliably labeled, and (2) asymmetric misclassification costs that increase with ordinal distance. We propose a mixed-integer programming (MIP) framework that jointly optimizes scoring weights and category thresholds under these constraints. Our approach handles partial supervision through per-instance feasible label sets, incorporates asymmetric distance-aware objectives, and prevents middle-category collapse via minimum threshold gaps. We further develop a CSO relaxation using softplus losses that preserves the ordinal structure while enabling efficient optimization. The framework supports governance constraints including sign restrictions, sparsity, and minimal modifications to incumbent tools, ensuring practical deployability in clinical workflows.

This paper studies prediction with multiple candidate models, where the goal is to combine their outputs. This task is especially challenging in heterogeneous settings, where different models may be better suited to different inputs. We propose input adaptive Bayesian Model Averaging (IA-BMA), a Bayesian method that assigns model weights conditional on the input. IA-BMA employs an input adaptive prior, and yields a posterior distribution that adapts to each prediction, which we estimate with amortized variational inference. We derive formal guarantees for its performance, relative to any single predictor selected per input. We evaluate IABMA across regression and classification tasks, studying data from personalized cancer treatment, credit-card fraud detection, and UCI datasets. IA-BMA consistently delivers more accurate and better-calibrated predictions than both non-adaptive baselines and existing adaptive methods. Many applications require adaptive predictions. In personalized medicine, different patients respond differently to the same treatment (Mahajan et al., 2023); in fairness-sensitive domains, predictions need to adapt to subpopulations (Wang et al., 2019; Grother et al., 2019); and in fraud detection, behavioral data is often heteroskedastic and varies substantially across inputs (V armedja et al., 2019).