Structured potential outcomes such as microscopy images may be recorded after an unknown, unit-specific transformation. If that transformation can depend on treatment, covariates or the intrinsic outcome, raw-coordinate analyses may mix biological effects with acquisition geometry. We study the unrestricted observation model X = {\Gamma} . Y(A) and characterize its observable information: a target is uniformly recoverable exactly when it is constant on group orbits, while a Borel maximal invariant retains every measurable invariant target. We then distinguish observability from statistical losslessness. A quotient-faithful reconstruction theorem shows that quotient reduction is sufficient for the full transformed experiment exactly when the conditional law of the raw observation given treatment, covariates and the quotient has a parameter-free version. Conditional Haar contamination on a compact group yields Blackwell equivalence as a special case; it is not imposed in the main model. We also separate independent site-specific product actions from shared diagonal actions and show why componentwise canonicalization can discard relative cross-site information. Under explicit metric and kernel regularity, an approximate-contamination theorem bounds quotient-law Wasserstein error and the induced perturbation of population maximum mean discrepancy. For finite-support multichannel lattice images, we construct a maximal invariant under integer translations and quarter turns, combine its characteristic Gaussian kernel with a complete paired-swap test, and retain the original simulations and RxRx1 HUVEC study. Under the sharp null, the quotient test rejected in 0.052 of simulation replicates; at unit effect strength its power was 0.992. The primary RxRx1 contrast had an enumerated paired-swap p-value of 0.0078.
Observational datasets frequently contain many baseline variables, yet investigators estimating causal effects may not know which variables to include in the adjustment set. Confounding information may also be distributed weakly across many variables. Propensity scores can simplify adjustment by reducing high-dimensional covariates to a scalar with binary treatment. Although the propensity score is the coarsest balancing score, this distributional optimality does not imply maximal specificity over causal graphs. We instead examine all causal graphs among a candidate score, treatment, and outcome while allowing latent variables. Under faithfulness, we identify the largest set of unconditional and conditional dependence relations whose truth is invariant to whether treatment causes the outcome, leaving treatment-effect estimation to the downstream analysis. This criterion defines the maximally specific graph class expressible through these relations. We then develop the proposed algorithm, which operationalizes the criterion through a generalized eigenvalue problem whose score space targets the span of a balancing coordinate and an outcome-guided coordinate. We show that sufficiently informative proxies can recover this span without direct observation of the adjustment variables, characterize the resulting estimation and causal errors, and establish bootstrap validity for the complete procedure. Simulations and a real-data application demonstrate superior performance over several alternatives.
Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler'25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.
We study counterfactual protocol evaluation: whether data collected under a realised observation protocol determine the predictive value of alternatives that were never deployed. Protocol value is the population $R^2$ of the Bayes-optimal predictor of a fixed trajectory-level target from the measurements an alternative would collect. We show that even infinite benchmark data need not determine this value: distinct latent covariance structures can induce the same benchmark measurement--target law while assigning different values to the same alternative. We develop a value-specific identification theory in which only latent ambiguity that changes the alternative's value matters. For linear targets, invisible covariance directions certify non-identification, while targeted measurements can restore identification without recovering the full latent covariance; an exact permutation construction extends the result to nonlinear aggregate targets. With finite dense calibration data, uniform error bounds control protocol-selection regret and distinguishable value gaps. Exact marginal gains then support cost-constrained, target-aware observation design. Simulations and retrospective analyses of Sleep-EDF and Long-Term AF show that broad temporal-layout differences can be more reliably distinguished than fine placements selected from finite data. Together, these results connect identification, calibration resolution and observation design for undeployed protocols.
ARM (Attribution by Rank Maxima), a wrapper that accepts a changepoint located by an arbitrary detector and returns the set of coordinates certified to have changed, each carrying a location or scale type label, is proposed.
Chenchen Peng, Mixia Wu, Qijing Yan et al.· 0 citations
We study causal inference under outcome interference for sequential, observational settings. Specifically, we consider settings where the binary outcomes over N units are Markovian across T time steps. At each time step, the outcomes of N units have dependencies captured through an Ising model; each outcome is also impacted through an external field capturing the effects of its treatment as well as latent confounders. Similar to panel data literature, these latent confounders are modeled to have a low-rank factor structure. Our data is a single sample from this high-dimensional distribution. To estimate causal quantities of interest, we provide a computationally efficient method based on Maximum Pseudo-Likelihood Estimation (MPLE) for learning the model parameters. Under mild assumptions, we establish non-asymptotic consistency for parameter estimation and show this translates to faithful estimation of causal quantities of interest after sampling from the learned model. We demonstrate the efficacy of the method through synthetic experiments as well as a real-world case-study investigating causal effects of vaccine rates on COVID-19 death rates within US counties nationwide.
Optimizer experiments observe responses to algorithmic configurations without uniquely revealing hidden mechanisms. We develop a causal optimizer interaction calculus that separates pathwise realization, Mobius decomposition, and experimental identification. Under a fixed innovation coupling, every finite-horizon innovation-driven optimizer admits a behaviorally minimal pathwise realization. For any finite effect support and intervention design, an incidence operator gives the complete observational gauge, exact identifiability, sharp quotient stability, held-out predictions, and exact noiseless configuration complexity. Smooth hidden relaxation generates interactions through inverse hidden-state stiffness. Building on this structural law, we prove an observable-readout transfer theorem: arbitrary smooth update or trace readouts inherit an explicit five-term interaction through first and second hidden responses. Unlike the reduced optimal value, a general readout has no universal interaction sign. Its Boolean effects remain exact integrals of continuous interaction curvature and can therefore be identified by factorial interventions. We also derive Gaussian quotient minimax risk, exact confidence sets and tests, misspecification decomposition, certified downstream decisions, and optimal replication. A controlled real-data experiment on a 65-dimensional strongly convex logistic model validates the complete reduced-value chain. Boolean effects and independently integrated curvature agree within 4.21e-11, while nine held-out continuous intensities agree within 8.88e-13. Gaussian campaigns attain the predicted coverage and power, and 4,500 real-minibatch observations reject an order-two interaction model. Neural trace audits provide complementary evidence that the declared response classes remain informative in nonconvex training.
Zavier Li· 0 citations
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