70 problems

In a continuous-time structural nested model, let $Y^{(t)}$ denote the outcome under treatment stopped at time $t$, and let $D$ be the infinitesimal shift-function in the structura…

Let an SDE system be an additive-noise system satisfying Assumption. d-separation do-calculus conjecture. The $d$-separation analogue of the do-calculus holds for these systems, in…

Let a system of causal stochastic differential equations be a class of SDE systems, and suppose that instantaneous cycles are excluded. d-separation Markov-property conjecture. The…

Let $X_A^{[0,t)}$, $X_B^t$, and $X_C^{[0,t)}$ denote the restrictions and time-$t$ values of the processes indexed by sets $A$, $B$, and $C$, respectively. Local-independence conje…

Let $\mathbf{Caus}$ be the category of finite acyclic directed graphs equipped with a chosen topological order, with order-preserving graph homomorphisms or refinements as morphism…

In the design-based adaptive Neyman allocation problem for augmented inverse probability weighted estimators, let $R$ denote the predictor-range parameter whose quadratic dependenc…

Let $\widehat{\pi}(\lambda)$ be the empirically trained policy obtained by regularized empirical welfare maximization, and let $\widehat{g}(\lambda)$ be the corresponding trained C…

Let $\varepsilon_i(0)$ and $\varepsilon_i(1)$ denote the potential-outcome errors, and let $\hat\imath_\text{SSE}$ and $\hat\jmath_\text{SSE}$ be the split location and covariate s…

Let $r_{mu,n}$ denote the convergence rate of the outcome-regression estimator, let $gamma_0$ govern the simulated propensity-score distribution, and let $b_n$ be the clipping thre…

Let $e_e$ be the order of a local polynomial regression estimator for the propensity score, let $d$ be the covariate dimension, let $r_{e,n}$ denote its global consistency rate, an…

Let $T$ denote the number of units in a finite-population adaptive randomized controlled trial, and let $\widetilde{O}(\sqrt{T})$ denote a regret rate up to polylogarithmic factors…

Landscape criterion. We conjecture that, for any additively optimal UTM, a good UFCC $U$ should have a landscape—that is, an ordering of codebooks—similar to the UTM's landscape in…

The Large Outliers setting refers to simulations in which the outcome distribution includes high-degree nodes with large outcomes. The relevant variance estimator is denoted by…

Let $\nu^{\mathsf{rd}}$, $\nu^{\mathsf{rd}\dag}$, and $\mathsf{var}(\widehat{\tau}_{\mathsf{unadj}})$ denote the variance quantities defined in the paper for the covariate-adjusted…

Let $d_{\bm Z}>d_{\bm \Phi}>1$ and let the solution set for the budget-assignment parameter $\bm\theta$ be defined through subset selection over…

A time-dependent adjustment set is a collection of covariates used at multiple treatment time points to identify and estimate a longitudinal treatment effect; a sufficient time-dep…

Let $\hat{\beta}$ denote the estimator of the latent position effect, and let $\rho_N$ and $\pi_N$ denote, respectively, the network sparsity parameter and the smallest non-zero ei…

Conical-space-time ACL conjecture. Compatible and non-degenerate embeddings of ACLs in conical space-times, and hence in higher-dimensional Minkowski space-times, are impossible.

Generalized clustering conjecture. The theorem that clustering implies fine-tuning, currently established for the conditional case when $X(W)=X$ (equivalently, when $X$ is not a ca…

Let structural nested accelerated/cumulative failure time models describe counterfactual failure times, and suppose treatment and covariate histories evolve as continuous-time proc…

Conservativeness conjecture. Given a specific value of $s$, classical tests should be conservative when both $\alpha_S=0$ and $\beta_M+\theta s=0$.

Let $G$ be a DAG and let $\mathcal{S}$ be a support. Say that $\mathcal{S}$ is trivially incompatible with $G$ when some $d$-separation relation of $G$ induces a conditional indepe…

Let $G$ be an mDAG. Write $\textsc{Algebraic}$ for the property that all causal compatibility constraints of $G$ are conditional independence relations, and let…

Let $p$ be the number of covariates and $n$ the sample size. In the regime $p\leq n$, the paper's DCal estimator achieves $\sqrt{n}$-consistency under the minimal sparsity conditio…

Let $\pi^\ast$ denote the true propensity score and let $\tilde{\pi}$ be its estimator. Let $r^\ast$ denote the true outcome regression, and suppose that only the outcome-regressio…