arXiv subjects

Sahil Loomba

Publications and source records attributed to Sahil Loomba.

4 recordsLinked to original sources

arXiv2026

Off-policy causal estimation in networks

In the presence of interference, where the treatment assigned to one unit can affect the outcomes of others, many causal estimands depend on the treatment-assignment policy under which the experiment is conducted. This policy dependence creates a fundamental challenge for off-policy estimation, where the goal is to estimate causal quantities under a hypothetical intervention policy different from the one used to collect data. We study this problem of off-policy estimation of causal effects for heterogeneous Bernoulli policies. By representing exposure-weighted potential outcomes in the biased Fourier basis of the experimental design, we construct, for any prespecified Fourier subspace encoding the assumed interference structure, the unique minimum-$L^2$ weight that transports every function in that subspace. Global and local inverse-probability weights, linear-interference weights, and no-interference weights are special cases. The weight variance is a structured chi-square distance between the experiment and target policies. When the assumed interference structure is misspecified, the introduced bias couples the omitted outcome spectrum with the corresponding policy-shift coefficients, yielding a sharp robustness bound and a bias-variance trade-off. A Fourier-neighborhood-overlap condition gives consistency under structured interference, and we state a Doob-martingale central limit theorem for off-policy estimators. As the variance is not identified, we derive identifiable bounds and associated conservative estimators of the variance. Simulations illustrate these theoretical results for the design and analysis of experiments under network interference and design mismatch.

stat.ME↗

arXiv2025

Limits of message passing for node classification: How class-bottlenecks restrict signal-to-noise ratio

Message passing neural networks (MPNNs) are powerful models for node classification but suffer from performance limitations under heterophily (low same-class connectivity) and structural bottlenecks in the graph. We provide a unifying statistical framework exposing the relationship between heterophily and bottlenecks through the signal-to-noise ratio (SNR) of MPNN representations. The SNR decomposes model performance into feature-dependent parameters and feature-independent sensitivities. We prove that the sensitivity to class-wise signals is bounded by higher-order homophily -- a generalisation of classical homophily to multi-hop neighbourhoods -- and show that low higher-order homophily manifests locally as the interaction between structural bottlenecks and class labels (class-bottlenecks). Through analysis of graph ensembles, we provide a further quantitative decomposition of bottlenecking into underreaching (lack of depth implying signals cannot arrive) and oversquashing (lack of breadth implying signals arriving on fewer paths) with closed-form expressions. We prove that optimal graph structures for maximising higher-order homophily are disjoint unions of single-class and two-class-bipartite clusters. This yields BRIDGE, a graph ensemble-based rewiring algorithm that achieves near-perfect classification accuracy across all homophily regimes on synthetic benchmarks and significant improvements on real-world benchmarks, by eliminating the ``mid-homophily pitfall'' where MPNNs typically struggle, surpassing current standard rewiring techniques from the literature. Our framework, whose code we make available for public use, provides both diagnostic tools for assessing MPNN performance, and simple yet effective methods for enhancing performance through principled graph modification.

cs.LG↗

arXiv2025

Policy relevance of causal quantities in networks

In settings where units' outcomes are affected by others' treatments, there has been a proliferation of ways to quantify effects of treatments on outcomes, including via indirect exposure to other units' treatments. Here we consider two properties we might want estimands to have: being interpretable as summaries of unit-level effects, and being relevant to choice of a policy governing treatment assignment. We characterize many estimands as involving one of two orders of averaging over units in a population and over treatment assignments under a policy. The more common representation often results in quantities that are insufficient for optimal policy choice. This occurs because these quantities summarize outcomes under homogeneous exposure to treatment, but even homogeneous policies often lead to heterogeneous exposures. The other representation often yields quantities that lack an interpretation as summaries of unit-level effects. We argue that, among various estimands, the expected average outcome, which averages over units and treatment assignments in either order, deserves further attention from researchers. This estimand, or contrasts among these estimands under different policies, is both a summary of unit-level effects and is sufficient for optimal policy choice with utilitarian welfare.

stat.ME↗

arXiv2021

Geodesic Length Distribution in Sparse Network Ensembles

A key task in the study of networked systems is to derive local and global properties that impact connectivity, synchronizability, and robustness; computing shortest paths or geodesics yields measures of network connectivity that can explain such phenomena. We derive an analytic distribution of geodesic lengths on the giant component in the supercritical regime -- when the giant component exists -- or on small components in the subcritical regime, of any sparse (and possibly directed) network with conditionally independent edges, in the infinite-size limit. We provide specific results for widely used network models like stochastic block models, dot product graphs, random geometric graphs, and sparse graphons. The survival function of the geodesic length distribution possesses a simple closed-form expression which is asymptotically tight for finite lengths, has a natural interpretation of traversing independent geodesics in the network, and delivers novel insight into the aforementioned network families.

cs.SI↗