arXiv subjects

Vydhourie Thiyageswaran

Publications and source records attributed to Vydhourie Thiyageswaran.

4 recordsLinked to original sources

arXiv2026

Optimal Design under Interference, Homophily, and Robustness Trade-offs

To minimize the mean squared error (MSE) in global average treatment effect (GATE) estimation under network interference, a popular approach is to use a cluster-randomized design. However, in the presence of homophily, which is common in social networks, cluster randomization can instead increase the MSE. We develop a novel potential outcomes model that accounts for interference, homophily, and heterogeneous variation. In this setting, we establish a framework for optimizing designs for worst-case MSE under the Horvitz-Thompson estimator. This leads to an optimization problem over the covariance matrices of the treatment assignment, trading off interference, homophily, and robustness. We frame and solve this problem using two complementary approaches. The first involves formulating a semidefinite program (SDP) and employing Gaussian rounding, in the spirit of the Goemans-Williamson approximation algorithm for MAXCUT. The second is an adaptation of the Gram-Schmidt Walk, a vector-balancing algorithm which has recently received much attention. Finally, we evaluate the performance of our designs through various experiments on simulated network data and a real village network dataset.

stat.ME↗

arXiv2026

Local EGOP for Continuous Index Learning

We introduce the setting of continuous index learning, in which a function of many variables varies only along a small number of directions at each point. For efficient estimation, it is beneficial for a learning algorithm to adapt, near each point $x$, to the subspace that captures the local variability of the function $f$. We pose this task as kernel adaptation along a manifold with noise, and introduce Local EGOP learning, a recursive algorithm that utilizes the Expected Gradient Outer Product (EGOP) quadratic form as both a metric and inverse-covariance of our target distribution. We prove that Local EGOP learning adapts to the regularity of the function of interest, showing that under a supervised noisy manifold hypothesis, intrinsic dimensional learning rates are achieved for arbitrarily high-dimensional noise. Empirically, we compare our algorithm to the feature learning capabilities of deep learning. Additionally, we demonstrate improved regression quality compared to two-layer neural networks in the continuous single-index setting.

stat.ML↗

arXiv2025

Data-adaptive exposure thresholds for the Horvitz-Thompson estimator of the Average Treatment Effect in experiments with network interference

Randomized controlled trials often suffer from interference, a violation of the Stable Unit Treatment Values Assumption (SUTVA) in which a unit's treatment assignment affects the outcomes of its neighbors. This interference causes bias in naive estimators of the average treatment effect (ATE). A popular method to achieve unbiasedness is to pair the Horvitz-Thompson estimator of the ATE with a known exposure mapping: a function that identifies which units in a given randomization are not subject to interference. For example, an exposure mapping can specify that any unit with at least $h$-fraction of its neighbors having the same treatment status does not experience interference. However, this threshold $h$ is difficult to elicit from domain experts, and a misspecified threshold can induce bias. In this work, we propose a data-adaptive method to select the "$h$"-fraction threshold that minimizes the mean squared error of the Hortvitz-Thompson estimator. Our method estimates the bias and variance of the Horvitz-Thompson estimator under different thresholds using a linear dose-response model of the potential outcomes. We present simulations illustrating that our method improves upon non-adaptive choices of the threshold. We further illustrate the performance of our estimator by running experiments on a publicly-available Amazon product similarity graph. Furthermore, we demonstrate that our method is robust to deviations from the linear potential outcomes model.

stat.ME↗

arXiv2024

General Covariance-Based Conditions for Central Limit Theorems with Dependent Triangular Arrays

We present a general central limit theorem with simple, easy-to-check covariance-based sufficient conditions for triangular arrays of random vectors when all variables could be interdependent. The result is constructed from Stein's method, but the conditions are distinct from related work. We show that these covariance conditions nest standard assumptions studied in the literature such as $M$-dependence, mixing random fields, non-mixing autoregressive processes, and dependency graphs, which themselves need not imply each other. This permits researchers to work with high-level but intuitive conditions based on overall correlation instead of more complicated and restrictive conditions such as strong mixing in random fields that may not have any obvious micro-foundation. As examples of the implications, we show how the theorem implies asymptotic normality in estimating: treatment effects with spillovers in more settings than previously admitted, covariance matrices, processes with global dependencies such as epidemic spread and information diffusion, and spatial process with Matérn dependencies.

stat.ME↗