arXiv subjects

Matthew Eichhorn

Publications and source records attributed to Matthew Eichhorn.

9 recordsLinked to original sources

arXiv2026

Low-order outcomes and clustered designs: combining design and analysis for causal inference under network interference

Variance reduction for causal inference in the presence of network interference is often achieved through either outcome modeling, typically analyzed under unit-randomized Bernoulli designs, or clustered experimental designs, typically analyzed without strong parametric assumptions. In this work, we study the intersection of these two approaches and make the following threefold contributions. First, we present an estimator of the total treatment effect (or global average treatment effect) in low-order outcome models when the data are collected under general experimental designs, generalizing previous results for Bernoulli designs. We refer to this estimator as the pseudoinverse estimator and give bounds on its bias and variance in terms of properties of the experimental design. Second, we evaluate these bounds for the case of Bernoulli graph cluster randomized (GCR) designs. Its variance scales like the smaller of the variance obtained by the estimator derived under a low-order assumption, and the variance obtained from cluster randomization, showing that combining these variance reduction strategies is preferable to using either individually. When the order of the potential outcomes model is correctly specified, our estimator is always unbiased, and under a misspecified model, we upper bound the bias by the closeness of the ground truth model to a low-order model. Third, we give empirical evidence that our variance bounds can be used to select a good clustering that minimizes the worst-case variance under a cluster randomized design from a set of candidate clusterings. Across a range of graphs and clustering algorithms, our method consistently selects clusterings that perform well on a range of response models, suggesting the practical use of our bounds.

stat.ME↗

arXiv2025

Analysis of Two-Stage Rollout Designs with Clustering for Causal Inference under Network Interference

Estimating causal effects under interference is pertinent to many real-world settings. Recent work with low-order potential outcomes models uses a rollout design to obtain unbiased estimators that require no interference network information. However, the required extrapolation can lead to prohibitively high variance. To address this, we propose a two-stage experiment that selects a sub-population in the first stage and restricts treatment rollout to this sub-population in the second stage. We explore the role of clustering in the first stage by analyzing the bias and variance of a polynomial interpolation-style estimator under this experimental design. Bias increases with the number of edges cut in the clustering of the interference network, but variance depends on qualities of the clustering that relate to homophily and covariate balance. There is a tension between clustering objectives that minimize the number of cut edges versus those that maximize covariate balance across clusters. Through simulations, we explore a bias-variance trade-off and compare the performance of the estimator under different clustering strategies.

stat.ME↗

arXiv2024

Exploiting Neighborhood Interference with Low Order Interactions under Unit Randomized Design

Network interference, where the outcome of an individual is affected by the treatment assignment of those in their social network, is pervasive in real-world settings. However, it poses a challenge to estimating causal effects. We consider the task of estimating the total treatment effect (TTE), or the difference between the average outcomes of the population when everyone is treated versus when no one is, under network interference. Under a Bernoulli randomized design, we provide an unbiased estimator for the TTE when network interference effects are constrained to low order interactions among neighbors of an individual. We make no assumptions on the graph other than bounded degree, allowing for well-connected networks that may not be easily clustered. We derive a bound on the variance of our estimator and show in simulated experiments that it performs well compared with standard estimators for the TTE. We also derive a minimax lower bound on the mean squared error of our estimator which suggests that the difficulty of estimation can be characterized by the degree of interactions in the potential outcomes model. We also prove that our estimator is asymptotically normal under boundedness conditions on the network degree and potential outcomes model. Central to our contribution is a new framework for balancing model flexibility and statistical complexity as captured by this low order interactions structure.

stat.ME↗

arXiv2023

Allocating with Priorities and Quotas: Algorithms, Complexity, and Dynamics

In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have motivated the following priority-respecting allocation problem: several categories, each with a quota of interchangeable items, wish to allocate the items among a set of agents. Each category has a list of eligible agents and a priority ordering over these agents; agents may be eligible in multiple categories. The goal is to select a valid allocation: one that respects quotas, eligibility, and priorities and ensures Pareto efficiency. We provide an algorithmic characterization of all valid allocations, exhibiting a bijection between sets of agents who can be allocated and maximum-weight matchings under carefully chosen rank-based weights. While prior work provides a polynomial-time algorithm to locate a valid allocation, our characterization admits a simpler algorithm that enables two wide-reaching extensions: 1. Selecting valid allocations that satisfy additional criteria: Via three examples -- inclusion/exclusion of some chosen agent; agent-side Pareto efficiency vs. welfare maximization; and fairness from the perspective of allocated vs. unallocated agents -- we show that finding priority-respecting allocations subject to some secondary constraint straddles a complexity knife-edge; in each example, one problem variant can be solved efficiently, while its variant is NP-hard. 2. Efficiency-envy tradeoffs in dynamic allocation: In settings where allocations must be made to T agents arriving sequentially via some stochastic process, we show that while insisting on zero priority violations leads to an Omega(T) loss in efficiency, one can design allocation policies ensuring that the sum of the efficiency loss and priority violations in hindsight is O(1).

cs.GT↗

arXiv2022

Staggered Rollout Designs Enable Causal Inference Under Interference Without Network Knowledge

Randomized experiments are widely used to estimate causal effects across a variety of domains. However, classical causal inference approaches rely on critical independence assumptions that are violated by network interference, when the treatment of one individual influences the outcomes of others. All existing approaches require at least approximate knowledge of the network, which may be unavailable and costly to collect. We consider the task of estimating the total treatment effect (TTE), or the average difference between the outcomes when the whole population is treated versus when the whole population is untreated. By leveraging a staggered rollout design, in which treatment is incrementally given to random subsets of individuals, we derive unbiased estimators for TTE that do not rely on any prior structural knowledge of the network, as long as the network interference effects are constrained to low-degree interactions among neighbors of an individual. We derive bounds on the variance of the estimators, and we show in experiments that our estimator performs well against baselines on simulated data. Central to our theoretical contribution is a connection between staggered rollout observations and polynomial extrapolation.

stat.ME↗

arXiv2022

Online Team Formation under Different Synergies

Team formation is ubiquitous in many sectors: education, labor markets, sports, etc. A team's success depends on its members' latent types, which are not directly observable but can be (partially) inferred from past performances. From the viewpoint of a principal trying to select teams, this leads to a natural exploration-exploitation trade-off: retain successful teams that are discovered early, or reassign agents to learn more about their types? We study a natural model for online team formation, where a principal repeatedly partitions a group of agents into teams. Agents have binary latent types, each team comprises two members, and a team's performance is a symmetric function of its members' types. Over multiple rounds, the principal selects matchings over agents and incurs regret equal to the deficit in the number of successful teams versus the optimal matching for the given function. Our work provides a complete characterization of the regret landscape for all symmetric functions of two binary inputs. In particular, we develop team-selection policies that, despite being agnostic of model parameters, achieve optimal or near-optimal regret against an adaptive adversary.

cs.GT↗

arXiv2021

Kaleidoscope: An Efficient, Learnable Representation For All Structured Linear Maps

Modern neural network architectures use structured linear transformations, such as low-rank matrices, sparse matrices, permutations, and the Fourier transform, to improve inference speed and reduce memory usage compared to general linear maps. However, choosing which of the myriad structured transformations to use (and its associated parameterization) is a laborious task that requires trading off speed, space, and accuracy. We consider a different approach: we introduce a family of matrices called kaleidoscope matrices (K-matrices) that provably capture any structured matrix with near-optimal space (parameter) and time (arithmetic operation) complexity. We empirically validate that K-matrices can be automatically learned within end-to-end pipelines to replace hand-crafted procedures, in order to improve model quality. For example, replacing channel shuffles in ShuffleNet improves classification accuracy on ImageNet by up to 5%. K-matrices can also simplify hand-engineered pipelines -- we replace filter bank feature computation in speech data preprocessing with a learnable kaleidoscope layer, resulting in only 0.4% loss in accuracy on the TIMIT speech recognition task. In addition, K-matrices can capture latent structure in models: for a challenging permuted image classification task, a K-matrix based representation of permutations is able to learn the right latent structure and improves accuracy of a downstream convolutional model by over 9%. We provide a practically efficient implementation of our approach, and use K-matrices in a Transformer network to attain 36% faster end-to-end inference speed on a language translation task.

cs.LG↗

arXiv2020

Learning Fast Algorithms for Linear Transforms Using Butterfly Factorizations

Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense matrix-vector multiplication, yet each has a specialized and highly efficient (subquadratic) algorithm. We ask to what extent hand-crafting these algorithms and implementations is necessary, what structural priors they encode, and how much knowledge is required to automatically learn a fast algorithm for a provided structured transform. Motivated by a characterization of fast matrix-vector multiplication as products of sparse matrices, we introduce a parameterization of divide-and-conquer methods that is capable of representing a large class of transforms. This generic formulation can automatically learn an efficient algorithm for many important transforms; for example, it recovers the $O(N \log N)$ Cooley-Tukey FFT algorithm to machine precision, for dimensions $N$ up to $1024$. Furthermore, our method can be incorporated as a lightweight replacement of generic matrices in machine learning pipelines to learn efficient and compressible transformations. On a standard task of compressing a single hidden-layer network, our method exceeds the classification accuracy of unconstrained matrices on CIFAR-10 by 3.9 points -- the first time a structured approach has done so -- with 4X faster inference speed and 40X fewer parameters.

cs.LG↗

arXiv2019

Fast Counting in Machine Learning Applications

We propose scalable methods to execute counting queries in machine learning applications. To achieve memory and computational efficiency, we abstract counting queries and their context such that the counts can be aggregated as a stream. We demonstrate performance and scalability of the resulting approach on random queries, and through extensive experimentation using Bayesian networks learning and association rule mining. Our methods significantly outperform commonly used ADtrees and hash tables, and are practical alternatives for processing large-scale data.

stat.ML↗