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Patrick Johnstone

Publications and source records attributed to Patrick Johnstone.

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Treatment Effect Learning Under Sequential Randomization

Sequential treatment assignments in online experiments lead to complex dependency structures, often rendering identification, estimation and inference over treatments a challenge. Treatments in one session (e.g., a user logging on) can have an effect that persists into subsequent sessions, leading to cumulative effects on outcomes measured at a later stage. This can render standard methods for identification and inference trivially misspecified. We propose T-Learners layered into the G-Formula for this setting, building on literature from causal machine learning and identification in sequential settings. In a simple simulation, this approach prevents decaying accuracy in the presence of carry-over effects, highlighting the importance of identification and inference strategies tailored to the nature of systems often seen in the tech domain.

stat.AP

Problem-dependent convergence bounds for randomized linear gradient compression

In distributed optimization, the communication of model updates can be a performance bottleneck. Consequently, gradient compression has been proposed as a means of increasing optimization throughput. In general, due to information loss, compression introduces a penalty on the number of iterations needed to reach a solution. In this work, we investigate how the iteration penalty depends on the interaction between compression and problem structure, in the context of non-convex stochastic optimization. We focus on linear schemes, where compression and decompression can be modeled as multiplication with a random matrix. We consider several distributions of matrices, among them Haar-distributed orthogonal matrices and matrices with random Gaussian entries. We find that the impact of compression on convergence can be quantified in terms of a smoothness matrix associated with the objective function, using a norm defined by the compression scheme. The analysis reveals that in certain cases, compression performance is related to low-rank structure or other spectral properties of the problem and our bounds predict that the penalty introduced by compression is significantly reduced compared to worst-case bounds that only consider the compression level, ignoring problem data. We verify the theoretical findings experimentally, including fine-tuning an image classification model.

math.OC