Patrick Kramer

I am a second-year PhD student in Machine Learning and Statistics at Carnegie Mellon University, where I am fortunate to be advised by Professor Edward Kennedy. My research interests lie at the intersection of Causal Inference, Machine Learning, and Optimization.

Most recently, my work has focused on causal inference with high-dimensional treatments. This research was honored with the 2026 JSM Student Paper Award from the Statistical Learning and Data Science (SLDS) section.

Prior to CMU, I completed an MSc and BSc in Mathematics (with distinction) and a BSc in Computer Science at Leipzig University, where I graduated top-of-my-class for all three degrees. My previous research includes my thesis on regression discontinuity designs with covariates, advised by Jun.-Prof. Alexander Fuchs-Kreiss.

Beyond academia, I have gained professional experience in consulting and tech, including my role as an associate for Finance Transformation at PricewaterhouseCoopers (PwC), where I consulted for major corporations on large-scale data migration and SAP S/4HANA Cloud implementations.

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Jan 22, 2026	I have received the 2026 JSM Student Best Paper Award in the SLDS section for my paper on causal inference with high-dimensional treatments.

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Causal Inference with High-Dimensional Treatments

Patrick Kramer, Isaac M. Opper, and Edward H. Kennedy

arXiv preprint arXiv:2602.21423, Feb 2026

JSM SLDS Student Best Paper Award Abs arXiv PDF

JSM SLDS Student Paper Award Website

In this work, we consider causal inference in various high-dimensional treatment settings, including for single multi-valued treatments and vector treatments with binary or continuous components, when the number of treatments can be comparable to or even larger than the number of observations. These settings bring unique challenges: first, the treatment effects of interest are a high-dimensional vector rather than a low-dimensional scalar; second, positivity violations are often unavoidable; and third, estimation can be based on a smaller effective sample size. We first discuss fundamental limits of estimating effects here, showing that consistent estimation is impossible without further assumptions. We go on to propose a novel sparse pseudo-outcome regression framework for arbitrary high-dimensional statistical functionals, which includes generic constrained regression estimators and error guarantees. We use the framework to derive new doubly robust estimators for mean potential outcomes of high-dimensional treatments, though it can also be applied to other scenarios. We analyze the proposed estimators under exact and approximate sparsity assumptions, giving finite-sample risk bounds. Finally, we derive minimax lower bounds to characterize optimal rates of convergence and show our risk bounds are unimprovable.

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