arXiv subjects

Bryan Park

Publications and source records attributed to Bryan Park.

6 recordsLinked to original sources

arXiv2026

Neyman Jackknife: Design-Based Variance Estimation for Causal Inference under Interference

We propose a framework, the Neyman Jackknife, for conservative variance estimation in finite-population causal inference under interference. Our approach provides a general, flexible blueprint that enables conservative variance estimation whenever we are able to recompute our target estimator with some treatment assignments omitted. In classical settings, our approach recovers estimators closely related to the Neyman estimator under SUTVA and the Newey-West HAC variance estimator for time series. Numerical experiments suggest that our general-purpose framework yields variance estimators that can match or even surpass the performance of baselines that were purpose-built for specific applications.

stat.ME↗

arXiv2026

Treatment effect estimation under convergent network interference

Under network interference, a unit's observed outcome depends on the treatment assignment of its neighboring units in an exposure graph. Existing design-based asymptotic theory typically considers local interference by restricting neighborhood sizes in the exposure graph. Such methods do not apply to dense exposure graphs, so prior work has often adopted a superpopulation approach instead, imposing regularity through random-graph models. In this paper, we introduce a notion of convergence for a sequence of finite populations under anonymous interference. Building on the graph limit framework of Lov\'{a}sz and Szegedy, we show that large-scale geometry of the exposure graph can provide a source of regularity beyond sparsity assumptions or random-graph modeling. Under Bernoulli assignment, our convergence notion yields asymptotic normality of standard estimators for the average direct effect, even on dense, non-random exposure graphs. As a special case, graphon-based random-graph models studied in prior work generate finite populations that converge in our sense. Under these models, graph randomness generates exposure graphs with stable large-scale geometry, while first-order uncertainty in average direct effect estimation is driven by treatment assignment.

math.ST↗

arXiv2024

Random walk in slowly changing environments

A Random Walk in Changing Environment (RWCE) is a weighted random walk on a locally finite, connected graph $G$ with random, time-dependent edge-weights. This includes self-interacting random walks, where the edge-weights depend on the history of the process. In general, even the basic question of recurrence or transience for RWCEs is difficult, especially when the underlying graph contains cycles. In this note, we derive a condition for recurrence or transience that is too restrictive for classical RWCEs but instead works for any graph $G.$ Namely, we show that any bounded RWCE on $G$ with "slowly" changing edge-weights inherits the recurrence or transience of the initial weighted graph.

math.PR↗

arXiv2024

A manufacturable platform for photonic quantum computing

Whilst holding great promise for low noise, ease of operation and networking, useful photonic quantum computing has been precluded by the need for beyond-state-of-the-art components, manufactured by the millions. Here we introduce a manufacturable platform for quantum computing with photons. We benchmark a set of monolithically-integrated silicon photonics-based modules to generate, manipulate, network, and detect photonic qubits, demonstrating dual-rail photonic qubits with $99.98\% \pm 0.01\%$ state preparation and measurement fidelity, Hong-Ou-Mandel quantum interference between independent photon sources with $99.50\%\pm0.25\%$ visibility, two-qubit fusion with $99.22\%\pm0.12\%$ fidelity, and a chip-to-chip qubit interconnect with $99.72\%\pm0.04\%$ fidelity, not accounting for loss. In addition, we preview a selection of next generation technologies, demonstrating low-loss silicon nitride waveguides and components, fabrication-tolerant photon sources, high-efficiency photon-number-resolving detectors, low-loss chip-to-fiber coupling, and barium titanate electro-optic phase shifters.

quant-ph↗

arXiv2023

A graph-theoretic remark on Stieltjes moment sequences

For any integer $k\geq 1,$ define $L_k: \mathbb{R}^\mathbb{N}\to \mathbb{R}^\mathbb{N}$ by $(a_n)_{n\in\mathbb{N}}\mapsto (a'_n)_{n\in\mathbb{N}}$ where $a'_n=\det(a_{n+i+j})_{i,j=0}^{k-1}$. Previously, Zhu showed that $L_k$ preserves the Stieltjes moment (SM) property of sequences (Proc. Am. Math. Soc., 2019). The proof used the characterization of SM sequences in terms of positive semidefinite Hankel matrices. In this note, we give another proof by viewing SM sequences as weighted enumerations of closed walks on $\mathbb{N}$. Our proof is essentially a double-counting argument that views a $k$-tuple of non-crossing Dyck paths as a single closed walk on some bipartite subgraph of $\mathbb{N}^k.$

math.CO↗

arXiv2023

A simple proof of the non-uniform Kahn-Kalai conjecture

We revisit the Kahn-Kalai conjecture, recently proved in striking fashion by Park and Pham, and present a slightly reformulated simple proof which has a few advantages: (1) it works for non-uniform product measures, (2) it gives near-optimal bounds even for sampling probabilities close to 1, (3) it gives a clean bound of $p_c \leq 4q_c \log_2 (7\ell)$ for every $\ell$-bounded set system, $\ell\geq 1$.

math.CO↗