arXiv subjects

James Leiner

Publications and source records attributed to James Leiner.

4 recordsLinked to original sources

arXiv2025

Adaptive Off-Policy Inference for M-Estimators Under Model Misspecification

When data are collected adaptively, such as in bandit algorithms, classical statistical approaches such as ordinary least squares and $M$-estimation will often fail to achieve asymptotic normality. Although recent lines of work have modified the classical approaches to ensure valid inference on adaptively collected data, most of these works assume that the model is correctly specified. The misspecified setting poses unique challenges because the parameter of interest itself may not be well-defined over a non-stationary distribution of rewards. We therefore tackle the problem of \emph{off-policy} inference in adaptive settings, where we uniquely define a projected solution over a stationary evaluation policy. Our method provides valid inference for $M$-estimators that use adaptively collected bandit data with a possibly misspecified working model. A key ingredient in our approach is the use of flexible approaches to stabilize the variance induced by adaptive data collection. A major novelty is that the procedure enables the construction of valid confidence sets even in settings where treatment policies are unstable and non-converging, such as when there is no unique optimal arm and standard bandit algorithms are used. Empirical results on semi-synthetic datasets constructed from the Osteoarthritis Initiative demonstrate that the method maintains type I error control, while existing methods for inference in adaptive settings do not cover in the misspecified case.

stat.ME↗

arXiv2024

Graph fission and cross-validation

We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge set in a way that splits the original graph's information amongst them in any desired proportion. Our proposal builds on data fission/thinning, a method that uses external randomization to create independent copies of an unstructured dataset. We extend this idea to the graph setting where there may be latent structure between observations. We demonstrate the utility of this framework via two applications: inference after structural trend estimation on graphs and a model selection procedure we term "graph cross-validation".

stat.ME↗

arXiv2023

Data fission: splitting a single data point

Suppose we observe a random vector $X$ from some distribution $P$ in a known family with unknown parameters. We ask the following question: when is it possible to split $X$ into two parts $f(X)$ and $g(X)$ such that neither part is sufficient to reconstruct $X$ by itself, but both together can recover $X$ fully, and the joint distribution of $(f(X),g(X))$ is tractable? As one example, if $X=(X_1,\dots,X_n)$ and $P$ is a product distribution, then for any $m<n$, we can split the sample to define $f(X)=(X_1,\dots,X_m)$ and $g(X)=(X_{m+1},\dots,X_n)$. Rasines and Young (2022) offers an alternative approach that uses additive Gaussian noise -- this enables post-selection inference in finite samples for Gaussian distributed data and asymptotically when errors are non-Gaussian. In this paper, we offer a more general methodology for achieving such a split in finite samples by borrowing ideas from Bayesian inference to yield a (frequentist) solution that can be viewed as a continuous analog of data splitting. We call our method data fission, as an alternative to data splitting, data carving and p-value masking. We exemplify the method on a few prototypical applications, such as post-selection inference for trend filtering and other regression problems.

stat.ME↗

arXiv2023

Scalable Causal Structure Learning via Amortized Conditional Independence Testing

Controlling false positives (Type I errors) through statistical hypothesis testing is a foundation of modern scientific data analysis. Existing causal structure discovery algorithms either do not provide Type I error control or cannot scale to the size of modern scientific datasets. We consider a variant of the causal discovery problem with two sets of nodes, where the only edges of interest form a bipartite causal subgraph between the sets. We develop Scalable Causal Structure Learning (SCSL), a method for causal structure discovery on bipartite subgraphs that provides Type I error control. SCSL recasts the discovery problem as a simultaneous hypothesis testing problem and uses discrete optimization over the set of possible confounders to obtain an upper bound on the test statistic for each edge. Semi-synthetic simulations demonstrate that SCSL scales to handle graphs with hundreds of nodes while maintaining error control and good power. We demonstrate the practical applicability of the method by applying it to a cancer dataset to reveal connections between somatic gene mutations and metastases to different tissues.

stat.ME↗