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Aaditya Ramdas develops statistical inference methods that remain valid when data are examined sequentially. His research also includes multiple testing and machine learning. A central practical question is how to report evidence while allowing data collection to continue or stop in response to the observations.^[ref]

He coauthored distillation for the conditional randomization test, combining conditional independence testing with flexible test statistics and reduced computational cost. The calibration relies on the assumed feature conditional distribution.^[ref]

A conditional randomization test tests $Y\perp X\mid Z$ by resampling the tested variable from its conditional law given the remaining covariates. For independent sample rows, hold the observed $Y,Z$ fixed and draw each replacement vector $X^{(b)}$ from the true product conditional law of $X\mid Z$. Under the null hypothesis, the original $X$ and these replacements are conditionally exchangeable. Applying the same prespecified test statistic and fitting rule to every dataset therefore gives the valid rank-based Monte Carlo testThe add-one convention and conservative treatment of ties give finite-sample type I error control. Other resampling constructions are possible when they preserve the same conditional exchangeability.^[ref]

Replacing the true conditional law by an estimate does not automatically preserve that guarantee. For a counterexample without $Z$, let the true $X$ be a fair Bernoulli random variable and let $Y$ be constant, so independence holds. If the resampling model incorrectly uses $P(X=1)=0.99$ and the test statistic is $T=1-X$, the model assigns upper-tail probability $0.01$ whenever the observed $X=0$. That event actually occurs with probability $0.5$, so the limiting simulation test rejects far more often than level $0.05$ permits.

Estimated conditional models require a separate calibration or approximation argument. More resamples reduce Monte Carlo error but do not correct a wrong conditional law. The method tests conditional independence; interpreting it as a causal effect test requires the appropriate additional causal inference assumptions.

Eugene Katsevich works on high-dimensional statistics, variable selection and multiple testing, motivated in part by genetics and genomics. These problems require distinguishing reproducible signals from the many associations that can arise when thousands of features are examined.^[ref]

His joint work on the conditional randomization test uses a known feature conditional distribution to calibrate tests of conditional independence. Distillation makes flexible prediction methods more practical as test statistics.^[ref]

Lucas Janson studies high-dimensional statistics and statistical machine learning, with scientific collaborations in genetics, climatology and political science. His current Stanford homepage describes this combination of methodological research and applications.^[ref]

He coauthored distillation for the conditional randomization test. Its computational motivation is that a powerful test statistic may involve expensive machine learning; distillation avoids repeating the most costly fitting step for every conditional resample.^[ref]

Molei Liu develops statistical inference and machine learning methods for heterogeneous data sources and populations. His research includes transfer across populations, imperfect statistical models and biomedical applications.^[ref]

With Eugene Katsevich, Lucas Janson and Aaditya Ramdas, he developed distillation for the conditional randomization test. The method tests conditional independence by resampling a feature from its known conditional distribution given the other features, while reducing repeated model-fitting costs.^[ref]

For one unit write $M=(M_1,M_2,M_3)$ and $W=(M,Z_1,Z_3)$. Since the graph makes $S$ independent of $M$, the known distributions determine the conditional assignment lawUnder the sharp causal null hypothesis that $A$ has no effect on $Y$, delete $A\to Y$. The D-separation criterion then gives$M_2$ blocks the route through $C$, $Z_3$ blocks the route through $S$, $M_1$ and $M_3$ block the collider-opened detours through $Z_1$ and $Z_3$, and $A$ remains a collider on routes through $U$.

For independent units $i=1,\dots ,n$, choose a test statistic $T(Z_{2,1:n},Y_{1:n},W_{1:n})$ that measures residual association between $Z_2$ and $Y$. Hold $(Y_i,W_i)$ fixed and independently drawRecompute $T^{(b)}$ after each draw. A valid Monte Carlo conditional randomization test useswith a two-sided statistic or absolute value when appropriate.

Under the null, conditional on $(Y_{1:n},W_{1:n})$, the observed $Z_{2,1:n}$ and its $B$ resamples are exchangeable because they have the same product law ${\prod }_{i}q(\cdot \mid W_i)$. The rank of $T^{\mathrm{obs}}$ among the $B+1$ values is therefore uniform after randomized tie breaking and conservative without it. ConsequentlyTaking expectations proves unconditional type I error control.