There remain theoretical gaps in deep neural network estimators for the nonparametric Cox proportional hazards model. In particular, it is unclear how gradient-based optimization error propagates to population risk under partial likelihood, how pointwise bias can be controlled to permit valid inference, and how ensemble-based uncertainty quantification behaves under realistic variance decay regimes. We develop an asymptotic distribution theory for deep Cox estimators that addresses these issues. First, we establish nonasymptotic oracle inequalities for general trained networks that link in-sample optimization error to population risk without requiring the exact empirical risk optimizer. We then construct a structured neural parameterization that achieves infinity-norm approximation rates compatible with the oracle bound, yielding control of the pointwise bias. Under these conditions and using the Hajek--Hoeffding projection, we prove pointwise and multivariate asymptotic normality for subsampled ensemble estimators. We derive a range of subsample sizes that balances bias correction with the requirement that the Hajek--Hoeffding projection remain dominant. This range accommodates decay conditions on the single-overlap covariance, which measures how strongly a single shared observation influences the estimator, and is weaker than those imposed in the subsampling literature. An infinitesimal jackknife representation provides analytic covariance estimation and valid Wald-type inference for relative risk contrasts such as log-hazard ratios. Finally, we illustrate the finite-sample implications of the theory through simulations and a real data application.

Inadditiontothememory limitation, there are other important concerns.

Differentsamplingapproaches were proposed, where probabilities are not uniform, and it is not currently clear which approach is the most effective. In this paper, we formulate the problem of randomization in SGB in terms of optimization of sampling probabilities to maximize the estimation accuracy of split scoring used to train decision trees.

We wish to optimize the likelihood of the sequence conditioned on the start and the goal frame p(o2:T 1|o1,T).

Recent efforts for developing general-purpose estimators with broader coverage, incorporating thefront-door adjustment (FD) (Pearl, 2000) andothers, are not scalable due to the high computational cost of summing over a highdimensional set of variables.

We thank all 3 reviewers for their thoughtful comments. " nearest neighbor theory papers have largely not worried too much about constants......This analysis is " In the evolution of the study of nearest neighbor, early work focused on consistency, and later Y ou are absolutely correct that very few work studies the constant. We argue that this is "a feature, not " The scope of the analysis is very limited to distributed nearest neighbor classification (along with some distributional The latter is a fairly interesting direction, due to its connection with deep learning. " Currently the paper has lots of small typos. Please proofread carefully and revise.. " Thanks for pointing out, and we " Also, I find T able 1 ... How is the risk percentage defined in comparison to the oracle KNN/OWNN? " I'd suggest adding error bars to T able 1 (for example, to denote standard deviations across experimental repeats).