BOUNDS ON THE CONDITIONAL AND AVERAGE TREATMENT EFFECT WITH UNOBSERVED CONFOUNDING FACTORS.

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semiparametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the opn-1/4 rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

The importance of better models in stochastic optimization.

Standard stochastic optimization methods are brittle, sensitive to stepsize choice and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate models for stochastic optimization and learning problems that exhibit better robustness to problem families and algorithmic parameters. With appropriately accurate models-which we call the aprox family-stochastic methods can be made stable, provably convergent, and asymptotically optimal; even modeling that the objective is nonnegative is sufficient for this stability. We extend these results beyond convexity to weakly convex objectives, which include compositions of convex losses with smooth functions common in modern machine learning. We highlight the importance of robustness and accurate modeling with experimental evaluation of convergence time and algorithm sensitivity.

Simultaneous dimension reduction and adjustment for confounding variation.

Dimension reduction methods are commonly applied to high-throughput biological datasets. However, the results can be hindered by confounding factors, either biological or technical in origin. In this study, we extend principal component analysis (PCA) to propose AC-PCA for simultaneous dimension reduction and adjustment for confounding (AC) variation. We show that AC-PCA can adjust for (i) variations across individual donors present in a human brain exon array dataset and (ii) variations of different species in a model organism ENCODE RNA sequencing dataset. Our approach is able to recover the anatomical structure of neocortical regions and to capture the shared variation among species during embryonic development. For gene selection purposes, we extend AC-PCA with sparsity constraints and propose and implement an efficient algorithm. The methods developed in this paper can also be applied to more general settings. The R package and MATLAB source code are available at https://github.com/linzx06/AC-PCA.