Related papers: Fundamental Limits and Optimal Methods for Sharp A…
Causal inference has received great attention across different fields from economics, statistics, education, medicine, to machine learning. Within this area, inferring causal effects at individual level in observational studies has become…
Often in the analysis of first-order methods, assuming the existence of a quadratic growth bound (a generalization of strong convexity) facilitates much stronger convergence analysis. Hence the analysis is done twice, once for the general…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…
In some causal inference scenarios, the treatment variable is measured inaccurately, for instance in epidemiology or econometrics. Failure to correct for the effect of this measurement error can lead to biased causal effect estimates.…
Estimating heterogeneous treatment effects is central to data-driven decision-making, yet industrial applications often face a fundamental tension between limited randomized controlled trial (RCT) budgets and abundant but biased…
Estimation and inference for the Average Treatment Effect (ATE) is a cornerstone of causal inference and often serves as the foundation for developing procedures for more complicated settings. Although traditionally analyzed in a batch…
Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB…
We study categorical instrumental variable (IV) models with instrument, treatment, and outcome taking finitely many values. We derive a simple closed-form characterization of the set of joint distributions of potential outcomes that are…
It is well-known that, without restricting treatment effect heterogeneity, instrumental variable (IV) methods only identify "local" effects among compliers, i.e., those subjects who take treatment only when encouraged by the IV. Local…
The inference of causal relationships using observational data from partially observed multivariate systems with hidden variables is a fundamental question in many scientific domains. Methods extracting causal information from conditional…
We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov functionals but satisfy different inequalities. The…
While estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have…
In causal inference, it is common to estimate the causal effect of a single treatment variable on an outcome. However, practitioners may also be interested in the effect of simultaneous interventions on multiple covariates of a fixed target…
This dissertation focuses on modern causal inference under uncertainty and data restrictions, with applications to neoadjuvant clinical trials, distributed data networks, and robust individualized decision making. In the first project, we…
This paper addresses the problem of estimating causal effects when adjustment variables in the back-door or front-door criterion are partially observed. For such scenarios, we derive bounds on the causal effects by solving two non-linear…
Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances…
Estimating causal effects in a target population with unmeasured confounders is challenging, especially when instrumental variables (IVs) are unavailable. However, IVs from auxiliary populations with similar problems can help infer causal…
Learning a causal effect from observational data is not straightforward, as this is not possible without further assumptions. If hidden common causes between treatment $X$ and outcome $Y$ cannot be blocked by other measurements, one…
In experimental and observational data settings, researchers often have limited knowledge of the reasons for missing outcomes. To address this uncertainty, we propose bounds on causal effects for missing outcomes, accommodating the scenario…