Related papers: Regularizing towards Causal Invariance: Linear Mod…

We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

Discovering causal relations is fundamental to reasoning and intelligence. In particular, observational causal discovery algorithms estimate the cause-effect relation between two random entities $X$ and $Y$, given $n$ samples from $P(X,Y)$.…

Popular debiased estimation methods for causal inference -- such as augmented inverse propensity weighting and targeted maximum likelihood estimation -- enjoy desirable asymptotic properties like statistical efficiency and double robustness…

Recent work has shown that Transformers can perform in-context learning for linear regression under restrictive assumptions, including i.i.d. data, Gaussian noise, and Gaussian regression coefficients. However, real-world data often violate…

Deep Neural Networks, despite their great success in diverse domains, are provably sensitive to small perturbations on correctly classified examples and lead to erroneous predictions. Recently, it was proposed that this behavior can be…

We consider a statistical inverse learning problem, where we observe the image of a function $f$ through a linear operator $A$ at i.i.d. random design points $X_i$, superposed with an additive noise. The distribution of the design points is…

Inverse optimal control can be used to characterize behavior in sequential decision-making tasks. Most existing work, however, is limited to fully observable or linear systems, or requires the action signals to be known. Here, we introduce…

Causal models are important tools to understand complex phenomena and predict the outcome of controlled experiments, also known as interventions. In this work, we present statistical rates of estimation for linear cyclic causal models under…

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…

We propose a novel data-dependent structured gradient regularizer to increase the robustness of neural networks vis-a-vis adversarial perturbations. Our regularizer can be derived as a controlled approximation from first principles,…

Distinguishing causal connections from correlations is important in many scenarios. However, the presence of unobserved variables, such as the latent confounder, can introduce bias in conditional independence testing commonly employed in…

Identifying variables responsible for changes to a biological system enables applications in drug target discovery and cell engineering. Given a pair of observational and interventional datasets, the goal is to isolate the subset of…

Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

The development of nonlinear optimization algorithms capable of performing reliably in the presence of noise has garnered considerable attention lately. This paper advocates for strategies to create noise-tolerant nonlinear optimization…

Conditional diffusion models have the generative controllability by incorporating external conditions. However, their performance significantly degrades with noisy conditions, such as corrupted labels in the image generation or unreliable…

We provide new results for nonparametric identification, estimation, and inference of causal effects using `proxy controls': observables that are noisy but informative proxies for unobserved confounding factors. Our analysis applies to…

Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…