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We consider the estimation of treatment effects in settings when multiple treatments are assigned over time and treatments can have a causal effect on future outcomes or the state of the treated unit. We propose an extension of the…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
Understanding the links between diet, metabolic changes, and health outcomes is a key focus in nutritional science and broader biological research. Analyzing relationships, such as those between ultra-processed food (UPF) intake and…
In precision medicine, Dynamic Treatment Regimes (DTRs) are treatment protocols that adapt over time in response to a patient's observed characteristics. A DTR is a set of decision functions that takes an individual patient's information as…
An enormous and ever-growing volume of data is nowadays becoming available in a sequential fashion in various real-world applications. Learning in nonstationary environments constitutes a major challenge, and this problem becomes orders of…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
In the absence of unobserved confounders, matching and weighting methods are widely used to estimate causal quantities including the Average Treatment Effect on the Treated (ATT). Unfortunately, these methods do not necessarily achieve…
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
We study the problem of observational causal inference with continuous treatments in the framework of inverse propensity-score weighting. To obtain stable weights, we design a new algorithm based on entropy balancing that learns weights to…
This paper presents an external wrench estimator that uses a hybrid dynamics model consisting of a first-principles model and a neural network. This framework addresses one of the limitations of the state-of-the-art model-based wrench…
Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which…
Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…
End-to-end representation learning has become a powerful tool for estimating causal quantities from high-dimensional observational data, but its efficiency remained unclear. Here, we face a central tension: End-to-end representation…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
Estimating causal effects of continuous treatments is a common problem in practice, for example, in studying average dose-response functions. Classical analyses typically assume that all confounders are fully observed, whereas in real-world…
Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…
We present a nonlinear non-convex model predictive control approach to solving a real-world labyrinth game. We introduce adaptive nonlinear constraints, representing the non-convex obstacles within the labyrinth. Our method splits the…
In the mixture of experts model, a common assumption is the linearity between a response variable and covariates. While this assumption has theoretical and computational benefits, it may lead to suboptimal estimates by overlooking potential…