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Variance estimation is important for statistical inference. It becomes non-trivial when observations are masked by serial dependence structures and time-varying mean structures. Existing methods either ignore or sub-optimally handle these…
We develop a class of optimal tests for a structural break occurring at an unknown date in infinite and growing-order time series regression models, such as AR($\infty$), linear regression with increasingly many covariates, and…
We find large deviations rates for consensus-based distributed inference for directed networks. When the topology is deterministic, we establish the large deviations principle and find exactly the corresponding rate function, equal at all…
Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…
We study high-dimensional, ridge-regularized logistic regression in a setting in which the covariates may be missing or corrupted by additive noise. When both the covariates and the additive corruptions are independent and normally…
We consider the problem of estimating change in the dependency structure between two $p$-dimensional Ising models, based on respectively $n_1$ and $n_2$ samples drawn from the models. The change is assumed to be structured, e.g., sparse,…
We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…
A stepped wedge design is a unidirectional crossover design where clusters are randomized to distinct treatment sequences. While model-based analysis of stepped wedge designs is standard practice to evaluate treatment effects accounting for…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
Gaussian mixture models are widely used to model data generated from multiple latent sources. Despite its popularity, most theoretical research assumes that the labels are either independent and identically distributed, or follows a Markov…
We study the problem of learning a directed acyclic graph from data generated according to an additive, non-linear structural equation model with Gaussian noise. We express each non-linear function through a basis expansion, and derive a…
We solve the problem of estimating the distribution of presumed i.i.d. observations for the total variation loss. Our approach is based on density models and is versatile enough to cope with many different ones, including some density…
Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…
We study theoretical predictive performance of ridge and ridge-less least-squares regression when covariate vectors arise from evaluating $p$ random, means-square continuous functions over a latent metric space at $n$ random and unobserved…
Adaptive designs dynamically update treatment probabilities using information accumulated during the experiment. Existing theory for causal inference from adaptive experiments primarily assumes the superpopulation framework with independent…
A meta-model of the input-output data of a computationally expensive simulation is often employed for prediction, optimization, or sensitivity analysis purposes. Fitting is enabled by a designed experiment, and for computationally expensive…
This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a data-dependent manner. Our bounds improve previous bounds…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
The win ratio is increasingly used in randomized trials due to its intuitive clinical interpretation, ability to incorporate the relative importance of composite endpoints, and its capacity for combining different types of outcomes (e.g.…
In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…