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Boson sampling is one of the main quantum computation models to demonstrate the quantum computational advantage. However, this aim may be hard to realize considering two main kinds of noises, which are photon distinguishability and photon…
This paper provides some useful tests for fitting a parametric single-index regression model when covariates are measured with error and validation data is available. We propose two tests whose consistency rates do not depend on the…
Machine learning models that are developed with invariance to certain types of data transformations have demonstrated superior generalization performance in practice. However, the underlying mechanism that explains why invariance leads to…
While neural networks have made significant strides in many AI tasks, they remain vulnerable to a range of noise types, including natural corruptions, adversarial noise, and low-resolution artifacts. Many existing approaches focus on…
A framework is developed using techniques from rate distortion theory in statistical testing. The idea is first to do optimal compression according to a certain distortion function and then use information divergence from the compressed…
We consider the problem of testing the parametric form of the volatility for high frequency data. It is demonstrated that in the presence of microstructure noise commonly used tests do not keep the preassigned level and are inconsistent.…
Learning models that are robust to distribution shifts is a key concern in the context of their real-life applicability. Invariant Risk Minimization (IRM) is a popular framework that aims to learn robust models from multiple environments.…
Inference and hypothesis testing are typically constructed on the basis that a specific model holds for the data. To determine the veracity of conclusions drawn from such data analyses, one must be able to identify the presence of the…
Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…
We study the problem of testing the covariance matrix of a high-dimensional Gaussian in a robust setting, where the input distribution has been corrupted in Huber's contamination model. Specifically, we are given i.i.d. samples from a…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
An artificial intelligence (AI) model can be viewed as a function that maps inputs to outputs in high-dimensional spaces. Once designed and well trained, the AI model is applied for inference. However, even optimized AI models can produce…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
We propose a permutation-based method for testing a large collection of hypotheses simultaneously. Our method provides lower bounds for the number of true discoveries in any selected subset of hypotheses. These bounds are simultaneously…
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…
We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic…
Recently, there has been growing concern about heavy-tailed and skewed noise in biological data. We introduce RobustPALMRT, a flexible permutation framework for testing the association of a covariate of interest adjusted for control…
The classic integrated conditional moment test is a promising method for testing regression model misspecification. However, it severely suffers from the curse of dimensionality. To extend it to handle the testing problem for parametric…
This paper studies one-sided hypothesis testing under random sampling without replacement. That is, when $n+1$ binary random variables $X_1,\ldots, X_{n+1}$ are subject to a permutation invariant distribution and $n$ binary random variables…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…