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The same machine learning model running on different edge devices may produce highly-divergent outputs on a nearly-identical input. Possible reasons for the divergence include differences in the device sensors, the device's signal…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…
In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…
Regulatory authorities guide the use of permutation tests or randomization tests so as not to increase the type-I error rate when applying covariate-adaptive randomization in randomized clinical trials. For non-inferiority and equivalence…
In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…
In this paper, we investigate local permutation tests for testing conditional independence between two random vectors $X$ and $Y$ given $Z$. The local permutation test determines the significance of a test statistic by locally shuffling…
Recent advances have demonstrated the possibility of solving the deconvolution problem without prior knowledge of the noise distribution. In this paper, we study the repeated measurements model, where information is derived from multiple…
Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…
We derive a new class of statistical tests for generalized linear models based on thresholding point estimators. These tests can be employed whether the model includes more parameters than observations or not. For linear models, our tests…
The authors discuss how general regularization schemes, in particular linear regularization schemes and projection schemes, can be used to design tests for signal detection in statistical inverse problems. It is shown that such tests can…
This paper deals with adaptive radar detection of a subspace signal competing with two sources of interference. The former is Gaussian with unknown covariance matrix and accounts for the joint presence of clutter plus thermal noise. The…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
Experimental research on behavior and cognition frequently rests on stimulus or subject selection where not all characteristics can be fully controlled, even when attempting strict matching. For example, when contrasting patients to…
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…
We develop techniques to convexify a set that is invariant under permutation and/or change of sign of variables and discuss applications of these results. First, we convexify the intersection of the unit ball of a permutation and…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance…
We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…