Related papers: On the Incommensurability Phenomenon
In this paper, we investigate threshold effects associated with swapping of signal and noise subspaces in estimating signal parameters from compressed noisy data. The term threshold effect refers to a sharp departure of mean-squared error…
We study inference on a low-dimensional functional $\beta$ in the presence of infinite-dimensional nuisance parameters. Classical inferential methods are typically based on Wald intervals, whose large-sample validity rests on asymptotic…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
Clinical machine learning applications are often plagued with confounders that can impact the generalizability and predictive performance of the learners. Confounding is especially problematic in remote digital health studies where the…
The interpretation of cosmological observations relies on a notion of an average Universe, which is usually considered as the homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker (FLRW) model. However, inhomogeneities may…
We study the Hausdorff dimension of Poissonian cutout sets defined via inhomogeneous intensity measures on Ahlfors-regular metric spaces. We obtain formulas for the Hausdorff dimension of such cutouts in self-similar and self-conformal…
Propensity Score Matching (PSM) stands as a widely embraced method in comparative effectiveness research. PSM crafts matched datasets, mimicking some attributes of randomized designs, from observational data. In a valid PSM design where all…
The era of big data has witnessed an increasing availability of multiple data sources for statistical analyses. We consider estimation of causal effects combining big main data with unmeasured confounders and smaller validation data with…
While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the interrelation of two stochastic variables $X$ and $Y$, it fails for multidimensional variables such as Cartesian coordinates.…
We investigate the problem of representing information measures in terms of the moments of the underlying random variables. First, we derive polynomial approximations of the conditional expectation operator. We then apply these…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…
We present two methods for bounding the probabilities of benefit and harm under unmeasured confounding. The first method computes the (upper or lower) bound of either probability as a function of the observed data distribution and two…
An important aspect of large-scale structure data analysis is the presence of non-negligible theoretical uncertainties, which become increasingly important on small scales. We show how to incorporate these uncertainties in realistic power…
We consider the problem of computing the smallest possible distortion for embedding of a given n-point metric space into R^d, where d is fixed (and small). For d=1, it was known that approximating the minimum distortion with a factor better…
Recently emerging large-scale biomedical data pose exciting opportunities for scientific discoveries. However, the ultrahigh dimensionality and non-negligible measurement errors in the data may create difficulties in estimation. There are…
A time series is a sequence of data items; typical examples are videos, stock ticker data, or streams of temperature measurements. Quite some research has been devoted to comparing and indexing simple time series, i.e., time series where…
A basic issue in both teaching of and practice of statistics is the interplay between modelling assumptions and inference performance. The general message conveyed is that stronger assumptions lead to better statistical performance of the…
In this work, we investigate the incompatibility of random quantum measurements. Most previous work has focused on characterizing the maximal amount of white noise that any fixed number of incompatible measurements with a fixed number of…