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R\'enyi Information Dimension (RID) plays a central role in quantifying the compressibility of random variables with singularities in their distribution, encompassing and extending beyond the class of sparse sources. The RID, from a high…
Regression discontinuity (RD) designs are popular quasi-experimental studies in which treatment assignment depends on whether the value of a running variable exceeds a cutoff. RD designs are increasingly popular in educational applications…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…
The sparsity and compressibility of finite-dimensional signals are of great interest in fields such as compressed sensing. The notion of compressibility is also extended to infinite sequences of i.i.d. or ergodic random variables based on…
This paper is concerned with the lossy compression of general random variables, specifically with rate-distortion theory and quantization of random variables taking values in general measurable spaces such as, e.g., manifolds and fractal…
We provide an inference procedure for the sharp regression discontinuity design (RDD) under monotonicity, with possibly multiple running variables. Specifically, we consider the case where the true regression function is monotone with…
Most entropy measures depend on the spread of the probability distribution over the sample space $\mathcal{X}$, and the maximum entropy achievable scales proportionately with the sample space cardinality $|\mathcal{X}|$. For a finite…
Compressed sensing is by now well-established as an effective tool for extracting sparsely distributed information, where sparsity is a discrete concept, referring to the number of dominant nonzero signal components in some basis for the…
In this paper we give a generalization of the discrete complex-valued random variable defined and investigated in \cite{ssa} and \cite{m8}. We prove the statements concerning the expressions for the excepted value and the variance of this…
This paper introduces robust twoblock (RTB) simultaneous dimension reduction, which is the first statistically robust method to perform simultaneous dimension reduction in two blocks of variables and allows to fine-tune the model complexity…
Regression discontinuity (RD) is a widely used quasi-experimental design for causal inference. In the standard RD, the assignment to treatment is determined by a continuous pretreatment variable (i.e., running variable) falling above or…
In this article we derive a regularity result for the disintegration of the invariant measure associated to a class of Random Dynamical Systems - RDS. The results of this work are obtained by constructing a suitable anisotropic normed space…
In this paper, we show that the Hadamard matrix acts as an extractor over the reals of the Renyi information dimension (RID), in an analogous way to how it acts as an extractor of the discrete entropy over finite fields. More precisely, we…
We consider machine learning, particularly regression, using locally-differentially private datasets. The Wasserstein distance is used to define an ambiguity set centered at the empirical distribution of the dataset corrupted by local…
In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian…
Fundamental rate-distortion-perception (RDP) trade-offs arise in applications requiring maintained perceptual quality of reconstructed data, such as neural image compression. When compressed data is transmitted over public communication…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
In many applications, piecewise continuous functions are commonly interpolated over meshes. However, accurate high-order manipulations of such functions can be challenging due to potential spurious oscillations known as the Gibbs phenomena.…
We derive fundamental accuracy limits for distributed localization when a fusion center has access only to independently rate-distortion (RD)-optimally compressed versions of multi-sensor observations, under a line-of-sight propagation…
The robustness of risk measures to changes in underlying loss distributions (distributional uncertainty) is of crucial importance in making well-informed decisions. In this paper, we quantify, for the class of distortion risk measures with…