Related papers: Bivariate one-sample optimal location test for sph…
We develop efficient binary (i.e., 1-bit) and multi-bit coding schemes for estimating the scale parameter of $\alpha$-stable distributions. The work is motivated by the recent work on one scan 1-bit compressed sensing (sparse signal…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
We study the reknown deconvolution problem of recovering a distribution function from independent replicates (signal) additively contaminated with random errors (noise), whose distribution is known. We investigate whether a Bayesian…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are…
I point out the mathematical correspondence between an incoherent imaging model proposed by my group in the study of quantum-inspired superresolution [Tsang, Nair, and Lu, Physical Review X 6, 031033 (2016)] and a noise spectroscopy model…
This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…
We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor linear systems driven by unbounded noise and controlled over discrete noiseless channels under fixed-rate information…
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…
Bistatic radar measurements offer unique spatial diversity and enhanced target characterization capabilities, rendering them increasingly vital for contemporary sensing application research. The reliability of such measurements is…
Given a single copy of a mixed state of the form \rho=\lambda\rho_1+(1-\lambda)\rho_2, what is the optimal measurement to estimate the parameter \lambda, if \rho_1 and \rho_2 are known? We present a general strategy to obtain the optimal…
This paper relaxes the restrictive symmetry conditions adopted in [4], [5] and extends their universal feature selection framework to accommodate noisy observations as well as attribute structures that may exhibit directional preferences.…
We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…
The standard procedure for detection of gravitational wave coalescing binaries signals is based on Wiener filtering with an appropriate bank of template filters. This is the optimal procedure in the hypothesis of addictive Gaussian and…
Diffusion models, typically formulated as discretizations of stochastic differential equations (SDEs), have achieved state-of-the-art performance in generative tasks. However, their theoretical analysis often involves complex proofs. In…
A Bayesian analysis of the probability of a signal in the presence of background is developed, and criteria are proposed for claiming evidence for, or the discovery of a signal. The method is general and in particular applicable to sparsely…
We discuss a one-sample location test that can be used in the case of high-dimensional data. For high-dimensional data, the power of Hotelling's test decrises when the dimension is close to the sample size. To address this loss of power,…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
We extend the validity of Hardy's nonlocality without inequalities proof to cover the case of special one-parameter classes of non-pure statistical operators. These mixed states are obtained by mixing the Hardy states with a completely…
For an empirical signed measure $\mu = \frac{1}{N} \left(\sum_{i=1}^P \delta_{x_i} - \sum_{i=1}^M \delta_{y_i}\right)$, particle annihilation (PA) removes $N_A$ particles from both $\{x_i\}_{i=1}^P$ and $\{y_i\}_{i=1}^M$ simultaneously,…