Related papers: Minimax Signal Detection Under Weak Noise Assumpti…
We show that galaxy ellipticity estimation for weak gravitational lensing with unweighted image moments reduces to the problem of measuring a combination of the means of three independent normal random variables. Under very general…
The nondispersive per-sample channel model for the optical fiber channel is considered. Under certain smoothness assumptions, the problem of finding the minimum amount of noise energy that can render two different input points…
Necessary and sufficient conditions of uniform consistency are explored. A hypothesis is simple. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$, $p >1$ with "small" balls deleted. The "small" balls have the…
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least…
This work establishes distribution-free upper and lower bounds on the minimax label complexity of active learning with general hypothesis classes, under various noise models. The results reveal a number of surprising facts. In particular,…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy,…
The symbol error rate of the minimum distance detector for an arbitrary multi-dimensional constellation impaired by additive white Gaussian noise is characterized as the product of a completely monotone function with a non-negative power of…
This work considers the problem of quickest detection of signals in a coupled system of $N$ sensors, which receive continuous sequential observations from the environment. It is assumed that the signals, which are modeled by general It\^{o}…
The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to…
Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as…
Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant…
Weak signal identification and inference are very important in the area of penalized model selection, yet they are under-developed and not well-studied. Existing inference procedures for penalized estimators are mainly focused on strong…
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithm's accuracy of inferring the frequencies and complex magnitudes…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
We consider the design of a linear sensing system with a fixed energy budget assuming that the sampling noise is the dominant noise source. The energy constraint implies that the signal energy per measurement decreases linearly with the…
The minimum mean square error of the estimation of a non Gaussian signal where observed from an additive white Gaussian noise channel's output, is analyzed. First, a quite general time-continuous channel model is assumed for which the…
The classical problem of quickest change detection is studied with an additional constraint on the cost of observations used in the detection process. The change point is modeled as an unknown constant, and minimax formulations are proposed…
Cognitive Radio requires efficient and reliable spectrum sensing of wideband signals. In order to cope with the sampling rate bottleneck, new sampling methods have been proposed that sample below the Nyquist rate. However, such techniques…
We consider the problem of frequency estimation of the periodic signal multiplied by a stationary Gaussian process (Ornstein-Uhlenbeck) and observed in the presence of the white Gaussian noise. We show the consistency and asymptotic…