Related papers: Constructing Confidence Intervals for the Signals …
Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics…
The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse…
We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…
Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…
In an empirical Bayes analysis, we use data from repeated sampling to imitate inferences made by an oracle Bayesian with extensive knowledge of the data-generating distribution. Existing results provide a comprehensive characterization of…
We propose a method for filling gaps and removing interferences in time series for applications involving continuous monitoring of environmental variables. The approach is non-parametric and based on an iterative pattern-matching between…
We consider the problem of estimating an unknown coordinate-wise monotone function given noisy measurements, known as the isotonic regression problem. Often, only a small subset of the features affects the output. This motivates the sparse…
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…
This paper deals with sparse phase retrieval, i.e., the problem of estimating a vector from quadratic measurements under the assumption that few components are nonzero. In particular, we consider the problem of finding the sparsest vector…
Privacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often produces complex and intractable sampling distributions. In this paper, we propose a simulation-based "repro…
We propose a new optimization framework for aleatoric uncertainty estimation in regression problems. Existing methods can quantify the error in the target estimation, but they tend to underestimate it. To obtain the predictive uncertainty…
We study the problem of estimating finite sample confidence intervals of the mean of a normal population under the constraint of differential privacy. We consider both the known and unknown variance cases and construct differentially…
The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
We propose a method for estimating disparity confidence intervals in stereo matching problems. Confidence intervals provide complementary information to usual confidence measures. To the best of our knowledge, this is the first method…
Existing conformal prediction algorithms estimate prediction intervals at target confidence levels to characterize the performance of a regression model on new test samples. However, considering an autonomous system consisting of multiple…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…
This paper proposes a recursive interval-valued estimation framework for identifying the parameters of linearly parameterized systems which may be slowly time-varying. It is assumed that the model error (which may consist in measurement…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…