Related papers: On the optimal stacking of noisy observations

Variational approaches to disparity estimation typically use a linearised brightness constancy constraint, which only applies in smooth regions and over small distances. Accordingly, current variational approaches rely on a schedule to…

We consider the problem of estimating the common mean of independently sampled data, where samples are drawn in a possibly non-identical manner from symmetric, unimodal distributions with a common mean. This generalizes the setting of…

In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function on a uniform grid. Both the problem of estimating the support function at a point and that of estimating…

We study the problem of recovering the latent ground truth labeling of a structured instance with categorical random variables in the presence of noisy observations. We present a new approximate algorithm for graphs with categorical…

In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…

In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate…

For systems analogous to a linear harmonic oscillator, the simplest way to characterize the state is by a covariance matrix containing the symmetrically-ordered moments of operators analogous to position and momentum. We show that using…

Summary statistics of the likelihood, such as the Bayesian evidence, offer a principled way of comparing models and assessing tension between, or within, the results of physical experiments. Noisy realisations of the data induce scatter in…

The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…

Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…

Compressed sensing (CS) is a sampling paradigm that allows to simultaneously measure and compress signals that are sparse or compressible in some domain. The choice of a sensing matrix that carries out the measurement has a defining impact…

When inferring unknown parameters or comparing different models, data must be compared to underlying theory. Even if a model has no closed-form solution to derive summary statistics, it is often still possible to simulate mock data in order…

We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…

The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…

We study feature selection in high-dimensional regression under two distinct sources of instability: sampling variability and measurement error in the design matrix. Stability Selection addresses the former through sub-sampling and…

Uncovering causal relationships is a fundamental problem across science and engineering. However, most existing causal discovery methods assume acyclicity and direct access to the system variables -- assumptions that fail to hold in many…

Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…

Explainable AI methods facilitate the understanding of model behaviour, yet, small, imperceptible perturbations to inputs can vastly distort explanations. As these explanations are typically evaluated holistically, before model deployment,…

The dichotomy between noise-stable and (completely) noise-sensitive stochastic models is of recent interest in probability theory. Of particular interest is the study of lattice models coming from statistical physics. The Fourier transform…

Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…