arXiv research

New estimators improve efficiency in two-phase designs with coarsened data.

Paper develops estimates for Lagrangian phase changes in 2D.

Solves Dirichlet problem for Lagrangian phase equation with critical and supercritical phase.

Paper proves gradient estimates for Lagrangian mean curvature equation.

Estimates for special Lagrangian curvature equations in critical and convex cases.

Paper proves estimates for Lagrangian flow singularities.

Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering. In the first stage a quaternion extended Kalman filter, which provides a unified…

Study on critical Lagrangian phase singularities in mean curvature flow.

Phase retrieval refers to the problem of recovering real- or complex-valued vectors from magnitude measurements. The best-known algorithms for this problem are iterative in nature and rely on so-called spectral initializers that provide accurate initialization vectors. We propose a novel class of estimators suitable fo…

Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.

Derives Hessian estimates for Lagrangian mean curvature equation.

The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.

Paper doubles Hessian estimates for special Lagrangian equation with constraints.

We derive a priori interior Hessian and gradient estimates for special Lagrangian equation of phase at least a critical value in dimension three.

Develops new strategy for Hessian estimates in Lagrangian mean curvature equation.

Paper tackles joint community detection and phase synchronization in stochastic block models.

We derive a priori interior Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. Our unified approach leads to sharper estimates even for the previously known three dimensional and convex solution cases.

Deep learning based speech enhancement and source separation systems have recently reached unprecedented levels of quality, to the point that performance is reaching a new ceiling. Most systems rely on estimating the magnitude of a target source by estimating a real-valued mask to be applied to a time-frequency represe…

Proves smoothness and estimates for special Lagrangian solutions with semi-convexity.

We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP) in methods such as PhaseLift and compete with recently developed non-convex techn…

This paper proposes an approach to the joint modeling of the short-time Fourier transform magnitude and phase spectrograms with a deep generative model. We assume that the magnitude follows a Gaussian distribution and the phase follows a von Mises distribution. To improve the consistency of the phase values in the time…

Study on estimating signals from shifted and noisy copies in high dimensions, revealing a phase transition.

Improved statistical inference for expensive data using machine learning predictions.

We construct singular solutions to special Lagrangian equa- tions with subcritical phases and minimal surface systems. A priori estimate breaking families of smooth solutions are also produced cor- respondingly. A priori estimates for special Lagrangian equations with certain convexity are largely known by now.

Phase filtering and pixel quality (coherence) estimation is critical in producing Digital Elevation Models (DEMs) from Interferometric Synthetic Aperture Radar (InSAR) images, as it removes spatial inconsistencies (residues) and immensely improves the subsequent unwrapping. Large amount of InSAR data facilitates Wide A…

A novel dose-finding design for cancer clinical trials using level set estimation.

Automated surgical workflow analysis and understanding can assist surgeons to standardize procedures and enhance post-surgical assessment and indexing, as well as, interventional monitoring. Computer-assisted interventional (CAI) systems based on video can perform workflow estimation through surgical instruments' recog…

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are suffici…

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent …

A new algorithm improves both computational efficiency and statistical optimality for robust low-rank matrix and tensor estimation.

Machine learning classifies phases of spin models using improved correlation configurations.

Proves well-posedness for hard phase model in general relativity.

Paper tackles sparse phase retrieval with a novel Bayesian approach.

Study phase transitions with prescribed mean curvature in Riemannian manifolds.

The intention with this paper is to provide all the estimation concepts and techniques that are needed to implement a two-phases approach to the parametric estimation of probability of default (PD) curves. In the first phase of this approach, a raw PD curve is estimated based on parameters that reflect discriminatory p…

Tyler's M-estimator's phase transition at DS-SNR = 1 is resolved.

We study a spectral initialization method that serves a key role in recent work on estimating signals in nonconvex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In this paper, we consider arbitrary generalized linear sensing models and present a …

Characterizes RFF regression in large $n,p,N$ setting, providing precise learning phases and double descent curve.

The probability of default (PD) estimation is an important process for financial institutions. The difficulty of the estimation depends on the correlations between borrowers. In this paper, we introduce a hierarchical Bayesian estimation method using the beta binomial distribution and consider a multi-year case with a …

A neural network learns phase space properties for time series analysis.

Study uses supervised learning to classify quantum phases with limited measurements.

Bayesian and simulation methods predict credit default probabilities.

We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of approximate ranking models, we characterize the exact optimal statistical error …

Most deep learning-based models for speech enhancement have mainly focused on estimating the magnitude of spectrogram while reusing the phase from noisy speech for reconstruction. This is due to the difficulty of estimating the phase of clean speech. To improve speech enhancement performance, we tackle the phase estima…

We derive explicit, uniform, a priori interior Hessian and gradient estimates for special Lagrangian equations of all phases in dimension two.

There is an increasing need for monitoring and controlling uncertainties brought by distributed energy resources in distribution grids. For such goal, accurate multi-phase topology is the basis for correlating measurements in unbalanced distribution networks. Unfortunately, such topology knowledge is often unavailable …

We consider the problem of sparse phase retrieval from Fourier transform magnitudes to recover the $k$-sparse signal vector and its support $\mathcal{T}$. We exploit extended support estimate $\mathcal{E}$ with size larger than $k$ satisfying $\mathcal{E} \supseteq \mathcal{T}$ and obtained by a trained deep neural net…

Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting bi…