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Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make…
Given a large set $U$ where each item $a\in U$ has weight $w(a)$, we want to estimate the total weight $W=\sum_{a\in U} w(a)$ to within factor of $1\pm\varepsilon$ with some constant probability $>1/2$. Since $n=|U|$ is large, we want to do…
The characterization of the spectral energy distribution (SED) of dust emission has become a critical issue in the quest for primordial B-modes. The dust SED is often approximated by a modified black body (MBB) emission law but the extent…
We present a new representation of light curves, which is quite different from the binning method. Instead of choosing uniform bins, the reciprocal of interval between two successive photons is adopted to represent the counting rate. A…
Minimum redundancy among different elements of an embedding in a latent space is a fundamental requirement or major preference in representation learning to capture intrinsic informational structures. Current self-supervised learning…
The underground rates of cosmic-ray muons exhibit seasonal variations correlated with effective atmospheric temperature, quantified via a single coefficient. We compare two analysis methods for studying the correlation: the standard…
The brisk progression of the industrial digital innovation, leading to high degree of automation and big data transfer in manufacturing technologies, demands continuous development of appropriate off-line metrology methods to support…
This paper proposes a semidefinite programming based method for estimating moments of a stochastic hybrid system (SHS). For polynomial SHSs -- which consist of polynomial continuous vector fields, reset maps, and transition intensities --…
Using the recently perfected sea-boson method, we compute the momentum distribution of the one-band Hubbard model in one and two spatial dimensions. We compute the asymptotic features of the momentum distribution explicitly away from half…
We describe various moment-based ensemble interpretation models for the construction of probabilistic temperature forecasts from ensembles. We apply the methods to one year of medium range ensemble forecasts and perform in and out of sample…
This paper establishes a continuous time approximation, a piece-wise continuous differential equation, for the discrete Heavy-Ball (HB) momentum method with explicit discretization error. Investigating continuous differential equations has…
Accurate reconstruction of probability density functions (PDFs) from data is essential in engineering applications. Classical global moment-based polynomial approximations often suffer from oscillations, instability in the tails, and…
We consider a method for approximate inference in hidden Markov models (HMMs). The method circumvents the need to evaluate conditional densities of observations given the hidden states. It may be considered an instance of Approximate…
This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming…
In spite of considerable progress, computing curvature in Volume of Fluid (VOF) methods continues to be a challenge. The goal is to develop a function or a subroutine that returns the curvature in computational cells containing an interface…
Monocular depth estimation is a fundamental task in computer vision and has drawn increasing attention. Recently, some methods reformulate it as a classification-regression task to boost the model performance, where continuous depth is…
In this paper, we propose a new simple and learning-free deep learning network named MomentsNet, whose convolution layer, nonlinear processing layer and pooling layer are constructed by Moments kernels, binary hashing and block-wise…
Discriminative deep learning models with a linear+softmax final layer have a problem: the latent space only predicts the conditional probabilities $p(Y|X)$ but not the full joint distribution $p(Y,X)$, which necessitates a generative…
This paper introduces measures for how each moment contributes to the precision of parameter estimates in GMM settings. For example, one of the measures asks what would happen to the variance of the parameter estimates if a particular…
We develop moment estimators for the parameters of affine stochastic volatility models. We first address the challenge of calculating moments for the models by introducing a recursive equation for deriving closed-form expressions for…