Related papers: Optimal Rescaling and the Mahalanobis Distance
We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known. Under a standard assumption on the concentration of the free energy, we show how…
A variety of optimization problems takes the form of a minimum norm optimization. In this paper, we study the change of optimal values between two incrementally constructed least norm optimization problems, with new measurements included in…
Nowadays government and private agencies use remote sensing imagery for a wide range of applications from military applications to farm development. The images may be a panchromatic, multispectral, hyperspectral or even ultraspectral of…
The analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
Multidimensional scaling (MDS) is a dimensionality reduction tool used for information analysis, data visualization and manifold learning. Most MDS procedures embed data points in low-dimensional Euclidean (flat) domains, such that…
Clustering of large-scale structure provides significant cosmological information through the power spectrum of density perturbations. Additional information can be gained from higher-order statistics like the bispectrum, especially to…
In modern large-scale machine learning applications, the training data are often partitioned and stored on multiple machines. It is customary to employ the "data parallelism" approach, where the aggregated training loss is minimized without…
In general, comprehension of any type of complex system depends on the resolution used to examine the phenomena occurring within it. However, identifying a priori, for example, the best time frequencies/scales to study a certain system…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
We produce methodology for regression analysis when the geographic locations of the independent and dependent variables do not coincide, in which case we speak of misaligned data. We develop and investigate two complementary methods for…
We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the…
Rescaling a vector $\vec{\delta} \in \mathbb{R}^n$ to a desired length is a common operation in many areas such as data science and machine learning. When the rescaled perturbation $\eta \vec{\delta}$ is added to a starting point $\vec{x}…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
We consider the centralized optimal estimation problem in spatially distributed systems. We use the setting of spatially invariant systems as an idealization for which concrete and detailed results are given. Such estimators are known to…
In this note we refine and improve some of the calculations in our 2019 article with Yair Censor (Applied Mathematics and Optimization, accepted for publication) where an analysis of the superiorization method is made via the principle of…
We present a general procedure for incorporating higher-order information into the scale-setting prescription of Brodsky, Lepage and Mackenzie. In particular, we show how to apply this prescription when the leading coefficient or…
We measure the clustering of dark matter halos in a large set of collisionless cosmological simulations of the flat LCDM cosmology. Halos are identified using the spherical overdensity algorithm, which finds the mass around isolated peaks…
Residuals are a key component of diagnosing model fit. The usual practice is to compute standardized residuals using expected values and standard deviations of the observed data, then use these values to detect outliers and assess model…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…