Related papers: Principal Moment Analysis
Most biological data are multidimensional, posing a major challenge to human comprehension and computational analysis. Principal component analysis is the most popular approach to rendering two- or three-dimensional representations of the…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…
For probabilistic programs, it is usually not possible to automatically derive exact information about their properties, such as the distribution of states at a given program point. Instead, one can attempt to derive approximations, such as…
Factor analysis, a classical multivariate statistical technique is popularly used as a fundamental tool for dimensionality reduction in statistics, econometrics and data science. Estimation is often carried out via the Maximum Likelihood…
In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…
We propose a novel model for nonlinear dimension reduction motivated by the probabilistic formulation of principal component analysis. Nonlinearity is achieved by specifying different transformation matrices at different locations of the…
Principal component analysis is a statistical method, which lowers the number of important variables in a data set. The use of this method for the bursts' spectra and afterglows is discussed in this paper. The analysis indicates that three…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
Inference in models where the parameter is defined by moment inequalities is of interest in many areas of economics. This paper develops a new method for improving the performance of generalized moment selection (GMS) testing procedures in…
The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite…
Principal component analysis is a widely-used method for the dimensionality reduction of a given data set in a high-dimensional Euclidean space. Here we define and analyze two analogues of principal component analysis in the setting of…
The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…
Prony's method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree. In this note, we give a generalization of this…
When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…
In extreme value analysis, sensitivity of inference to the definition of extreme event is a paramount issue. Under the peaks-over-threshold (POT) approach, this translates directly into the need of fitting a Generalized Pareto distribution…
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy…
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…
Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…