Related papers: Reducing multi-dimensional information into a 1-d …
We consider the task of lossy compression of high-dimensional vectors through quantization. We propose the approach that learns quantization parameters by minimizing the distortion of scalar products and squared distances between pairs of…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
Technological innovations have revolutionized the process of scientific research and knowledge discovery. The availability of massive data and challenges from frontiers of research and development have reshaped statistical thinking, data…
The redshift-space bispectrum (three point statistics) of galaxies depends on the expansion rate, the growth rate, and geometry of the Universe, and hence can be used to measure key cosmological parameters. In a homogeneous Universe the…
We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging…
The simple entropic method to statistical reconstructing of heterogeneous three-dimensional media from a single two-dimensional image is briefly reported. We apply the entropic descriptor quantifying spatial inhomogeneity that depends on…
This paper provides an overview of recent developments in quickest change detection (QCD) for high-dimensional multi-sensor systems, with an emphasis on settings involving structural constraints and limited sensing resources. Classical QCD…
We present new findings in regard to data analysis in very high dimensional spaces. We use dimensionalities up to around one million. A particular benefit of Correspondence Analysis is its suitability for carrying out an orthonormal…
Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to provide a novel categorization of the data…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…
The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…
The time domain waveform of a speech signal carries all of the auditory information. From the phonological point of view, it little can be said on the basis of the waveform itself. However, past research in mathematics, acoustics, and…
Dimension reduction is a common strategy to study non-linear dynamical systems composed by a large number of variables. The goal is to find a smaller version of the system whose time evolution is easier to predict while preserving some of…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…
Multidimensional scaling (MDS) is a widely used approach to representing high-dimensional, dependent data. MDS works by assigning each observation a location on a low-dimensional geometric manifold, with distance on the manifold…
Here, I focus on the use of microscopic, few-body techniques that are relevant in the many-body problem. These methods can be divided into indirect and direct. In particular, indirect methods are concerned with the simplification of the…
Statisticians and quantitative neuroscientists have actively promoted the use of independence relationships for investigating brain networks, genomic networks, and other measurement technologies. Estimation of these graphs depends on two…
For a high-dimensional parameter of interest, tests based on quadratic statistics are known to have low power against subsets of the parameter space (henceforth, parameter subspaces). In addition, they typically involve an inverse…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Accurate Monte Carlo (MC) modelling in high-energy physics is challenging, particularly in complex scenarios where simulations fail to reproduce observed data. In practice, experimental information is often limited to one-dimensional (1D)…