Statistical methods for high dimensional data

  • How do you handle high dimensional data?

    There are two common ways to deal with high dimensional data:

    1. Choose to include fewer features.
      2. The most obvious way to avoid dealing with high dimensional data is to simply include fewer features in the dataset.
    2. Use a regularization method

  • What are the approaches for high dimensional data clustering?

    Approaches

    Subspace clustering.Projected clustering.Projection-based clustering.Bootstrap-based clustering.Hybrid approaches.Correlation clustering..

  • What is high dimensional data statistics?

    High-dimensional statistics focuses on data sets in which the number of features is of comparable size, or larger than the number of observations.
    Data sets of this type present a variety of new challenges, since classical theory and methodology can break down in surprising and unexpected ways..

  • What statistical techniques are used to visualize high dimensional data?

    t-SNE is one of the common statistical methods for visualization of high-dimensional data points.
    It provides a location in a two- or three-dimensional map to each data point..

  • Approaches

    Subspace clustering.Projected clustering.Projection-based clustering.Bootstrap-based clustering.Hybrid approaches.Correlation clustering.
  • High-dimensional statistics focuses on data sets in which the number of features is of comparable size, or larger than the number of observations.
    Data sets of this type present a variety of new challenges, since classical theory and methodology can break down in surprising and unexpected ways.
$79.99Peter Bühlmann is Professor of Statistics at ETH Zürich. His main research areas are high-dimensional statistical inference, machine learning, graphical  Table of contentsAbout this bookReviews
Methods for the analysis of high dimensional data rely heavily on multivariate statistical methods. Therefore a large part of the course content is devoted to multivariate methods, but with a focus on high dimensional settings and issues. Multivariate statistical analysis covers many methods.

Can high-dimensional statistics be hopeless if a data has a low-dimensional structure?

Nevertheless, the situation in high-dimensional statistics may not be hopeless when the data possess some low-dimensional structure.
One common assumption for high-dimensional linear regression is that the vector of regression coefficients is sparse, in the sense that most coordinates of are zero.

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What are the prerequisites for the high dimensional data analysis course?

The prerequisites for the High Dimensional Data Analysis course are the successful completion of a basic course of statistics that covers topics on data exploration and descriptive statistics, statistical modeling, and inference:

  1. linear models
  2. confidence intervals
  3. t-tests
  4. F-tests
  5. anova
  6. chi-squared test
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What is high dimensional statistics?

In statistical theory, the field of high-dimensional statistics studies data whose dimension is larger than typically considered in classical multivariate analysis.

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Who wrote statistics for high-dimensional data?

Statistics for high-dimensional data:

  1. methods
  2. theory and applications

Heidelberg; New York:Springer.
Martin J.
Wainwright (2019).
High-dimensional Statistics:A non-asymptotic viewpoint.
Cambridge, UK:Cambridge University Press.

Technique for updating numerical model with observed data

Data assimilation is a mathematical discipline that seeks to optimally combine theory with observations.
There may be a number of different goals sought – for example, to determine the optimal state estimate of a system, to determine initial conditions for a numerical forecast model, to interpolate sparse observation data using knowledge of the system being observed, to set numerical parameters based on training a model from observed data.
Depending on the goal, different solution methods may be used.
Data assimilation is distinguished from other forms of machine learning, image analysis, and statistical methods in that it utilizes a dynamical model of the system being analyzed.

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