Statistical Learning and High Dimensional Data Analysis

Introductions to statistical learning, modelling, and inference using large, complex, and high-dimensional data. Model selection, dimension reduction, matrix factorization, latent variable models, graphical models, interpretability, and causality are among the topics covered. Health, social sciences, and engineering applications
This is the data science course for you if you’re interested in data analysis and interpretation. We begin by learning the mathematical definition of distance, which we then use to motivate the use of singular value decomposition (SVD) for dimension reduction and multi-dimensional scaling, as well as its relationship to principal component analysis. We will learn about the batch effect, which is currently the most difficult data analytical problem in genomics, and how techniques can be used to detect and adjust for batch effects. We will specifically describe principal component analysis and factor analysis, as well as show how these concepts are applied to data visualisation and data analysis of high-throughput experimental data.

KEY FEATURE

Statistical learning is the task of extracting information from potentially high-dimensional and noisy data in order to provide some guarantees of performance on unseen data.

High-dimensional statistics is concerned with data sets where the number of features is comparable to or greater than the number of observations.

It allows us to study the mathematical nature of objects. It includes lengths, angles, and geometrical properties like flatness and straightness.

The fundamental concept is that we can only add and subtract quantities that have the same dimensions. Two physical quantities can only be equal if their dimensions are the same.

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Key Topics

    Statistical Learning and High Dimensional Data Analysis

    Finally, we provide a brief overview of machine learning and demonstrate its application to high-throughput data. We describe the general concept of clustering analysis, as well as K-means and hierarchical clustering and how they are used in genomics. We also describe prediction algorithms such as k-nearest neighbours, as well as the concepts of training sets, test sets, error rates, and cross-validation.
    • Mathematical Distance
    • Dimension Reduction
    • Singular Value Decomposition and Principal Component Analysis
    • Multiple Dimensional Scaling Plots
    • Factor Analysis
    • Dealing with Batch Effects

    High Dimensional Data Analysis Assignment Help

    High-dimensional statistics is concerned with data sets where the number of features is comparable to or greater than the number of observations. Because classical theory and methodology can break down in surprising and unexpected ways, data sets of this type present a variety of new challenges.

    a) Correct Data Analysis – Berkeley researchers investigate both the statistical and computational challenges that arise in a high-dimensional setting. On the theoretical front, they apply techniques from statistics, probability, and information theory, such as empirical process theory, concentration inequalities, random matrix theory, and free probability. New estimators for spectral properties of matrices, randomised procedures for sketching and optimization, and algorithms for decision-making in sequential settings are among the methodological innovations. The research is motivated by and applied to a variety of scientific and engineering disciplines, such as computational biology, astronomy, recommender systems, financial time series, and climate forecasting.

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