An introduction to statistical learning with applications in R

By Fariha Sohil, Muhammad Umair Sohali, Javid Shabbir. 2021

The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. This textbook considers statistical learning applications when interest centers on the conditional distribution of a response variable, given a set of predictors, and in the absence of a credible model that can be specified before the data analysis begins. Consistent with modern data analytics, it emphasizes that a proper statistical learning data analysis depends in an integrated fashion on sound data collection, intelligent data management, appropriate statistical procedures, and an

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Citations in the corpus

Variational Autoencoders Pursue PCA Directions (by Accident) (2018, methodology): “This decomposition resembles the classical biasvariance decomposition of the square error [20].”
AutoScore: A Machine Learning–Based Automatic Clinical Score Generator and Its Application to Mortality Prediction Using Electronic Health Records (2020, methodology): “The second model was built using stepwise multivariable logistic regression [26].”
A Random Forests Approach to Predicting Clean Energy Stock Prices (2021, unknown): “RFs are ensembles of decision trees and work by introducing decorrelation between the trees by randomly selecting a small set of predictors at each split of the tree (James et al. 2013).”
The Role of Network Topology for Distributed Machine Learning (2019, unknown): “…a vector in R p and y l ∈ R , the standard linear regression method determines the optimal parameter vector considering is the squared Euclidean norm or the 1-norm, one obtains respectively ridge and lasso regression ([8] provides a simple introduction to these methods and those we mention below).”
Assessing the socio-demographic, technical, economic and behavioral factors of Nordic electric vehicle adoption and the influence of vehicle-to-grid preferences (2020, background): “06) indicating multicollinearity among all the variables was not a problem [76] and not causing high standard”
Learning Adaptive Discriminative Correlation Filters via Temporal Consistency Preserving Spatial Feature Selection for Robust Visual Object Tracking (2018, background): “, lying in a p-norm ball around 0 [62], [63].”
Forest aboveground biomass estimation using Landsat 8 and Sentinel-1A data with machine learning algorithms (2020, background): “Meanwhile, a regularization term is added to the objective function to control the complexity of the tree to obtain a simpler model and avoid overfitting 34 .”
Neural-adjoint method for the inverse design of all-dielectric metasurfaces. (2020, background): “[25] A DNN – once trained – can effectively act as a high-speed simulator that may be used to find the electromagnetic scattering of a candidate geometry substantially faster (e.”
Supervised machine learning: A brief primer (2020, methodology): “multiple trees are averaged together to provide more accurate and stable predictions (James et al., 2013).”
Rogue waves and analogies in optics and oceanography (2019, unknown): “In particular, for complex physical systems where there is no obvious model linking input and output, a machine learning algorithm can be trained using measured or simulated input and output data to determine an effective input-output model that can subsequently be used for predictive purposes [173]”
scPred: accurate supervised method for cell-type classification from single-cell RNA-seq data (2019, methodology): “By enlarging the feature space using a polynomial kernel, the cells are linearly separated in H [54].”
Evaluation of Ridge, Elastic Net and Lasso Regression Methods in Precedence of Multicollinearity Problem: A Simulation Study (2021, unknown): “(James et al., 2013).”
Current and future applications of statistical machine learning algorithms for agricultural machine vision systems (2019, methodology): “In addition to the Euclidian distance, Manhattan, Chebyshev and Mahalanobis can be used for numerical data (depending on the properties of data), while the Hamming distance can be used for the categorical or binary data (Tibshirani et al., 2013) (Table 3).”