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Mathematics of Data Science

arXiv 2607.11938 ↗First posted 11 Jul 2026cs.LG cs.AI cs.ITcited by 0

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Abstract (arXiv)

This book is about the mathematical foundations of data science. 1. Introduction 2. Curses, Blessings, and Surprises in High Dimensions 3. Singular Value Decomposition and Principal Component Analysis 4. Linear Regression and Regularization 5. Graphs, Networks, and Clustering 6. Nonlinear Dimension Reduction and Diffusion Maps 7. Linear Dimension Reduction via Random Projections 8. Optimization for Data Science 9. Classification 10. A Mathematical Introduction to Deep Learning 11. Large Sample Limit of Graph Laplacians 12. Community 13. Concentration of Measure and Gaussian Analysis 14. Matrix Concentration Inequalities 15. Compressive Sensing and Sparsity 16. Low-Rank Matrix Recovery

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 26 of its 478 references that are in the map. First posted on arXiv 11 Jul 2026.

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26 of 478 references.

References · 26

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2013Efficient Estimation of Word Representations in Vector Spacecited by 4,375
  4. 2014Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translationcited by 4,057
  5. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
  6. 2016Understanding deep learning requires rethinking generalizationcited by 1,674
  7. 2023Gemini: A Family of Highly Capable Multimodal Modelscited by 872
  8. 2016End-to-end Optimized Image Compressioncited by 696
  9. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  10. 2019Are Transformers universal approximators of sequence-to-sequence functions?cited by 406
  11. 2015Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decompositioncited by 64
  12. 2016Optimality of the Johnson-Lindenstrauss Lemmacited by 42
14 more
  1. 2013A Proof Of The Block Model Threshold Conjecturecited by 36
  2. 2014Achieving Exact Cluster Recovery Threshold via Semidefinite Programmingcited by 33
  3. 2024Mathematical theory of deep learningcited by 23
  4. 2020Strong Consistency, Graph Laplacians, and the Stochastic Block Modelcited by 21
  5. 2015Random Laplacian matrices and convex relaxationscited by 14
  6. 2017Permutation methods for factor analysis and PCAcited by 9
  7. 2015Detectability thresholds and optimal algorithms for community structure in dynamic networkscited by 8
  8. 2016Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronizationcited by 8
  9. 2024Acceleration by Random Stepsizes: Hedging, Equalization, and the Arcsine Stepsize Schedulecited by 6
  10. 2013The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into ℓ1cited by 4
  11. 2015Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gapcited by 3
  12. 2025Randomstrasse101: Open Problems of 2024cited by 3
  13. 2024Auto-Calibration and Biconvex Compressive Sensing with Applications to Parallel MRIcited by 2
  14. 2023An Introduction to Transformerscited by 1

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