Statistics

• A First Course in Monte Carlo Methods

  D. Sanz-Alonso & O. Al-Ghattas · Book

  A First Course in Monte Carlo Methods D. Here, B10000 = 7854 draws fell within the unit circle, leading to an estimate bπ10000 = 3.1416. 2 2.1 A strictly increasing c.d.f. 10 2.2 Inverse transformation method for sampling from an Exponential(1) distribu- tion.

  Also filed under Quant Finance, Math

• An Introduction To Statistical Learning with Applications in Python

  Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani, Jonathan Taylor · Book

  "An Introduction to Statistical Learning with Applications in Python" is an essential guide to statistical and machine learning methods, providing a clear and accessible introduction to the field. Designed for students, researchers, and practitioners, this book offers a balance between theory and practical implementation, focusing on Python-based applications for data analysis and predictive modeling. Key Highlights: Comprehensive Coverage of Statistical Learning: The book explains core machine learning principles, including supervised and unsupervised learning, model evaluation, and statistical inference. Regression and Classification Techniques: Topics include linear regression, logistic regression, decision trees, and support vector machines (SVMs), providing practical guidance on applying these models effectively. Resampling Methods and Model Selection: Introduces cross-validation and bootstrap techniques, helping readers understand how to improve model performance and avoid overfitting. Tree-Based and Ensemble Methods: Covers random forests, gradient boosting, and bagging, which are widely used in modern machine learning applications. Unsupervised Learning Techniques: Introduces principal component analysis (PCA), k-means clustering, and hierarchical clustering, essential for working with high-dimensional data. Python-Based Implementation: The book provides hands-on coding examples using scikit-learn, NumPy, pandas, and Matplotlib, enabling readers to apply theoretical concepts in real-world scenarios. This book serves as a valuable resource for those looking to build a strong foundation in statistical learning, blending intuitive explanations, practical examples, and Python-based applications to make complex concepts accessible to a broad audience.

  Also filed under Python, Machine Learning

• Artificial Intelligence Index Report 2024

  Ray Perrault & Jack Clark · Book

  The "Artificial Intelligence Index Report 2024" is the seventh edition of an annual comprehensive analysis that tracks, collates, distills, and visualizes data related to artificial intelligence (AI). Produced by the Stanford Institute for Human-Centered Artificial Intelligence (HAI), this report aims to provide unbiased, rigorously vetted, and broadly sourced data to inform policymakers, researchers, executives, journalists, and the general public about the complex field of AI. Key Highlights: Expansion of Scope: This edition broadens its coverage to include essential trends such as technical advancements in AI, public perceptions of the technology, and the geopolitical dynamics surrounding its development. Original Data and New Analyses: Featuring more original data than previous editions, the report introduces new estimates on AI training costs, detailed analyses of the responsible AI landscape, and an entirely new chapter dedicated to AI's impact on science and medicine. Generative AI Investment Surge: Despite a decline in overall AI private investment in 2023, funding for generative AI surged, nearly octupling from 2022 to reach $25.2 billion. Major players in the generative AI space, including OpenAI, Anthropic, Hugging Face, and Inflection, reported substantial fundraising rounds. U.S. Leadership in AI Investment: The United States saw AI investments reach $67.2 billion in 2023, nearly 8.7 times more than China, the next highest country. Impact on Science and Medicine: An entirely new chapter is dedicated to AI's impact on science and medicine, reflecting the growing influence of AI technologies in these critical fields. This report serves as an essential resource for understanding the current state and future trajectory of AI, offering a blend of data-driven insights and comprehensive analyses across various dimensions of artificial intelligence.

  Also filed under AI, Machine Learning

• Artificial Intelligence/ Machine Learning Explained

  Steve Blank · Guide

  about the competitive edge they’d have by today in business or as a nation. That’s where we are today with Artificial Intelligence and Machine Learning. These technologies will transform businesses and government agencies. Today, 100s of billions of dollars in private capital have been invested in 1,000s of AI startups.

  Also filed under Machine Learning, AI

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

  Sergey Ioffe and Christian Szegedy (Google) · Report

  The 2015 paper introducing batch normalization — a technique that normalizes layer inputs during training, dramatically accelerating convergence and enabling higher learning rates. Standard component of modern CNN and Transformer architectures.

  Also filed under AI, Machine Learning

• Brownian Motion: The Foundation

  Author Unknown · Notes

  Brownian Motion: The Foundation When you look at a stock’s price over time, it doesn't move in a straight line. Instead, it fluctuates, moving up and down in an unpredictable manner. This kind of movement can be modeled using Brownian Motion, a fundamental stochastic process. Brownian Motion models the random movement observed in particles suspended in a fluid, and in finance, it models the random fluctuations of asset prices over time.

  Also filed under Math, Quant Finance

• correlation-vs-causation

  Author Unknown · Book

  Overview of Correlation and Causation 2. Pearson Correlation Coefficient (r) 2. Spearman Rank Correlation Coefficient (￿or rs) 3. Kendall Tau Rank Correlation Coefficient (￿or Kendall’s ￿) 4.

  Also filed under Risk Management

• Data Science from Scratch

  Steven Cooper · Book

  "Data Science from Scratch" by Steven Cooper is an excellent introduction to the world of data science for beginners and intermediate learners alike. The book focuses on the foundational concepts of data science and offers a practical approach to understanding its key principles, including algorithms, statistical analysis, and machine learning. The author breaks down complex topics into digestible pieces, providing a hands-on, Python-based approach for readers to learn and apply data science concepts from scratch. Key Highlights: Introduction to Data Science: The book begins with an overview of data science, its applications, and its importance in various industries. Cooper introduces the core concepts and workflows in data science, including data collection, cleaning, analysis, visualization, and modeling. He emphasizes the iterative process of working with data and the need for solid foundational knowledge to excel in the field. Python Basics for Data Science: Since the book assumes no prior experience in data science or programming, it starts with a primer on Python. The author introduces basic Python concepts, such as variables, loops, conditionals, functions, and data structures (lists, dictionaries, and tuples). The use of Python as a tool for data science is emphasized, with practical examples to illustrate key programming concepts. Data Collection and Preparation: A large portion of the book focuses on the critical step of data collection and preparation. Cooper walks readers through methods of gathering data from various sources, including APIs and databases. He also discusses techniques for cleaning data, handling missing values, and transforming raw data into a format suitable for analysis. The importance of data quality is stressed, and readers learn how to manage and preprocess data to get meaningful results. Exploratory Data Analysis (EDA): The book introduces exploratory data analysis (EDA) as a vital part of the data science process. Cooper explains how to summarize and visualize data using various Python libraries such as pandas, NumPy, and Matplotlib. Readers learn how to analyze distributions, detect patterns, and identify outliers in their datasets through descriptive statistics and visualizations. Probability and Statistics: The author covers the essential statistical concepts needed for data science, including probability theory, distributions, hypothesis testing, and confidence intervals. The book introduces concepts like mean, median, variance, correlation, and regression analysis to help readers understand how to quantify uncertainty and make inferences about data. Machine Learning: One of the key aspects of data science is machine learning, and the book provides a comprehensive introduction to this area. Cooper discusses supervised and unsupervised learning, explaining key algorithms like linear regression, k-nearest neighbors (KNN), decision trees, and clustering. The author also covers model evaluation techniques, such as cross-validation and confusion matrices, helping readers understand how to assess the performance of machine learning models.

  Also filed under Computer Science, Python

• Dropout: A Simple Way to Prevent Neural Networks from Overfitting

  Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky, Ilya Sutskever, Ruslan Salakhutdinov (University of Toronto) · Report

  The 2014 JMLR paper introducing dropout as a regularization technique. Randomly dropping units during training prevents co-adaptation and acts as an approximate ensemble method. A foundational technique used in nearly every deep neural network.

  Also filed under AI, Machine Learning

• Generative Adversarial Nets

  Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, Yoshua Bengio · Report

  The 2014 paper that introduced GANs — a framework where a generator and discriminator are trained in a minimax game. Opened the era of modern generative modeling and led directly to the image synthesis breakthroughs of the late 2010s.

  Also filed under AI, Machine Learning

• Introduction to Bayesian Statistics

  Brendon J. Brewer · Book

  Introduction to Bayesian Statistics Brendon J. Brewer This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License. 5 1.2 This Version of the Notes . 12 3.1.2 Finding the Likelihood Values .

  Also filed under Risk Management, Quant Finance

• Introduction to Probability for Data Science

  Stanley H.Chan · Book

  "Introduction to Probability for Data Science" by Stanley H. Chan is an undergraduate-level textbook that emphasizes the integration of data computing and probability theory. The book aims to elucidate the motivations, intuitions, and implications of probabilistic tools used in science and engineering, highlighting their inseparability in modern data science. Key Concepts Covered: Mathematical Foundations: The book begins with essential mathematical concepts such as infinite series, approximations, integration, linear algebra, and basic combinatorics. These topics provide the necessary groundwork for understanding more advanced probabilistic theories. Probability Theory: Chan introduces fundamental probability concepts, including set theory, probability spaces, axioms of probability, and conditional probability. The text delves into independence, Bayes' theorem, and the law of total probability, offering a comprehensive understanding of these foundational principles. Random Variables and Distributions: The book explores discrete and continuous random variables, their probability mass functions (PMFs), probability density functions (PDFs), cumulative distribution functions (CDFs), expectations, moments, variances, and common distributions like Bernoulli, binomial, geometric, Poisson, uniform, exponential, and Gaussian. Joint Distributions and Multidimensional Analysis: Chan discusses joint PMFs and PDFs, marginal distributions, conditional distributions, covariance, correlation coefficients, and transformations of multivariate Gaussian distributions. The text also covers principal-component analysis and its applications. Sample Statistics and Estimation: The book addresses moment-generating and characteristic functions, probability inequalities, the law of large numbers, central limit theorem, regression principles, overfitting, bias-variance trade-off, regularization, and various estimation techniques such as maximum-likelihood estimation, maximum a posteriori estimation, and minimum mean-square estimation. Confidence, Hypothesis Testing, and Advanced Topics: Chan concludes with discussions on confidence intervals, bootstrapping, hypothesis testing, Neyman-Pearson tests, and other advanced topics, providing a holistic view of statistical inference methods used in data science.

  Also filed under Computer Science, Quant Finance

• Introduction to Scientific Programming with Python

  Joakim Sundnes · Book

  This book is an open access publication. The images or other third party material in this book are included in the book's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the book's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. The use of general descriptive names, registered names, trademarks, service marks, etc.

  Also filed under Python, Computer Science

• Introduction to Statistical and Machine Learning Methods for Data Science

  Carlos Andre Reis Pinheiro & Mike Patetta · Book

  "Introduction to Statistical and Machine Learning Methods for Data Science" by Carlos Andre Reis Pinheiro & Mike Patetta provides a comprehensive guide to the foundational techniques used in modern data science. The book bridges the gap between traditional statistical approaches and contemporary machine learning methods, offering readers a well-rounded understanding of data-driven decision-making. Key Topics Covered: Fundamentals of Statistical Methods: Covers core concepts such as probability distributions, hypothesis testing, regression analysis, and statistical inference. Machine Learning Techniques: Introduces supervised and unsupervised learning algorithms, including decision trees, random forests, support vector machines (SVMs), and neural networks. Feature Engineering & Data Preprocessing: Explores methods to clean, transform, and optimize data for machine learning models. Model Evaluation & Validation: Discusses key metrics like accuracy, precision, recall, and ROC curves to assess model performance. Real-World Applications: Demonstrates how statistical and machine learning methods are applied in finance, healthcare, and business analytics. This book is designed for data scientists, analysts, and professionals looking to enhance their knowledge of both classical statistical methods and modern machine learning techniques. With practical examples and code implementations, it serves as an essential resource for anyone aiming to leverage data science in their field.

  Also filed under Machine Learning, Math

• Introduction to Statistical Concepts

  William Astle · Slides

  to think, understand, and form judgements logically.

  Also filed under Risk Management, Data Visualization

• Lecture 2: Prediction

  Alexandra Chouldechova · Slides

  Lecture 2: Prediction Part I: Splines, Additive Models Part II: Model Selection and Validation Prof.

  Also filed under Machine Learning, Risk Management

• Mathematics for Inference and Machine Learning

  Marc Deisenroth & Stefanos Zafeiriou · Report

  5 1.2.1 Means and Covariances . 6 1.2.1.1 Sum of Random Variables . 7 1.2.1.2 Affine Transformation . 7 1.2.2 Statistical Independence .

  Also filed under Math, Machine Learning

• Monte Carlo methods Introduction, Course structure, Motivating Examples, Applications

  A. Taylan Cemgil · Slides

  Introduction, Course structure, Motivating Examples, Applications Department of Computer Engineering, Bo˘gazic¸i University, Istanbul, Turkey Instructor: A. Taylan Cemgil Cemgil CMPE 58N Monte Carlo Methods. , Bo˘gazic¸i University, Istanbul Main study materials ▶Handouts, Papers ▶Jun S. Liu, Monte Carlo Strategies in Scientific Computing, 2001, Springer.

  Also filed under Math, Quant Finance

• Multilevel Monte Carlo Simulation Using Terminal Stratification

  Yuquan Li · Notes

  Abstract This thesis improves the multilevel Monte Carlo simulation introduced in Giles [2008a] for option pricing. We use stratified sampling on the initial level and thus obtain a further variance reduction. Then we programme the whole procedure of option pricing using this algorithm by C++. Chapter 1 introduces the mathematical background needed for under- standing multilevel Monte Carlo methods.

  Also filed under Risk Management, Quant Finance

• Pattern Recognition and Machine Learning

  Christopher M. Bishop · Book

  Pattern Recognition and Machine Learning by Christopher M. Bishop is a fundamental textbook that provides a comprehensive introduction to statistical pattern recognition and machine learning. The book is well-regarded for its probabilistic approach, making it an essential resource for students, researchers, and practitioners in data science, artificial intelligence, and related fields. Key Highlights: Foundations of Pattern Recognition Introduces the Bayesian approach to pattern recognition, emphasizing probability distributions and decision theory. Covers fundamental concepts such as linear regression, classification, and generative models. Probability and Machine Learning Discusses core probability distributions, including Gaussian, Multivariate Gaussian, and Exponential families. Explains Bayesian inference, its role in machine learning, and its advantages over frequentist methods. Supervised Learning Techniques Covers linear and logistic regression, support vector machines (SVMs), and neural networks. Introduces regularization techniques to prevent overfitting. Unsupervised Learning and Clustering Explores principal component analysis (PCA), mixture models, and expectation-maximization (EM) algorithms. Discusses clustering techniques such as k-means and Gaussian mixture models (GMMs). Graphical Models and Probabilistic Inference Introduces Bayesian networks and Markov random fields for modeling dependencies between variables. Covers approximate inference techniques, including variational inference and Markov chain Monte Carlo (MCMC). Kernel Methods and Advanced Topics Discusses kernel-based learning, including Gaussian processes and support vector machines (SVMs). Covers hidden Markov models (HMMs) and their applications in sequential data analysis.

  Also filed under Machine Learning, Computer Science

• Python Machine Learning: A Beginner's Guide to Scikit-Learn

  Rajender Kumar · Book

  No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright owner. This book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. Trad...

  Also filed under Machine Learning, Python

• Scaling Laws for Neural Language Models

  Jared Kaplan et al. (OpenAI) · Report

  The 2020 Kaplan paper establishing empirical scaling laws for language models: loss is predictable as a power law in model size, dataset size, and compute. The paper that convinced OpenAI to bet on scale and led directly to GPT-3.

  Also filed under AI, Machine Learning

• STAT0029 Statistical Design Of Investigations

  Department of Statistical Science University College London · Book

  Introduction 4 1.1 Why design? 4 1.3 Experimentation versus sampling . 8 2.1.1 Principles of experimental design . 8 2.1.2 Planning of experiments .

  Also filed under Risk Management, Software Engineering

• Statistical Analysis Handbook

  Michael J de Smith · Book

  The moral right of the authors has been asserted. Copies of this edition are available in electronic book and web-accessible formats only. Disclaimer: This publication is designed to offer accurate and authoritative information in regard to the subject matter. It is provided on the understanding that it is not supplied as a form of professional or advisory service.

  Also filed under Data Visualization, Risk Management

• Storytelling with data

  Cole Nussbaumer Knaflic · Book

  A guide based on Cole Nussbaumer Knaflic's influential book on effective data communication. It covers how to choose appropriate visuals, eliminate clutter, and use narrative structure to transform data into compelling stories for business audiences.

  Also filed under Data Visualization, Python

• Think Stats

  Allen B. Downey · Book

  "Think Stats" by Allen B. Downey is a practical guide to exploring and analyzing real-world data using Python. It introduces statistical concepts and techniques through hands-on exercises, focusing on understanding data distributions, probability, and statistical inference. The book emphasizes computational thinking and encourages readers to apply statistical methods to solve problems and make data-driven decisions.

  Also filed under Python, Data Visualization

• Training Compute-Optimal Large Language Models (Chinchilla)

  Jordan Hoffmann et al. (DeepMind) · Report

  The 2022 Chinchilla paper that corrected Kaplan's scaling laws. Trained 400+ models from 70M to 16B parameters, showing that model size and training tokens should scale equally — a 70B Chinchilla with 4× more data beat 280B Gopher. Reshaped the training strategy for every subsequent frontier LLM.

  Also filed under AI, Machine Learning

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