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ToggleData-Science Lectures: Statistics, Machine Learning, and Deep Learning
Explore our Data Science learning resources, featuring a wide array of comprehensive lectures and practical exercises in Probability, Statistics, Machine Learning, and Information Theory. Designed to cater to all skill levels, from novice learners to seasoned experts, our materials are crafted to elevate your knowledge and proficiency in the field.
I . Statistics: Univariate & Multivariate Data
Multivariate Statistics Theory webpage offers comprehensive statistics course on both univariate and multivariate analysis techniques, catering to beginners and advanced practitioners. Our resources encompass a wide range of topics to enhance your statistical expertise.
- Basic Statistics: We will explore the fundamental concepts of statistical estimation, confidence intervals, hypothesis testing, and likelihood, along with their practical applications. These crucial topics serve as the building blocks for advanced statistical methods and play a pivotal role in various domains, such as scientific research, business analytics, and engineering.
- Linear Fitting and Regression: In this lecture, we delve into the heart of statistical modeling and analysis, focusing on understanding variable relationships and predictive techniques. We explore the intricacies of linear models, covering both deterministic fitting and probabilistic regression approaches. The session encompasses analysis in both univariate and multivariate contexts, and introduces Gaussian models as a framework for regression analysis.
- Logistic Regression: In statistical modeling, logistic regression is a crucial technique for analyzing discrete outcome variables. Unlike linear regression, which is tailored for continuous outcomes, logistic regression is particularly suitable for scenarios where the output variable is categorical. This lecture provides an overview of logistic regression, discussing its applications in both binary and multiclass contexts, as well as the prediction methods employed.
- Principal Component and Factor Analysis: Principal Component Analysis (PCA) and Factor Analysis are indispensable techniques in multivariate statistics, employed to reduce redundancy among observed variables while preserving crucial information. While both techniques share a common objective, they possess distinct characteristics and methodologies. This lecture provides a comprehensive exploration of PCA and Factor Analysis, elucidating their principles, applications, and offering comparative insights.
II. Machine and Deep Learning
Machine and Deep Learning webpage includes an extensive library of machine learning and deep learning resources, featuring eight detailed lectures available in both PDF and video formats. Immerse yourself in a curated educational experience designed to enhance your grasp of essential artificial intelligence principles.
- Machine Learning Frameworks: The foundational principles for machine learning models are presented with mathematical rigor. From basic learning frameworks to addressing noise and extending to more general learning scenarios, we explore the theoretical underpinnings essential for understanding various machine-learning algorithms.
- Vapnik-Chervonenkis Theory: We present the profound concept of establishing uniform bounds between empirical and true loss within an infinite hypothesis class. Through rigorous exploration of Vapnik-Chervonenkis (VC) theory, we unravel the intricacies of covering and packing numbers, growth functions, and VC dimension, crucial elements for comprehending the complexities of learning in machine learning and statistics.
- Results from Empirical Processes Theory: This lecture complements Vapnik-Chervonenkis theory, providing essential instruments to determine consistent limits on the divergence between empirical and actual losses across an an infinite class of hypotheses. Through rigorous derivation of tail bounds, we uncover essential principles that support the robustness and generalization capabilities of machine learning algorithms.
- Learnability Characterization: This session reveals the key attributes that determine the learnability of infinite hypothesis classes within machine learning. Employing thorough analysis and drawing upon core theories like Vapnik-Chervonenkis and empirical processes, we strive to elucidate the sample complexity necessary for learning algorithms to reach peak efficacy. Building on earlier conversations, we expand our comprehension from finite to infinite hypothesis classes, setting forth the standards for learnability across diverse conditions.
- Examples of Machine-Learning Problems: Our session explores a range of real-world situations where machine learning methods are utilized for problem-solving. We examine supervised and unsupervised learning models, featuring instances from binary classification using nearest neighbors to clustering techniques. Through analyzing these cases, we intend to offer perspectives on the wide-ranging uses of machine learning and the strategies implemented to address these challenges.
- Neural Networks: This course presents the computational models that mirror the complex architecture of the human brain. Our lecture is designed to impart an in-depth comprehension of neural networks, encompassing their precise definitions, functionalities, and refinement methods. From layered architectures to the intricacies of stochastic gradient descent, we demystify the sophisticated mechanisms of neural networks and their implementation in the fields of machine learning and artificial intelligence.
- Approximation Theory in Neural Networks: We explore the core principles that dictate how neural networks can mimic functions, an essential aspect of their versatility across different fields. Our examination of the universal approximation theorem aims to clarify the potential and constraints of neural networks in emulating functions. Additionally, we tackle critical inquiries about the nature of functions that are subject to approximation and the requisite neuron count for attaining specific precision goals.
- Python Software for Machine Learning and Deep Learning – Tutorial: Explore our in-depth guide on leveraging Python for your machine learning and deep learning endeavors. Our objective is to equip you with a clear, sequential process for setting up the required software from the ground up and crafting your initial Python scripts for data science applications. Upon completing this tutorial, you’ll possess the proficiency to build your personal neural network with PyTorch and handle data with ease for various machine learning projects.
Data-Science Book: Coming Soon on this Webpage
Keep an eye on this page for the upcoming launch of our book:
- B. Błaszczyszyn, M.K. Karray: « Data science : From multivariate statistics to machine, deep learning ».