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Toggle## Lectures on Machine-Learning and Deep-Learning

Welcome to the comprehensive collection of machine-learning and deep-learning lectures, presented in both PDF and video formats. Dive into a wealth of knowledge spanning eight enlightening lectures, each meticulously crafted to deepen your understanding of key concepts in the field of artificial intelligence.

- In Lecture 1, explore the foundational principles of
**Machine-Learning frameworks**, unraveling the intricate relationship between input data and output predictions. - Delve into the intricate world of
**Vapnik-Chervonenkis theory**in Lecture 2, where you’ll uncover the theoretical underpinnings behind the learnability of hypothesis classes. - In Lecture 3, embark on a journey through
**Results from empirical processes theory**, gaining insights into the statistical methods crucial for analyzing learning algorithms. - Lecture 4 offers a deep dive into
**Learnability characterization**, providing essential insights into the factors influencing the learnability of machine-learning models. - In Lecture 5, discover real-world
**Examples of Machine-Learning problems**, showcasing practical applications of machine-learning techniques across diverse domains. - Unravel the complexities of
**neural networks**in Lecture 6, as we explore their architecture, training methodologies, and practical applications in deep learning. - In Lecture 7, immerse yourself in the world of
**Approximation theory in neural networks**, where we explore the mathematical foundations underlying the universal approximation capabilities of neural networks. - Finally, in Lecture 8, unlock the power of
**Python software for Machine-Learning and Deep-Learning**, with a comprehensive tutorial covering essential libraries, tools, and techniques for building and deploying machine-learning models.

Unlock the boundless potential of machine learning with our comprehensive collection of courses, meticulously crafted to deepen your understanding of key concepts and methodologies. Whether you’re delving into the intricacies of machine learning, exploring the mathematical foundations essential for mastering the field, or unraveling the theoretical underpinnings of empirical processes and statistical machine learning, our platform offers a wealth of resources to propel your journey. Dive into topics ranging from binary classification and supervised learning to advanced techniques like convolutional neural networks and deep learning.

With practical examples, tutorials, and code snippets, including Python machine learning code examples, our courses cater to learners of all levels, empowering you to embark on a transformative learning experience in the dynamic realm of machine learning and beyond.

Machine learning is grounded in robust mathematical principles derived from measure and probability theories and multivariate statistics theory. We will explore foundational findings concerning the performance assurance of machine learning algorithms, surpassing conventional heuristic methods reliant on test sequences.

Illustrating the essence of the machine-learning conundrum, we’re tasked with discerning the relationship between input and output. With n input samples and their corresponding outputs, the objective is to deduce the function f that connects the output y with the input x, encapsulating the quintessence of the machine learning endeavor.

### 1. Machine-Learning Frameworks

In this lecture on « Machine-Learning Frameworks, » we delve into the foundational structures guiding the learning process in artificial intelligence systems. 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.

**Basic Learning Framework**: The basic learning framework lays the groundwork by defining fundamental concepts such as target functions, hypotheses, and empirical loss minimization (ELM). Through meticulous definitions and theorems, we establish the relationship between the training sequence, hypothesis class cardinality, and true loss, particularly focusing on scenarios where the hypothesis class is finite. This section provides a solid foundation for comprehending the subsequent complexities of machine-learning frameworks.**Noisy Learning Framework**: As we transition into the noisy learning framework, we encounter scenarios where the relationship between input and output is no longer deterministic. Here, we introduce the concept of probability kernels to account for randomness in the learning process. Propositions regarding Bayes optimal hypotheses and agnostic PAC-learnability shed light on how to navigate the complexities of learning in noisy environments, laying the groundwork for robust machine-learning models.**General Learning Framework**: Expanding our understanding further, the general learning framework challenges traditional notions by allowing for more diverse data spaces and hypothesis spaces. We explore the extension of agnostic PAC-learnability into this broader context, emphasizing concepts like empirical loss minimization and uniform convergence. Through lemmas and corollaries, we illuminate the relationship between learnability and uniform convergence, providing insights into the efficiency and efficacy of learning algorithms in diverse settings. This section broadens our perspective, preparing us to tackle the multifaceted challenges of modern machine learning.

For those seeking comprehensive insights into Machine-Learning frameworks, our lecture delves deep into the intricacies of learning algorithms and their applications. Whether you’re delving into supervised machine learning or exploring probabilistic approaches, our discussion covers essential topics such as empirical risk minimization, PAC-learnability, and the uniform convergence property. With a focus on understanding machine learning from both theoretical and practical perspectives, our content serves as a valuable resource for individuals navigating the complex landscape of data science and machine learning.

**Course Outline**:

1 Basic learning framework

1.1 Empirical loss minimization (ELM)

1.2 PAC-learnability

2 Noisy learning framework

2.1 Bayes optimal hypothesis

2.2 Agnostic PAC-learnability

3 General learning framework

3.1 Empirical loss minimization (ELM)

3.2 Learnability versus uniform-convergence

3.3 Finite hypothesis class

### 2. Vapnik-Chervonenkis Theory

In our lecture on « Vapnik-Chervonenkis Theory, » we embark on a journey to understand 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.

**VC Classes of Sets**: In the foundational section of our lecture, we delve into VC classes of sets, elucidating the fundamental concepts of covering and packing numbers, growth functions, and VC dimension. Through meticulously crafted definitions and lemmas, we establish the theoretical framework necessary to comprehend the interplay between these concepts and their implications on learning and generalization. With illustrative examples and theorems such as Sauer’s lemma, we pave the way for understanding how covering numbers of VC classes of sets grow polynomially, laying the groundwork for subsequent explorations.**VC Classes of Functions**: Expanding our understanding, we transition into VC classes of functions, where we delve into the intricacies of defining VC dimension for classes of functions and introducing the concept of envelope functions. Through rigorous analysis and theorems, we demonstrate how the covering numbers of VC classes of functions also exhibit polynomial growth, reinforcing the theoretical underpinnings of Vapnik-Chervonenkis theory in the context of function spaces. This section further solidifies our understanding of how the theory applies across different domains within machine learning and statistics.**Covering Numbers of Convex Hulls**: In the concluding segment of our lecture, we explore the application of Vapnik-Chervonenkis theory to convex hulls, particularly in Hilbert space. Leveraging Maurey’s lemma and other foundational results, we elucidate how covering numbers of convex hulls exhibit certain growth properties crucial for understanding the complexity of learning in high-dimensional spaces. By connecting theoretical insights with practical applications, we bridge the gap between abstract concepts and real-world implications, providing a comprehensive understanding of Vapnik-Chervonenkis theory and its significance in modern statistical learning theory.

For those delving into the intricate realms of Vapnik-Chervonenkis theory and its applications in machine learning, our comprehensive lecture provides invaluable insights into key concepts such as VC dimension, covering numbers, packing numbers, growth functions, and Sauer’s lemma. Our discussion elucidates the theoretical underpinnings essential for understanding learning complexity and generalization in high-dimensional spaces. With a focus on bridging theory and practice, our content serves as a definitive resource for unraveling the mysteries of Vapnik-Chervonenkis theory and its implications in modern machine learning algorithms.

**Course Outline**:

1 VC classes of sets

1.1 Covering and packing numbers

1.2 Growth function

1.3 VC dimension

1.4 Covering number bound

2 VC classes of functions

3 Covering numbers of convex hulls

### 3. Results from Empirical Processes Theory

In our lecture on « Results from Empirical Processes Theory, » we explore crucial insights that bridge theoretical foundations with practical applications in machine learning. These insights serve as vital tools alongside Vapnik-Chervonenkis theory to establish uniform bounds on the deviation of empirical loss from true loss within an infinite class of hypotheses. Through meticulous examination of empirical measures, measurability of the supremum, and derivation of tail bounds, we uncover essential principles that underpin the robustness and generalization capabilities of machine learning algorithms.

**Empirical Processes**: At the core of our discussion lies the understanding of empirical processes, where we define key concepts such as empirical measure and process. Leveraging foundational lemmas like the Law of Large Numbers and Central Limit Theorem, we establish the statistical underpinnings necessary for comprehending the behavior of empirical processes in machine learning contexts. This section serves as a primer, laying the groundwork for deeper exploration into the measurability of the supremum and derivation of tail bounds.**Measurability of the Supremum**: Delving deeper, we investigate the measurability of the supremum over classes of functions, particularly focusing on scenarios where the class may be uncountable. Introducing essential tools such as pointwise separability and envelope functions, we navigate the challenges posed by uncountable classes and establish criteria for verifying measurability. Through rigorous definitions and lemmas, we equip ourselves with the necessary analytical tools to tackle complex machine learning problems involving uncountable classes of functions.**Tail Bounds**: In the final segment of our lecture, we shift our focus to deriving tail bounds for the supremum of empirical processes. Building upon the concept of bracketing numbers and examples illustrating their application, we establish tail bounds for uniformly bounded classes of functions and sets. Through theorems and corollaries, we elucidate how these tail bounds facilitate the estimation of empirical cumulative distribution functions (CDFs), providing invaluable insights into the behavior of empirical processes and enabling robust statistical inference in machine learning tasks. This section serves as a culmination of our exploration, demonstrating the practical relevance of empirical processes theory in the realm of machine learning.

Delve into the intricate realm of empirical processes theory and its profound implications for statistical inference in machine learning. Our comprehensive lecture not only elucidates fundamental concepts like the Law of Large Numbers and the Central Limit Theorem but also explores advanced topics such as tail bounds and envelope functions. With a focus on practical applications and real-world relevance, we delve into the nuances of empirical measures and processes, offering insights into weak convergence and its applications to statistics.

**Course Outline**:

1 Empirical processes

2 Measurability of the supremum

3 Tail bounds

### 4. Learnability Characterization

This lecture on « Learnability Characterization, » uncovers the essential characteristics of infinite classes of hypotheses that are learnable in the context of machine learning. Through meticulous analysis and leveraging foundational theories such as Vapnik-Chervonenkis theory and empirical processes theory, we aim to provide insights into the sample-complexity required for learning algorithms to achieve optimal performance. This lecture builds upon previous discussions, extending our understanding from finite classes to infinite classes of hypotheses and establishing criteria for learnability in various scenarios.

**Finite VC Dimension Implies Learnability**: In the foundational segment of our lecture, we explore the relationship between finite VC dimension and learnability, particularly focusing on binary classification tasks. Through corollaries derived from concentration inequalities and theoretical insights, we establish that finite VC dimension implies learnability for both binary classification and finite range loss functions. By elucidating the importance of prior knowledge and the limitations of infinite VC dimension, we lay the groundwork for understanding the fundamental theorem of learning for binary classification.**Learning for Binary Classification**: Expanding our exploration, we delve deeper into the nuances of learning for binary classification, unveiling critical insights into the requirements for learnability. Through discussions on the absence of a « free lunch » in binary classification and the necessity of finite VC dimension for learnability, we highlight the interplay between theoretical concepts and practical implications in machine learning. Finally, we unveil the fundamental theorem of learning for binary classification, providing a comprehensive framework that encapsulates the essential conditions for achieving learnability in noisy learning environments. This section serves as a culmination of our exploration, offering a holistic understanding of learnability characterization in the context of binary classification tasks.

Explore the concept of ‘no free lunch’ theorem and its significance in the realm of machine learning within our comprehensive lecture on Learnability Characterization. We delve into the implications of this theorem for binary classification tasks, emphasizing the importance of prior knowledge in shaping learning outcomes. By elucidating the limitations of a universal learning algorithm and highlighting the necessity of informed decision-making, we shed light on the nuanced interplay between theoretical principles and practical applications in machine learning.

**Course Outline**:

1 Finite VC dimension implies learnablity

1.1 Binary classification

1.2 Finite range loss function

2 Learning for binary classification

2.1 No free lunch

2.2 Learnability requires finite VC dimension

2.3 Fundamental theorem of learning for binary classification

### 5. Examples of Machine-Learning Problems

In our lecture on « Examples of Learning Problems, » we delve into a variety of scenarios where machine learning techniques are applied to solve real-world problems. We explore both supervised and unsupervised learning paradigms, showcasing examples ranging from binary classification with nearest neighbors to clustering algorithms. By dissecting these examples, we aim to provide insights into the diverse applications of machine learning and the methodologies employed to tackle them.

**Supervised Learning Problems**: In the first section of our lecture, we focus on supervised learning problems, where the learner is provided with a training sequence and aims to infer patterns from labeled data. We begin by examining binary classification tasks using nearest neighbor and halfspace methods. Through definitions and propositions, we elucidate the concepts of 1-NN and k-NN hypotheses, as well as the class of affine and linear halfspaces. Furthermore, we explore the VC dimensions of these classes, providing theoretical insights into their expressive power and learnability. This section serves as a foundational exploration of supervised learning techniques, laying the groundwork for more advanced methodologies.**ELM by Perceptron**: Transitioning to a specific algorithmic approach, we delve into the Perceptron algorithm for supervised learning tasks. By introducing the algorithm and discussing its convergence rate, we showcase how iterative learning algorithms can be employed to find optimal decision boundaries in linearly separable datasets. Additionally, we explore applications of linear and polynomial fitting with multidimensional input, demonstrating the versatility of the Perceptron algorithm in various learning scenarios. This section offers a practical understanding of algorithmic approaches to supervised learning, equipping learners with the tools to tackle real-world classification problems.**Unsupervised Learning Problems**: In the final section of our lecture, we shift our focus to unsupervised learning problems, where the goal is to uncover patterns in data without labeled training examples. Although unsupervised learning does not fit neatly into the traditional learning framework, we explore common techniques such as clustering. Through discussions on clustering algorithms like linkage-based clustering and the k-means algorithm, we delve into the methodologies employed to group data points based on similarity criteria. This section provides insights into the challenges and methodologies of unsupervised learning, highlighting its importance in understanding complex datasets and extracting meaningful insights.

Explore a diverse array of machine-learning problems and methodologies within our comprehensive lecture on Examples of Learning Problems. From supervised learning to unsupervised techniques, we dissect real-world scenarios and showcase the efficacy of algorithms like k-nearest neighbors (KNN) in both supervised and unsupervised contexts. By defining and illustrating supervised and unsupervised learning paradigms, we provide clarity on fundamental concepts while delving into practical examples and algorithms.

**Course Outline**:

1 Supervised learning problems

1.1 Binary classification with nearest neighbor

1-NN hypothesis

k-NN hypothesis

1.2 Binary classification with halfspaces

Halfspaces

ELM by linear optimization

2 ELM by Perceptron

2.1 Linear fitting with multidimensional input

2.2 Polynomial fitting

3 Unsupervised learning problems

3.1 Clustering

3.2 Linkage-based clustering

### 6. Neural Networks

In our lecture on « Neural Networks, » we delve into the fascinating realm of computational models inspired by the intricate structure of the human brain. Through a systematic exploration, we aim to provide a comprehensive understanding of neural networks, including their formal definitions, capabilities, and optimization techniques. From multilayer representations to stochastic gradient descent algorithms, we unravel the complexities of neural networks and their practical applications in machine learning and artificial intelligence.

**Neural Networks**: In the foundational section of our lecture, we delve into the architecture and functionality of neural networks. We begin by defining multilayer neural networks and elucidating the role of each layer in the network’s computation process. Through examples and discussions on activation functions, we showcase how neural networks can capture nonlinear relationships within data. Additionally, we explore the VC dimension of neural networks, providing insights into their expressive power and generalization capabilities, particularly in the context of binary classification tasks. This section serves as a foundational exploration of neural network fundamentals, laying the groundwork for deeper insights into optimization techniques.**Stochastic Gradient Descent**: Transitioning to optimization methodologies, we explore the powerful technique of stochastic gradient descent (SGD) for training neural networks. We start by discussing gradient descent optimization algorithms and then focus specifically on the stochastic variant. Through a detailed examination of backpropagation, we illustrate how gradients are computed and propagated through the network to update the model parameters. By presenting examples and algorithms for basic neural networks, including the use of quadratic loss functions, we provide practical insights into the application of SGD in neural network training. This section equips learners with essential techniques for efficiently optimizing neural network models, ensuring convergence to optimal solutions.**Convolutional Neural Networks**: In the final segment of our lecture, we delve into the advanced architecture of convolutional neural networks (CNNs), which are widely used in tasks like image recognition, natural language processing, and deep learning. We introduce key components such as convolutional layers, subsampling layers, and fully-connected layers, providing a comprehensive understanding of CNN architecture. Through examples and definitions, we elucidate the structure and functionality of CNNs, showcasing how they leverage hierarchical feature extraction to achieve superior performance in complex tasks. This section offers a glimpse into the cutting-edge advancements in neural network design and their applications in modern machine learning paradigms.

Discover the transformative power of neural networks and convolutional neural networks (CNNs) within our comprehensive lecture on Neural Networks. From understanding the intricacies of artificial neural networks to delving into advanced topics like fully convolutional networks, our content offers valuable insights into the fundamentals and applications of deep learning. Explore the optimization algorithms driving neural network training, including stochastic gradient descent, and unravel the architecture and functionality of CNNs.

**Course Outline**:

1 Neural networks

1.1 Multilayer neural networks

1.2 VC dimension of neural network

2 Stochastic gradient descent

2.1 Gradient descent optimization algorithms

2.2 Back propagation to train a neural network

3 Convolutional neural networks

### 7. Approximation Theory in Neural Networks

In our lecture on « Approximation Theory in Neural Networks, » we delve into the foundational principles governing the ability of neural networks to approximate functions, a concept central to their utility in various domains. By exploring the universal approximation theorem, we aim to provide precise statements regarding the capabilities and limitations of neural networks in function approximation tasks. Furthermore, we address pertinent questions such as the types of functions that can be approximated and the necessary number of neurons to achieve a desired accuracy level.

**Approximation of Continuous Functions**: In the first section of our lecture, we lay the groundwork by discussing the approximation of continuous functions using neural networks. We start by defining sigmoidal functions and their essential properties, setting the stage for Cybenko’s theorem, a pivotal result in approximation theory. Through rigorous analysis and theoretical insights, we elucidate the conditions under which neural networks can approximate a wide range of continuous functions, offering a fundamental understanding of their expressive power and versatility.**Rate of Approximation**: Transitioning to a more nuanced exploration, we delve into the rate of approximation for functions in various spaces, shedding light on the precision achievable by neural networks. We introduce preliminary notations and results, including Makovoz lemma, to facilitate our discussion on the rate of approximation in Hilbert and Lq spaces. Through propositions, we explore the rate of approximation with respect to different norms and activation functions, providing insights into the factors influencing approximation accuracy in neural networks. This section serves as a comprehensive analysis of the quantitative aspects of function approximation, offering valuable insights for practitioners and researchers alike.**Sufficient Condition for Approximation to Hold**: In the final segment of our lecture, we explore sufficient conditions for approximation to hold, delving into the theoretical underpinnings that guarantee the effectiveness of neural networks in approximating functions. By elucidating the conditions under which approximation is guaranteed, we provide practitioners with essential guidelines for designing and training neural networks effectively. This section serves as a culmination of our exploration, offering practical insights into the application of approximation theory in neural network design and optimization.

Dive deeper into the fascinating realm of approximation theory in neural networks with our comprehensive lecture. From exploring the properties of sigmoidal functions to unraveling the intricacies of Cybenko’s theorem, we delve into the theoretical underpinnings that govern function approximation in deep neural networks. With insights into bounded variation and the Heaviside activation function, our course provides a holistic understanding of approximation theory and its applications in modern machine learning. Our content bridges the gap between theory and practice in approximation theory, offering invaluable insights for enthusiasts and researchers alike.

**Course Outline**:

1 Approximation of continuous functions

2 Rate of approximation

2.1 Rate of approximation in Hilbert and Lq spaces

2.2 Rate of approximation in neural networks

2.3 Rate of approximation with respect to supremum norm

3 Sufficient condition for approximation to hold

### 8. Python Sftwares for Machine-Learning and Deep-Learning: Tutorial

Welcome to our comprehensive tutorial on Python software for machine learning and deep learning. In this lecture, our goal is to provide you with a step-by-step guide to installing the necessary software from scratch and writing your first Python code for data science. By the end of this tutorial, you’ll have the skills to construct your own neural network using the PyTorch library and manipulate data effortlessly for machine learning tasks.

**Python Software**: In the first section of our tutorial, we walk you through the process of installing essential Python software components from scratch. From setting up Python interpreters to installing, importing, and utilizing packages crucial for data science tasks, we ensure that you have a solid foundation to begin your journey into machine learning and deep learning. Through practical examples like linear fitting with the sklearn package, we demonstrate how to leverage Python’s powerful libraries for data analysis and modeling.**PyTorch Package**: Transitioning to the PyTorch framework, we delve into its key functionalities and capabilities for building neural networks. We start by introducing tensors and exploring how they form the backbone of data manipulation in PyTorch. Next, we discuss devices and processors, essential for optimizing performance and scalability. Additionally, we delve into working with image datasets and differentiation techniques within PyTorch, empowering you to handle complex data and tasks with ease.**PyTorch for Neural Networks**: In the final section of our tutorial, we focus specifically on leveraging PyTorch for building neural networks. We begin with simple examples such as linear fitting and logistic regression, gradually progressing to more complex tasks like multiclass logistic regression and multilayer neural networks. Through hands-on examples and demonstrations, we guide you through the process of model optimization and showcase the flexibility and power of PyTorch for deep learning tasks. By the end of this section, you’ll have the knowledge and skills to construct and train sophisticated neural networks for a variety of machine learning applications.

Explore the world of Python software for machine learning and deep learning with our comprehensive tutorial. From mastering fundamental concepts like tensors and scikit-learn to diving into advanced topics like PyTorch and deep learning, our course equips you with the skills needed to excel in the field of artificial intelligence and machine learning. Our tutorial offers a step-by-step guide to Python programming for machine learning and deep learning. Join us on this journey to unlock the full potential of Python for data science and machine learning, and take your AI projects to new heights.

**Course Outline**:

1 Python softwares

1.1 Install softwares from scratch

1.2 Install, import and use packages

1.3 Example : Linear fitting with sklearn package

2 PyTorch package

2.1 Tensors

2.2 Devices (processors)

2.3 Image datasets

2.4 Differentiation with Pytorch

3 PyTorch for neural networks

3.1 Example : Linear fitting with PyTorch

3.2 Logistic regression with PyTorch

3.3 Multiclass logistic regression with PyTorch

3.4 Optimization in PyTorch

3.5 Multilayer neural network

## Python Code Examples

**Source codes on GitHub**

In the « Python code examples » section, we provide a series of illustrative notebook examples aimed at facilitating learning and practical application of Python and associated packages. These examples serve as valuable resources for both beginners and experienced users alike, offering hands-on experience with essential Python functionalities and tools. Each example is accompanied by detailed explanations and code snippets, enabling users to understand and implement concepts effectively. Below is the structured content and description of each example:

- Example 0 : Rapid tutorial on Python. This introductory example serves as a rapid tutorial on Python, covering fundamental concepts such as variable declaration, basic arithmetic operations, control structures (if-else statements, loops), and function definition. It provides a solid foundation for beginners to get started with Python programming.
- Example 1 : Import and use basic Python packages: math, numpy, and pandas. In this example, we demonstrate how to import and utilize essential Python packages including math, numpy, and pandas. Users learn how to perform mathematical operations, manipulate arrays and matrices, and handle data structures like data frames efficiently using these packages.
- Example 2 : Linear fitting using sklearn package. This example focuses on linear fitting using the sklearn package, a popular machine learning library in Python. Users learn how to import and utilize sklearn’s regression models to perform linear fitting on datasets, gaining practical insights into regression analysis.
- Example 3 : Tensor object in PyTorch package. Here, we explore the tensor object in the PyTorch package, a powerful framework for deep learning. Users learn how to create, manipulate, and perform operations on tensors, gaining a deeper understanding of PyTorch’s data representation and manipulation capabilities.
- Example 4 : Devices to run Python code (processors). This example delves into the concept of devices used to run Python code, particularly focusing on processors. Users learn how to specify and manage devices for executing Python code efficiently, gaining insights into optimizing code performance.
- Example 5 : Image datasets. In this example, we explore working with image datasets in Python. Users learn how to load, preprocess, and visualize image data using Python libraries, gaining practical experience in handling image datasets for machine learning tasks.
- Example 6 : Differentiation with PyTorch. This example provides an in-depth exploration of automatic differentiation capabilities offered by the PyTorch framework. Participants will learn how PyTorch enables efficient computation of gradients, a critical component in training neural networks using techniques like backpropagation.
- Example 7 : Linear fitting using a neural network with PyTorch. Building upon the linear fitting example using sklearn, this example demonstrates linear fitting using a neural network implemented in PyTorch. Users gain hands-on experience in building and training neural networks for regression tasks, highlighting the flexibility and power of PyTorch for deep learning.
- Example 8 : Multilayer neural networks to fit data. In the final example, we explore the use of multilayer neural networks to fit complex datasets. Users learn how to design, train, and evaluate multilayer neural networks using PyTorch, gaining insights into building more sophisticated models for machine learning tasks.

These Python code examples offer a comprehensive and practical approach to learning Python and associated packages, empowering users to develop proficiency in Python programming and machine learning techniques.

Explore a plethora of Python code examples tailored for machine learning enthusiasts. Our comprehensive collection covers a wide range of topics, including practical demonstrations of machine learning algorithms, data manipulation with pandas, and numerical computing using numpy. Dive into our GitHub repository to access a treasure trove of Python code snippets, designed to simplify complex machine learning concepts and provide hands-on learning experiences. Embark on your machine learning journey today with our Python code examples!

## Book on Machine-Learning and Deep-Learning: 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 ».