Machine Learning
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Real Machine Learning โ€” simple, practical, and built on experience.
Learn step by step with clear explanations and working code.

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๐Ÿš€ ๐‹๐ˆ๐๐„๐€๐‘ ๐‘๐„๐†๐‘๐„๐’๐’๐ˆ๐Ž๐: ๐“๐‡๐„ ๐…๐Ž๐”๐๐ƒ๐€๐“๐ˆ๐Ž๐ ๐Ž๐… ๐๐‘๐„๐ƒ๐ˆ๐‚๐“๐ˆ๐•๐„ ๐€๐ˆ

Linear regression is one of the most fundamental algorithms in machine learning, serving as the starting point for understanding how models learn from data. It is a supervised learning technique used to predict a continuous numerical output based on one or more input features.

๐Ÿ. ๐“๐‡๐„ ๐‚๐Ž๐‘๐„ ๐‚๐Ž๐๐‚๐„๐๐“
At its heart, linear regression assumes there is a linear relationship between the input (X) and the output (y).
๐“๐ก๐ž ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง: It maps to the classic line equation y = mx + b, where m represents the weight (slope) and b represents the bias (intercept).
๐“๐ก๐ž ๐†๐จ๐š๐ฅ: The model aims to find the "line of best fit" that minimizes the vertical distance between the predicted points on the line and the actual data points.

๐Ÿ. ๐Ž๐๐“๐ˆ๐Œ๐ˆ๐‰๐€๐“๐ˆ๐Ž๐: ๐‡๐Ž๐– ๐ˆ๐“ ๐‹๐„๐€๐‘๐๐’
Linear regression is the perfect example of how math drives optimization in machine learning.
๐‹๐จ๐ฌ๐ฌ ๐…๐ฎ๐ง๐œ๐ญ๐ข๐จ๐ง: We use ๐Œ๐ž๐š๐ง ๐’๐ช๐ฎ๐š๐ซ๐ž๐ ๐„๐ซ๐ซ๐จ๐ซ (๐Œ๐’๐„) to measure the "wrongness" of our line.
๐†๐ซ๐š๐๐ข๐ž๐ง๐ญ ๐ƒ๐ž๐ฌ๐œ๐ž๐ง๐ญ: The model uses calculus to calculate gradients, allowing it to iteratively adjust its weights (m) and bias (b) to find the lowest point of the error landscape.

๐Ÿ‘. ๐•๐€๐‘๐ˆ๐€๐“๐ˆ๐Ž๐๐’ ๐Ž๐… ๐‘๐„๐†๐‘๐„๐’๐’๐ˆ๐Ž๐
๐’๐ข๐ฆ๐ฉ๐ฅ๐ž ๐‹๐ข๐ง๐ž๐š๐ซ ๐‘๐ž๐ ๐ซ๐ž๐ฌ๐ฌ๐ข๐จ๐ง: Predicting an outcome based on a single input variable (e.g., predicting house price based only on square footage).
๐Œ๐ฎ๐ฅ๐ญ๐ข๐ฉ๐ฅ๐ž ๐‹๐ข๐ง๐ž๐š๐ซ ๐‘๐ž๐ ๐ซ๐ž๐ฌ๐ฌ๐ข๐จ๐ง: Using multiple features to make a prediction (e.g., predicting house price based on square footage, age, and location).
๐๐จ๐ฅ๐ฒ๐ง๐จ๐ฆ๐ข๐š๐ฅ ๐‘๐ž๐ ๐ซ๐ž๐ฌ๐ฌ๐ข๐จ๐ง: Used when the relationship between data points is curved rather than a straight line.

๐Ÿ’. ๐‘๐„๐€๐‹-๐–๐Ž๐‘๐‹๐ƒ ๐”๐’๐„ ๐‚๐€๐’๐„๐’
Linear regression remains highly relevant in 2026 because of its interpretability and efficiency:
๐…๐ข๐ง๐š๐ง๐œ๐ž: Forecasting stock prices or market trends based on historical performance.
๐‡๐ž๐š๐ฅ๐ญ๐ก๐œ๐š๐ซ๐ž: Predicting patient recovery times or blood pressure based on age and lifestyle factors.
๐๐ฎ๐ฌ๐ข๐ง๐ž๐ฌ๐ฌ: Sales forecasting and determining the impact of marketing spend on revenue.

๐Ÿ’ก ๐’๐“๐‘๐€๐“๐„๐†๐ˆ๐‚ ๐“๐€๐Š๐„๐€๐–๐€๐˜
While deep learning and transformers often grab the headlines, linear regression is the "workhorse" of data science. It is essential for establishing baselines and remains the preferred choice when you need a model that is easy to explain and computationally light.

The beauty of linear regression lies in its simplicity. By mastering the relationship between data and the "line of best fit," you build the intuition necessary to tackle far more complex neural architectures.
โค3
๐Ÿš€ ๐“๐‡๐„ ๐€๐ˆ ๐€๐‘๐‚๐‡๐ˆ๐“๐„๐‚๐“๐”๐‘๐„ ๐Ž๐๐“๐ˆ๐Œ๐ˆ๐™๐„๐ƒ โ€” ๐†๐€๐“๐„๐ƒ ๐‘๐„๐‚๐”๐‘๐‘๐„๐๐“ ๐”๐๐ˆ๐“๐’ (๐†๐‘๐”) ๐ŸŒŸ

GRUs are a simplified yet powerful variation of the LSTM architecture. ๐Ÿง  Introduced to solve the vanishing gradient problem while reducing computational overhead, GRUs merge gates to create a more efficient "memory" system. โšก๏ธ They are the go-to choice when you need the performance of an LSTM but have limited compute resources or smaller datasets. ๐Ÿ“‰๐Ÿ“ˆ

๐Ÿ. ๐‚๐Ž๐‘๐„ ๐€๐‘๐‚๐‡๐ˆ๐“๐„๐‚๐“๐”๐‘๐„ & ๐–๐Ž๐‘๐Š๐…๐‹๐Ž๐– ๐Ÿ”ง

The GRU streamlines the gating process by combining the cell state and hidden state. ๐Ÿ”„
๐”๐ฉ๐๐š๐ญ๐ž ๐†๐š๐ญ๐ž: Determines how much of the previous memory to keep and how much new information to add. ๐Ÿ“ฅโž•๐Ÿ“ค
๐‘๐ž๐ฌ๐ž๐ญ ๐†๐š๐ญ๐ž: Decides how much of the past information to forget before calculating the next state. ๐Ÿ—‘โณ
๐‚๐š๐ง๐๐ข๐๐š๐ญ๐ž ๐€๐œ๐ญ๐ข๐ฏ๐š๐ญ๐ข๐จ๐ง: A "hidden" layer that suggests a potential update based on the current input and the reset memory. ๐Ÿงฉ๐Ÿ”

๐Ÿ. ๐Š๐„๐˜ ๐€๐ƒ๐•๐€๐๐“๐€๐†๐„๐’ ๐Ž๐•๐„๐‘ ๐‹๐’๐“๐Œ ๐Ÿš€

Why choose GRU over its predecessor, the LSTM? ๐Ÿค”
๐…๐ž๐ฐ๐ž๐ซ ๐†๐š๐ญ๐ž๐ฌ: 2 instead of 3, GRUs train faster and use less memory. ๐ŸŽ๐Ÿ’จ
๐‹๐ž๐ฌ๐ฌ ๐๐š๐ซ๐š๐ฆ๐ž๐ญ๐ž๐ซ๐ฌ: By merging the cell and hidden states, information flow is more direct. ๐Ÿ“‰๐Ÿ“Š
๐๐ž๐ญ๐ญ๐ž๐ซ ๐Ž๐ง ๐’๐ฆ๐š๐ฅ๐ฅ ๐ƒ๐š๐ญ๐š๐ฌ๐ž๐ญ๐ฌ: GRUs often outperform LSTMs due to having fewer parameters (reducing the risk of overfitting). ๐ŸŽฏ๐Ÿ“‰

๐Ÿ‘. ๐‚๐Ž๐Œ๐๐€๐‘๐€๐“๐ˆ๐•๐„ ๐Œ๐Ž๐ƒ๐„๐‹๐’ ๐Ÿ“Š

๐‘๐๐: The basic loop; prone to short-term memory loss. ๐Ÿ”„โŒ
๐‹๐’๐“๐Œ: The "Heavyweight"; highly accurate but computationally expensive. ๐Ÿ‹๏ธโ€โ™‚๏ธ๐Ÿ”‹
๐†๐‘๐”: The "Lightweight"; optimized for speed and modern efficiency. ๐Ÿชถโšก๏ธ

๐Ÿ’. ๐‘๐„๐€๐‹-๐–๐Ž๐‘๐‹๐ƒ ๐€๐๐๐‹๐ˆ๐‚๐€๐“๐ˆ๐Ž๐๐’ ๐ŸŒ

GRUs excel in environments where latency matters: โฑ๏ธ
๐•๐จ๐ข๐œ๐ž ๐“๐จ ๐“๐ž๐ฑ๐ญ: Converting voice to text with minimal delay. ๐ŸŽ™๐Ÿ“
๐ˆ๐จ๐“ & ๐„๐๐ ๐ž ๐ƒ๐ž๐ฏ๐ข๐œ๐ž๐ฌ: Running sequential models on low-power hardware (like smart sensors). ๐Ÿ“ก๐Ÿ 
๐Œ๐ฎ๐ฌ๐ข๐œ ๐†๐ž๐ง๐ž๐ซ๐š๐ญ๐ข๐จ๐ง: Learning the structure of melodies and rhythm for AI-composed audio. ๐ŸŽต๐ŸŽน

๐Ÿ“. ๐“๐‡๐„ ๐Œ๐€๐“๐‡ ๐๐„๐‡๐ˆ๐๐ƒ ๐†๐‘๐”๐’ ๐Ÿงฎ

๐”๐ฉ๐๐š๐ญ๐ž ๐†๐š๐ญ๐ž: Unlike LSTMs, which use separate input and forget gates, GRU update handles both simultaneously. ๐Ÿ”„๐Ÿ”„
๐‘๐ž๐ฌ๐ž๐ญ ๐†๐š๐ญ๐ž: Both gates use sigmoid activations to regulate the information flow between 0 and 1. ๐Ÿ“ˆ๐Ÿ“‰
๐‚๐š๐ง๐๐ข๐๐š๐ญ๐ž ๐€๐œ๐ญ๐ข๐ฏ๐š๐ญ๐ข๐จ๐ง: Used to calculate the candidate hidden state before it is merged into the final output. ๐Ÿงฉโž•๐Ÿ

๐Ÿ”. ๐†๐‘๐” ๐„๐’๐’๐„๐๐“๐ˆ๐€๐‹๐’ ๐Ÿ“š

๐‘๐ž๐ฌ๐ž๐ญ: Decide how much of the past to ignore. ๐Ÿ™ˆ
๐‚๐š๐ง๐๐ข๐๐š๐ญ๐ž: Create a potential new memory step. ๐Ÿ†•
๐”๐ฉ๐๐š๐ญ๐ž: Blend the old state and the new candidate based on the update gate's weight. โš–๏ธ
๐Ž๐ฎ๐ญ๐ฉ๐ฎ๐ญ: Pass the new hidden state to the next time step. ๐Ÿšช๐Ÿƒโ€โ™‚๏ธ

"GRUs taught machines that sometimes, simplicity is the ultimate sophistication in intelligence." ๐Ÿค–โœจ

#GRU #AI #MachineLearning #DeepLearning #NeuralNetworks #Tech
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Overfitting ๐Ÿ“‰๐Ÿ“Š

๐Ÿค–๐Ÿง 

#MachineLearning #AI #DataScience #DeepLearning #Algorithm #NeuralNetworks
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๐Ÿ‘ฃ Rust Interview Deep Dive ๐Ÿฆ€๐Ÿ”

A repository for systematic preparation for Rust interviews at the middle, senior, and staff levels. ๐Ÿ’ผ๐Ÿ“š

Inside 100 real questions from interviews in product and infrastructure companies, detailed analyses with code examples and scenarios of tasks that occur in production. ๐Ÿ’ป๐Ÿ—๏ธ Not "guess the program's output", but the mechanics on which real services are built. ๐Ÿ› ๏ธ๐Ÿš€

Here are lock-free structures, self-referential types in async, FFI with tensor libraries, correct Send on guards via await, memory ordering under loom, soundness of custom collections. ๐Ÿ”’โšก And it all starts with the basics. Ownership, borrowing, lifetimes. ๐Ÿงฑ๐Ÿ”„ Those who want can start from scratch or at the staff level. ๐Ÿšถโ€โ™‚๏ธ๐Ÿ‘จโ€๐Ÿ’ป

https://github.com/Develp10/rustinterviewquiestions ๐Ÿ”—

#Rust #Programming #InterviewPrep #SoftwareEngineering #SystemsProgramming #CareerGrowth
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"Dive into Deep Learning" ๐Ÿ“˜๐Ÿค– is an open-source book that forms the mathematical foundation for large language models. ๐Ÿง ๐Ÿ“

It covers linear algebra, mathematical analysis, probability theory, optimization methods, backpropagation, attention mechanisms, and transformer architectures. ๐Ÿงฎ๐Ÿ“‰๐Ÿ”„

The book progressively moves from classical neural networks and convolutional neural networks to modern transformers and practical techniques used in large language models. ๐Ÿš€๐Ÿ”—๐Ÿง 

It contains over 1,000 pages ๐Ÿ“– and provides clear explanations, practical examples, and exercises. โœ…๐Ÿ“ Making it one of the most comprehensive free resources for understanding the mathematical structure of modern artificial intelligence systems and language models. ๐ŸŒ๐Ÿ”๐Ÿค–

arxiv.org/pdf/2106.11342 ๐Ÿ”—

#DeepLearning #AI #MachineLearning #NeuralNetworks #Transformers #OpenSource
โค4
๐Ÿค– Designing an RAG with search for 10 million documents while minimizing hallucinations ๐Ÿ“š

1๏ธโƒฃ Document ingestion and normalization ๐Ÿ“„
Removing duplicates, converting to a single format, extracting metadata, and maintaining versioning. ๐Ÿ”„

2๏ธโƒฃ Hybrid search (BM25 + vector representations) ๐Ÿ”
BM25 handles exact keyword matches, while vector search handles semantic relevance. One approach without the other typically suffers from low accuracy at this scale. ๐Ÿ“‰

3๏ธโƒฃ Approximate nearest neighbor search + re-ranking โš–๏ธ
Approximate nearest neighbor search quickly retrieves candidates from millions of fragments. Next, a ranking model recalculates relevance through a more rigorous comparison of the query and fragments. ๐Ÿง 

4๏ธโƒฃ Trust scoring for sources ๐Ÿ›ก๏ธ
Each fragment receives an evaluation based on freshness, source reliability, overlap, and consistency with other found results. Data with low trust should not significantly influence the final response. ๐Ÿšซ

5๏ธโƒฃ Generation with strict context constraints ๐Ÿšง
The model only operates within the extracted context. Adding knowledge outside the context is prohibited by the pipeline logic. ๐Ÿšซ

6๏ธโƒฃ Answers with source attribution ๐Ÿ“
Every significant statement must refer to a specific fragment, document, or timestamp. โฐ

7๏ธโƒฃ Fallback for low search confidence ๐Ÿ“‰
If the total context confidence falls below a threshold, a response like "not enough data" is returned. ๐Ÿ›‘

8๏ธโƒฃ Continuous quality checks ๐Ÿงช
Running attack queries, measuring search completeness, testing for hallucinations, and monitoring ranking degradation. ๐Ÿ“Š

9๏ธโƒฃ Caching and memory layer ๐Ÿ’พ
Frequent queries and search chains are cached to reduce latency and computational cost. โšก

๐Ÿ”Ÿ Observability at all stages ๐Ÿ‘๏ธ
Tracing the query path, fragment ranking, and the impact of tokens and failure points. ๐Ÿ› ๏ธ

๐Ÿš€ At the scale of 10 million documents, search quality becomes a more critical factor than the choice of generative model.

#RAG #AI #Search #LLM #DataEngineering #Tech
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๐Ÿš€ Master Binary Classification with Neural Networks! ๐Ÿง โœจ

Ever wondered how to build a neural network from scratch in Python using NumPy? ๐Ÿ๐Ÿ“Š

Binary classification is at the heart of many machine learning applications. ๐ŸŽฏ๐Ÿค–

Our super-detailed guide walks you through the entire process step by step. ๐Ÿ“๐Ÿ“š

๐Ÿ’ก Dive in and start building your own neural network today! ๐Ÿ—๐Ÿ”ฅ
https://tinztwinshub.com/data-science/a-beginners-guide-to-developing-an-artificial-neural-network-from-zero/

#MachineLearning #NeuralNetworks #Python #DataScience #AI #Tech
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๐Ÿ”ฅ Awesome open-source project to learn more about Transformer Models! ๐Ÿค–โœจ

We found this interactive website that shows you visually how transformer models work. ๐ŸŒ๐Ÿ“Š

Transformer Explainer:
https://poloclub.github.io/transformer-explainer/

#TransformerModels #OpenSource #AI #MachineLearning #DataScience #Tech

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Forwarded from Data Analytics
Pandas vs Polars vs DuckDB: Which Library Should You Choose? ๐Ÿค”๐Ÿ“Š

pandas remains the default choice for notebooks, exploratory analysis, visualization, and machine learning workflows ๐Ÿ“๐Ÿ“ˆ. Polars focus on fast, memory-efficient DataFrame processing โšก๐Ÿ’พ, while DuckDB brings a SQL-first approach for querying local files and embedded analytics ๐Ÿ—„๏ธ๐Ÿ”.

Each tool fits a different kind of local data workflow ๐Ÿ› ๏ธ. In this article, we compare pandas, Polars, and DuckDB across performance, architecture, interoperability, and real-world use cases ๐Ÿ†๐Ÿ”—.

More: https://www.analyticsvidhya.com/blog/2026/05/pandas-vs-polars-vs-duckdb/ ๐Ÿ”—

#DataScience #Pandas #Polars #DuckDB #Python #Analytics
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Found an easy way to learn math for ML: Mathematics for Machine Learning ๐ŸŽ“๐Ÿ“š

This is a curated collection on GitHub, including books, research papers, video lectures, and basic materials on math for studying and reviewing the mathematical foundations of machine learning. ๐Ÿ“–๐Ÿ“Š

It helps build a stronger knowledge base by bringing together trusted resources around topics that machine learning engineers constantly encounter: linear algebra, mathematical analysis, probability theory, statistics, information theory, matrix calculus, and deep learning mathematics. ๐Ÿงฎ๐Ÿค–

Free public repository on GitHub. ๐Ÿ’ปโœจ

https://github.com/dair-ai/Mathematics-for-ML

#MachineLearning #Mathematics #DataScience #Learning #GitHub #AI
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๐Ÿ”– A huge open-source course on AI Engineering from scratch

In the repository, we've collected:
โ€” 435 lessons;
โ€” 320+ hours of content;
โ€” Python, TypeScript, and Rust;
โ€” AI agents, MCP servers, prompts, and AI skills.

Moreover, almost every lesson includes practical tasks, so this isn't just theory, but a full-fledged roadmap for AI Engineering. ๐Ÿš€

โ›“๏ธ Link to the repository
https://github.com/rohitg00/ai-engineering-from-scratch

#AI #MachineLearning #Python #Rust #OpenSource #Tech

โœจ Join Best TG Channels https://t.me/addlist/0f6vfFbEMdAwODBk

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Transformer implementations for vision, audio, and AI agents ๐Ÿค–๐Ÿ‘๏ธ๐ŸŽต

Repo: https://github.com/Nicolepcx/transformers-the-definitive-guide

#AI #MachineLearning #Vision #Audio #Agents #Tech

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"Calculus: Early Transcendentals" is an excellent free textbook for building a solid foundation in mathematical analysis. ๐Ÿ“˜

The book is written in a clear and accessible language, while maintaining the necessary mathematical rigor. It contains a large number of examples and problems, making it suitable for both self-study and use in the educational process. ๐ŸŽ“

The textbook covers a wide range of topics, including:
โ€ข limits;
โ€ข derivatives;
โ€ข integrals;
โ€ข sequences and series;
โ€ข differential equations;
โ€ข multivariate analysis.

I consider this book another valuable tool in the arsenal of anyone studying mathematics. ๐Ÿ› ๏ธ

If you are a student and want to master or review key topics in mathematical analysis, or a teacher looking for new ideas and alternative explanations, this textbook is definitely worth attention.


https://open.umn.edu/opentextbooks/textbooks/415

https://github.com/antoniolupetti/algebrica

#Calculus #Math #FreeTextbook #StudyGuide #Mathematics #STEM

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Data leakage is one of the main reasons why ML demos look impressive... and then fail in production. ๐Ÿ“‰

The model didn't become smarter.
It just happened to see the correct answers in advance.

In 4 minutes, you'll understand where data leaks hide. ๐Ÿ”

Let's break it down below: ๐Ÿ‘‡

1. Data Leakage ๐Ÿ•ณ๏ธ

Data leakage occurs when information that won't be available at the time of actual prediction is used during the model training process.

Because of this, metrics on the validation stage can look much better than the actual quality of the model on new, previously unseen data.

2. Model Evaluation โš–๏ธ

The test set isn't just "additional data".
It's a simulation of the future.

Only train the model on the information that would have been available to you at the time of prediction.
Evaluate it on examples that the model couldn't have influenced during training.

3. Direct Leakage ๐Ÿšจ

This is the most obvious type of leakage.

Examples:
- a field with information from the future;
- an ID that encodes the target variable;
- a variable that appears only after an event has occurred;
- duplicate records in both the training and test sets.

If a feature doesn't exist at the time of inference (prediction), then it's likely a source of data leakage.

4. Indirect Leakage ๐Ÿ•ต๏ธ

This is the type of leakage that most often traps teams.

You perform normalization, imputation, feature selection, outlier removal, or dimensionality reduction before splitting the data into a training and test set.

The model didn't directly see the data from the test set.
But your preprocessing pipeline already saw it.

5. Train/Test Split โœ‚๏ธ

Wrong:
fit the scaler on all data โ†’ split the data โ†’ evaluate

Right:
split the data โ†’ fit the scaler only on the training set โ†’ apply it to both the training and test sets

The same idea applies to imputers, encoders, feature selection, PCA, and any preprocessing step that is trained on the data.

6. Cross-Validation ๐Ÿ”„

Each fold is a mini-experiment with a training and test set.
Therefore, preprocessing should be performed within each fold.

If you prepared the entire dataset once and then ran cross-validation, each fold would already have had access to its held-out data.

7. Pipelines ๐Ÿ› ๏ธ

A pipeline isn't just a way to make the code cleaner.
It's also a defense against data leakage.

Combine preprocessing, feature selection, and the model into a single pipeline, and then pass this pipeline to cross-validation or hyperparameter search (grid search).

8. AI Engineering Version ๐Ÿค–

Data leaks also occur in RAG systems and when evaluating LLMs.

Leakage occurs when you tune chunks, prompts, re-rankers, thresholds, or examples on the same evaluation dataset that you later present as "held-out".

As a result, your benchmark turns into training data.

9. Leakage Checklist โœ…

Before trusting the obtained metric, ask yourself:

- Could this feature exist at the time of prediction?
- Was any transformation (transform) step trained (fit) on the test data?
- Did cross-validation include the entire pipeline?
- Were we tuning parameters on the final evaluation dataset?

If the answer is "yes", then the metric likely doesn't reflect the actual quality of the model.

#MachineLearning #DataScience #MLOps #DataLeakage #ArtificialIntelligence #TechTips

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FREE MIT books on AI and Machine Learning: ๐Ÿ“š๐Ÿค–

1. Foundations of Machine Learning cs.nyu.edu/~mohri/mlbook/
2. Understanding Deep Learning udlbook.github.io/udlbook/
3. Introduction to Machine Learning Systems โฏ Vol 1: mlsysbook.ai/vol1/assets/do โฏ Vol 2: mlsysbook.ai/vol2/assets/do
4. Algorithms for ML algorithmsbook.com
5. Deep Learning deeplearningbook.org
6. Reinforcement Learning andrew.cmu.edu/course/10-703/
7. Distributional Reinforcement Learning direct.mit.edu/books/oa-monog
8. Multi Agent Reinforcement Learning marl-book.com
9. Agents in the Long Game of AI direct.mit.edu/books/oa-monog
10. Fairness and Machine Learning fairmlbook.org
11. Probabilistic Machine Learning
โฏ Part 1 : probml.github.io/pml-book/book1
โฏ Part 2 : probml.github.io/pml-book/book2

#MIT #AI #MachineLearning #DeepLearning #ReinforcementLearning #FreeBooks

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