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In this article, we are going to understand how self-attention works from scratch. This means we will code it ourselves one step at a time. Since its introduction via the original transformer paper (Attention Is All You Need), self-attention has become a cornerstone of many state-of-the-art deep learning models, particularly in the field of Natural Language Processing (NLP). Since self-attention i
Large language models have taken the public attention by storm – no pun intended. In just half a decade large language models – transformers – have almost completely changed the field of natural language processing. Moreover, they have also begun to revolutionize fields such as computer vision and computational biology. Since transformers have such a big impact on everyone’s research agenda, I wan
Jul 24, 2022 by Sebastian Raschka [Last updated: Jan 23, 2023] In my lectures, I emphasize that deep learning is really good for unstructured data (essentially, that’s the opposite of tabular data). Deep learning is sometimes referred to as “representation learning” because its strength is the ability to learn the feature extraction pipeline. Most tabular datasets already represent (typically manu
May 18, 2022 by Sebastian Raschka Today, PyTorch officially introduced GPU support for Apple’s ARM M1 chips. This is an exciting day for Mac users out there, so I spent a few minutes tonight trying it out in practice. In this short blog post, I will summarize my experience and thoughts with the M1 chip for deep learning tasks. My M1 Experience So Far Back at the beginning of 2021, I happily sold m
Machine Learning with PyTorch and Scikit-Learn has been a long time in the making, and I am excited to finally get to talk about the release of my new book. Initially, this project started as the 4th edition of Python Machine Learning. However, we made so many changes to the book that we thought it deserved a new title to reflect that. So, what’s new, you may wonder? In this post, I am excited to
Since many students in my Stat 451: Introduction to Machine Learning and Statistical Pattern Classification class are relatively new to Python and NumPy, I was recently devoting a lecture to the latter. Since the course notes are based on an interactive Jupyter notebook file, which I used as a basis for the lecture videos, I thought it would be worthwhile to reformat it as a blog article with the
A single-PDF version of Model Evaluation parts 1-4 is available on arXiv: https://arxiv.org/abs/1811.12808 Introduction Machine learning has become a central part of our life – as consumers, customers, and hopefully as researchers and practitioners! Whether we are applying predictive modeling techniques to our research or business problems, I believe we have one thing in common: We want to make “g
Oh god, another one of those subjective, pointedly opinionated click-bait headlines? Yes! Why did I bother writing this? Well, here is one of the most trivial yet life-changing insights and worldly wisdoms from my former professor that has become my mantra ever since: “If you have to do this task more than 3 times just write a script and automate it.” By now, you may have already started wondering
Python, Machine Learning, and Language Wars. A Highly Subjective Point of View Oh god, another one of those subjective, pointedly opinionated click-bait headlines? Yes! Why did I bother writing this? Well, here is one of the most trivial yet life-changing insights and worldly wisdoms from my former professor that has become my mantra ever since: “If you have to do this task more than 3 times just
I'm Sebastian: a machine learning & AI researcher, programmer, and author. As Staff Research Engineer at Lightning AI, I focus on the intersection of AI research, software development, and large language models (LLMs). I used to hold a position as an Assistant Professor of Statistics at the University of Wisconsin-Madison (on a tenure track from 2018-2025). However, with a heavy heart, I recently
Mar 24, 2015 by Sebastian Raschka This article offers a brief glimpse of the history and basic concepts of machine learning. We will take a look at the first algorithmically described neural network and the gradient descent algorithm in context of adaptive linear neurons, which will not only introduce the principles of machine learning but also serve as the basis for modern multilayer neural netwo
The Matrix Cheatsheet by Sebastian Raschka is licensed under a Creative Commons Attribution 4.0 International License.
Naive Bayes classifiers, a family of classifiers that are based on the popular Bayes’ probability theorem, are known for creating simple yet well performing models, especially in the fields of document classification and disease prediction. In this first part of a series, we will take a look at the theory of naive Bayes classifiers and introduce the basic concepts of text classification. In follow
Sections Sections Principal Component Analysis PCA and linear dimensionality reduction Nonlinear dimensionality reduction Kernel functions and the kernel trick Gaussian radial basis function (RBF) Kernel PCA Implementing the RBF kernel PCA step-by-step 1. Computation of the kernel (similarity) matrix. 2. Eigendecomposition of the kernel matrix. Examples of RBF Kernel PCA Half-moon shapes Linear PC
When I was working on my next pattern classification application, I realized that it might be worthwhile to take a step back and look at the big picture of pattern classification in order to put my previous topics into context and to provide and introduction for the future topics that are going to follow. Pattern classification and machine learning are very hot topics and used in almost every mode
Aug 3, 2014 by Sebastian Raschka Sections Sections Introduction Principal Component Analysis vs. Linear Discriminant Analysis What is a “good” feature subspace? Summarizing the LDA approach in 5 steps Preparing the sample data set About the Iris dataset Reading in the dataset Histograms and feature selection Normality assumptions LDA in 5 steps Step 1: Computing the d-dimensional mean vectors Step
Many beginning Python users are wondering with which version of Python they should start. My answer to this question is usually something along the lines “just go with the version your favorite tutorial was written in, and check out the differences later on.” But what if you are starting a new project and have the choice to pick? I would say there is currently no “right” or “wrong” as long as both
Sections Sections About standardization About Min-Max scaling Z-score standardization or Min-Max scaling? Standardizing and normalizing - how it can be done using scikit-learn Loading the wine dataset Standardization and Min-Max scaling Plotting Bottom-up approaches Vanilla Python NumPy Visualization The effect of standardization on PCA in a pattern classification task Reading in the dataset Divid
An introduction to parallel programming using Python's multiprocessing module -- written by Sebastian Raschka June 20, 2014 Tweet CPUs with multiple cores have become the standard in the recent development of modern computer architectures and we can not only find them in supercomputer facilities but also in our desktop machines at home, and our laptops; even Apple's iPhone 5S got a 1.3 Ghz Dual-co
In this short tutorial I want to provide a short overview of some of my favorite Python tools for common procedures as entry points for general pattern classification and machine learning tasks, and various other data analyses. Sections Sections Installing Python packages About the dataset Downloading and saving CSV data files from the web Reading in a dataset from a CSV file Visualizating of a da
Sections Sections Introduction Principal Component Analysis (PCA) Vs. Multiple Discriminant Analysis (MDA) What is a “good” subspace? Summarizing the PCA approach Generating some 3-dimensional sample data Why are we chosing a 3-dimensional sample? 1. Taking the whole dataset ignoring the class labels 2. Computing the d-dimensional mean vector 3. a) Computing the Scatter Matrix 3. b) Computing the
Moving from MATLAB matrices to NumPy arrays - A Matrix Cheatsheet -- written by Sebastian Raschka on January 22, 2014 Tweet Over time Python became my favorite programming language for the quick automation of tasks, such as manipulating and analyzing data. Also, I grew fond of the great matplotlib plotting library for Python. MATLAB/Octave was usually my tool of choice when my tasks involved matr
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