The Machine Learning Specialization is a foundational online program created in collaboration between DeepLearning.AI and Stanford Online. This beginner-friendly program will teach you the fundamentals of machine learning and how to use these techniques to build real-world AI applications. This Specialization is taught by Andrew Ng, an AI visionary who has led critical research at Stanford University and groundbreaking work at Google Brain, Baidu, and Landing.AI to advance the AI field. This 3-course Specialization is an updated version of Andrew's pioneering Machine Learning course, rated 4.9 out of 5 and taken by over 4.8 million learners since it launched in 2012. It provides a broad introduction to modern machine learning, including supervised learning (multiple linear regression, logistic regression, neural networks, and decision trees), unsupervised learning (clustering, dimensionality reduction, recommender systems), and some of the best practices used in Silicon Valley for artificial intelligence and machine learning innovation (evaluating and tuning models, taking a data-centric approach to improving performance, and more.)
This article belongs to the series "Probabilistic Deep Learning". This weekly series covers probabilistic approaches to deep learning. The main goal is to extend deep learning models to quantify uncertainty, i.e., know what they do not know. In this article, we will introduce the concept of probabilistic logistic regression, a powerful technique that allows for the inclusion of uncertainty in the prediction process. We will explore how this approach can lead to more robust and accurate predictions, especially in cases where the data is noisy, or the model is overfitting.
The mathematics of least squares would have been so trivial for Gauss that even had he come upon the method he might have passed it over as but one of many, not noticing its true significance until Legendre's book prodded his memory and produced a post facto priority claim. There have been many extraordinary equations that changed the world (whether they were discovered or invented depends on whether you subscribe to mathematical Platonism--I do) but among the 17 equations that changed the world, the legendary Ordinary Least Squares (OLS) wasn't listed among them (though it is heavily related to both the Normal Distribution and Information Theory). It's a shame because the article and tweets referencing the "17 Equations" have been floating around for nearly ten years. So I will tell you about the magic of OLS, a little about its history, some of its extensions, and its applications (yes, to Fintech too). Subscribe for free to receive new posts and support my work.
Statistical Learning with Math and R: The most crucial ability for machine learning and data science is mathematical logic for grasping their essence rather than knowledge and experience. This textbook approaches the essence of machine learning and data science by considering math problems and building R programs. As the preliminary part, Chapter 1 provides a concise introduction to linear algebra, which will help novices read further into the following main chapters. Each chapter mathematically formulates and solves machine learning problems and builds the programs. The body of a chapter is accompanied by proofs and programs in an appendix, with exercises at the end of the chapter.
Additionally, the chance is you won't be working with a dataset, so merging data is also a common operation you'll use. Extracting meaningful information from data becomes easier if you visualize it. In Python, there are many libraries you can use to visualize your data. You should use this stage to detect the outliers and correlated predictors. If undetected, they will decrease your machine-learning model performance.
Regression is a statistical method used to analyze the relationship between one or more independent variables and a continuous dependent variable. It can be used to predict the value of the dependent variable based on the values of the independent variables. Linear regression is the most common type of regression and is used when the relationship between the variables is linear. Non-linear regression is used when the relationship between the variables is non-linear. Other types of regression include logistic regression, which is used when the dependent variable is binary, and polynomial regression, which is used when the relationship between the variables is non-linear but can be modeled by a polynomial equation.
Recently I have written an article about the risks of using the train_test_split() function provided by the scikit-learn Python package. That article has raised a lot of comments, some positives, and others with some concerns. The main concern in the article was that I used a small dataset to demonstrate my theory, which was: be careful when you use the train_test_split() function, because the different seeds may produce very different models. The main concern was that the train_test_split() function does not behave strangely; the problem is that I used a small dataset to demonstrate my thesis. In this article, I try to discover which is the performance of a Linear Regression model by varying the dataset size.
Statsmodels provides a wide range of statistical and econometric tools for data analysis. It is particularly useful for estimating and testing statistical models and includes functions for linear regression, generalized linear models, time series analysis, and other types of statistical analysis. Statsmodels also includes a suite of diagnostic tools for checking the assumptions of statistical models and tools for model selection and evaluation. In addition, Statsmodels provides several visualization tools for creating publication-quality plots and graphs. JAX by Google allows users to easily and efficiently perform mathematical operations on arrays, including linear algebra and differentiation.
Abstract: Fast transforms correspond to factorizations of the form Z X(1)…X(J), where each factor X(ℓ) is sparse and possibly structured. This paper investigates essential uniqueness of such factorizations, i.e., uniqueness up to unavoidable scaling ambiguities. Our main contribution is to prove that any N N matrix having the so-called butterfly structure admits an essentially unique factorization into J butterfly factors (where N 2J), and that the factors can be recovered by a hierarchical factorization method, which consists in recursively factorizing the considered matrix into two factors. This hierarchical identifiability property relies on a simple identifiability condition in the two-layer and fixed-support setting. This approach contrasts with existing ones that fit the product of butterfly factors to a given matrix via gradient descent. The proposed method can be applied in particular to retrieve the factorization of the Hadamard or the discrete Fourier transform matrices of size N 2J.