Introduction To Calculus With Derivatives Written February 18, 2018 Suppose you need to calculate 1012 but you don't have a calculator handy. How would you estimate it? Or suppose you had to estimate 4.12. What if I told you that 4.12 is 16.81. Derivatives will help answer these questions. Estimating squares 42 is 16, and 4.12 is 16.81. 52 is 25, and 5.12 is 26.01. Lets look at some other increases: At 4.1, the increase was around 8. We know 72 is 49, and now we guess that there's an increase of 14 happening here. 7.12 is actually 50.41, so we were really close! Going back to the original question, what is 1012? These numbers seem to magically tell you how to calculate values like 4.12, 7.12, or 1012: Here's the big reveal: those numbers are the derivative at those points. We know the value of f(x) for different values of x: Here x is the input, and f(x) is the output. The derivative of f(x) (written f′(x) -- note the apostrophe) is 2x. That last column has all the ratios we were just using! So our estimate is 5.12=26. P.S. Limits
Applied Machine Learning in Python with scikit-learn — scikit-learn tutorial v0.7+ documentation Statistical learning Machine learning is a technique with a growing importance, as the size of the datasets experimental sciences are facing is rapidly growing. Problems it tackles range from building a prediction function linking different observations, to classifying observations, or learning the structure in an unlabeled dataset. This tutorial will explore statistical learning, that is the use of machine learning techniques with the goal of statistical inference: drawing conclusions on the data at hand. scikits.learn is a Python module integrating classic machine learning algorithms in the tightly-knit world of scientific Python packages (numpy, scipy, matplotlib). Warning In scikit-learn release 0.9, the import path has changed from scikits.learn to sklearn. try: from sklearn import somethingexcept ImportError: from scikits.learn import something
The matrix calculus you need for deep learning Terence Parr and Jeremy Howard (We teach in University of San Francisco's MS in Data Science program and have other nefarious projects underway. You might know Terence as the creator of the ANTLR parser generator. For more material, see Jeremy's fast.ai courses and University of San Francisco's Data Institute in-person version of the deep learning course.) Printable version (This HTML was generated from markup using bookish) Abstract This paper is an attempt to explain all the matrix calculus you need in order to understand the training of deep neural networks. Introduction Most of us last saw calculus in school, but derivatives are a critical part of machine learning, particularly deep neural networks, which are trained by optimizing a loss function. For example, the activation of a single computation unit in a neural network is typically calculated using the dot product (from linear algebra) of an edge weight vector w with an input vector x plus a scalar bias (threshold): . . with the and .
Stephen Marsland This webpage contains the code and other supporting material for the textbook "Machine Learning: An Algorithmic Perspective" by Stephen Marsland, published by CRC Press, part of the Taylor and Francis group. The first edition was published in 2009, and a revised and updated second edition is due out towards the end of 2014. The book is aimed at computer science and engineering undergraduates studing machine learning and artificial intelligence. The table of contents for the second edition can be found here. There are lots of Python/NumPy code examples in the book, and the code is available here. Note that the chapter headings and order below refer to the second edition. All of the code is freely available to use (with appropriate attribution), but comes with no warranty of any kind. Option 1: Zip file of all code, arranged into chapters Option 2: Choose what you want from here: Many of the datasets used in the book are available from the UCI Machine Learning Repository.
Markov Chains explained visually Explained Visually By Victor Powell with text by Lewis Lehe Markov chains, named after Andrey Markov, are mathematical systems that hop from one "state" (a situation or set of values) to another. A simple, two-state Markov chain is shown below. With two states (A and B) in our state space, there are 4 possible transitions (not 2, because a state can transition back into itself). Of course, real modelers don't always draw out Markov chain diagrams. If the state space adds one state, we add one row and one column, adding one cell to every existing column and row. One use of Markov chains is to include real-world phenomena in computer simulations. One way to simulate this weather would be to just say "Half of the days are rainy. Did you notice how the above sequence doesn't look quite like the original? We can minic this "stickyness" with a two-state Markov chain. You can also access a fullscreen version at setosa.io/markov
Mining of Massive Datasets Big-data is transforming the world. Here you will learn data mining and machine learning techniques to process large datasets and extract valuable knowledge from them. The book The book is based on Stanford Computer Science course CS246: Mining Massive Datasets (and CS345A: Data Mining). The book, like the course, is designed at the undergraduate computer science level with no formal prerequisites. The Mining of Massive Datasets book has been published by Cambridge University Press. By agreement with the publisher, you can download the book for free from this page. We welcome your feedback on the manuscript. The MOOC (Massive Open Online Course) We are running the third edition of an online course based on the Mining Massive Datases book: Mining Massive Datasets MOOC The course starts September 12 2015 and will run for 9 weeks with 7 weeks of lectures. The 2nd edition of the book (v2.1) The following is the second edition of the book. The Errata for the second edition of the book: HTML.
What is (Gaussian) curvature? A previous article already introduced manifolds and some of their properties. Along the way, I briefly mentioned curvature but never got around to explain it properly. This article aims to fill in some of the gaps in a very visual way that is accessible to many people. Unfortunately, curvature is one of the concepts that crops up in very different contexts in mathematics. This can cause quite a lot of confusion! Since most of the initial discoveries of this form of curvature are due to Carl Friedrich Gauss, mathematician extraordinaire, we should credit him appropriately and use the term Gaussian curvature throughout this article. Let us dive into curvature by thinking about triangles. Let us call all objects that satisfy the same angle sum property planar or flat objects because their geometry is the same as that of the plane. We call spaces or objects with angle sums larger than spherical spaces. When doing so, however, we notice two interesting things: Until next time, stay curvy!
Calculus Explained with pics and gifs - 0a.io - Calculus is just a fanciful name for the study of change in maths. Calculus in general refers to the branch of maths that was made famous by Newton in the 17th century. Don’t confuse it with Lambda calculus, propositional calculus, and unicorns, which are completely different things. To understand calculus, one needs to be able to visualize the concepts of function, limit, differentiation, and integration. 1. What is a function? A function can be seen as a machine that takes in value and gives you back another value. f(input)=output A function is normally defined by an equation like this: f(x)=x+10 Now if you put 2 into this function you will get 12 in return. f(2)=12 The set of numbers that you can put into a function is known as the domain of the function. 2. A limit is the number you are “expected” to get from a function (or algebraic expression) when it takes in a certain input. Here is an example where the limit (the expected output) is the same as the actual output. limx→25x25=1 3. 4. 5.
Mathematics for Machine Learning | Companion webpage to the book “Mathematics for Machine Learning”. Copyright 2020 by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong. Published by Cambridge University Press. An Intuitive Guide to Linear Algebra Despite two linear algebra classes, my knowledge consisted of “Matrices, determinants, eigen something something”. Why? Well, let’s try this course format: Name the course Linear Algebra but focus on things called matrices and vectorsTeach concepts like Row/Column order with mnemonics instead of explaining the reasoningFavor abstract examples (2d vectors! 3d vectors!) and avoid real-world topics until the final week The survivors are physicists, graphics programmers and other masochists. Linear algebra gives you mini-spreadsheets for your math equations. We can take a table of data (a matrix) and create updated tables from the original. Here’s the linear algebra introduction I wish I had, with a real-world stock market example. What’s in a name? “Algebra” means, roughly, “relationships”. “Linear Algebra” means, roughly, “line-like relationships”. Straight lines are predictable. Lines are nice and predictable: Linear Operations An operation is a calculation based on some inputs. No! Ok. x y z