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Essential Math for Data Science: Visual Introduction to Singular Value Decomposition (SVD)

04-17-2021 / hadrienj | essential-math python numpy

Transformation of the unit circle and basis vectors.

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Essential Math for Data Science: Eigenvectors and application to PCA

02-23-2021 / hadrienj | essential-math python numpy

The variance of the data in the direction of the vector $\vu$ (red) is larger than in the direction of the vector $\vv$ (green).

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Essential Math for Data Science: Basis and Change of Basis

02-01-2021 / hadrienj | essential-math python numpy

The basis vectors in the Cartesian plane.

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Essential Math for Data Science: Introduction to Systems of Linear Equations

01-13-2021 / hadrienj | essential-math python numpy

Plot of the equation $y=2x+1$ .

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Essential Math for Data Science: Linear Transformation with Matrices

12-28-2020 / hadrienj | essential-math python numpy

Each point corresponds to the combination of x and y values.

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Essential Math for Data Science - Introduction to Matrices and the Matrix Product

12-16-2020 / hadrienj | essential-math python numpy

Steps of the product between a matrix and a vector.

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Essential Math for Data Science: Scalars and Vectors

12-10-2020 / hadrienj | essential-math python numpy

A geometric vector running from $A$ to $B$ .

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Essential Math for Data Science: Information Theory

11-26-2020 / hadrienj | essential-math python numpy

The cross-entropy as a measure of difference between two distributions

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Essential Math for Data Science: The Poisson Distribution

11-24-2020 / hadrienj | essential-math python numpy

Emails received by Sarah in one-hour intervals for the last 100 hours.

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Essential Math for Data Science: Probability Density and Probability Mass Functions

11-12-2020 / hadrienj | essential-math python numpy

The probability to draw a number between 0 and 0.2 is the highlighted area under the curve.

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Essential Math for Data Science: Integrals And Area Under The Curve

11-05-2020 / hadrienj | essential-math python numpy

Area under the curve.

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Essential Math for Data Science: New Chapters

08-03-2020 / hadrienj | essential-math python numpy

Update concerning "Essential Math for Data Science" and complete table of content of the book. $Contour L1 Regularization$ L1 Regularization

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Essential Math for Data Science

02-28-2020 / hadrienj | essential-math python numpy

Introduction of my book "Essential Math for Data Science". The goal of the book is to provide an introduction to the mathematics needed for data science and machine learning. The idea is to use a hands-on approach using examples in... $SVD Geometry$ SVD Geometry

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Deep Learning Book Series 3.4 and 3.5 Marginal and Conditional Probability

07-17-2019 / hadrienj | probability python numpy deep-learning-book

In this article, we'll cover marginal and conditional probability for discrete and continuous variables. We'll also see the concept of dependent and independent events. We'll introduce the math smoothly with Python and drawings. Sum rule to calculate marginal probability. The sum rule allows to calculate marginal probability from joint probability.

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Deep Learning Book Series 3.1 to 3.3 Probability Mass and Density Functions

05-01-2019 / hadrienj | probability python numpy deep-learning-book

The goal of probability is to deal with uncertainty. It gives ways to describe random events. A random variable is a variable that can take multiple values depending of the outcome of a random event. The possible outcomes are the... Illustration of the probability density function and the area under the curve corresponding to the range 0.5-0.7 Probability density function and area under the curve between 0.5 and 0.7.

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Preprocessing for deep learning: from covariance matrix to image whitening

08-27-2018 / hadrienj | computer-vision python numpy deep-learning

The goal of this post/notebook is to go from the basics of data preprocessing to modern techniques used in deep learning. My point is that we can use code to better understand abstract mathematical notions! Thinking by coding! 💥 Rotation to decorrelate the data The left plot shows correlated data. For instance, if you take a data point with a big $x$ value, chances are that $y$ will also be quite big. Now take all data points and do a rotation (maybe around 45 degrees counterclockwise): the new data (plotted on the right) is not correlated anymore.

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Deep Learning Book Series · 2.12 Example Principal Components Analysis

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

This post on linear algebra is about Principal Components Analysis (PCA). We will use Python/Numpy/Matplotlib to get a better intuition and understanding of this important data analysis tool! Representation of the variance explained across directions Projection of the data point: the line direction is the one with the largest variance

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Deep Learning Book Series · 2.11 The determinant

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

In this post, we will see what is the meaning of the determinant of a matrix. This special number can tell us a lot of things about our matrix! Comparison of positive and negative determinant The determinant of a matrix can tell you a lot of things about the transformation associated with this matrix

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Deep Learning Book Series · 2.10 The Trace Operator

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

This short post introduces you to the trace operator. We will see what is the Trace of a matrix and how to compute it. Calculating the trace of a matrix The trace of matrix

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Deep Learning Book Series · 2.9 The Moore Penrose Pseudoinverse

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

In this post, we will learn about the Moore Penrose pseudoinverse as a way to find an approaching solution where no solution exists. In some cases, a system of equation has no solution, and thus the inverse doesn't exist. However... Example of three linear equations in 2 dimensions. This is an overdetermined system There is more equations (3) than unknowns (2) so this is an overdetermined system of equations

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Deep Learning Book Series · 2.8 Singular Value Decomposition

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

This post introduces the details Singular Value Decomposition or SVD. We will use code example (Python/Numpy) like the application of SVD to image processing. You can see matrices as linear transformation in space. With the SVD, you decompose a matrix... Plot of the unit circle and its transformation The unit circle and its transformation by a matrix

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Deep Learning Book Series · 2.7 Eigendecomposition

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

This post introduces the concept of eigendecomposition. We will start with getting some intuitions on eigenvectors and eigenvalues. We will develop on the idea that a matrix can be seen as a linear transformation and that applying a matrix on... Plot of the unit circle and its transformation by the matrix A The unit circle and its transformation by the matrix A. The vectors are the eigenvectors of A.

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Deep Learning Book Series · 2.6 Special Kinds of Matrices and Vectors

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

In this post, we will see special kinds of matrix and vectors the diagonal and symmetric matrices, the unit vector and the concept of orthogonality. Example of diagonal and symmetric matrices

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Deep Learning Book Series · 2.5 Norms

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

This post explains what is a norm using examples with Python/Numpy. The norm is what is generally used to evaluate the error of a model. You can think of the norm as the length of a vector. It is a... Representation of the squared L2 norm The squared L2 norm

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Deep Learning Book Series · 2.4 Linear Dependence and Span

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

We will see how to represent systems of equations graphically, how to interpret the number of solutions of a system, what is linear combination and more. As usual, we will use Numpy/Matplotlib as a tool to experiment these concepts and... Examples of systems of equations with 0, 1 and an infinite number of solutions A system of equations has no solution, 1 solution or an infinite number of solutions

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Deep Learning Book Series · 2.3 Identity and Inverse Matrices

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

This post will introduce you to special kind of matrices: the identity matrix and the inverse matrix. We will use Python/Numpy as a tool to get a better intuition behind these concepts. Example of an identity matrix A 3 by 3 identity matrix

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Deep Learning Book Series · 2.2 Multiplying Matrices and Vectors

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

This short introduction will give you the intuition and Python/Numpy code behind matrices and vectors multiplication. Multiplying matrices and understanding the dot product is crucial to more advanced linear algebra needed for data science, machine learning and deep learning. Multiplying matrices. An example of how to calculate the dot product between a matrix and a vector The dot product between a matrix and a vector

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Deep Learning Book Series · 2.1 Scalars Vectors Matrices and Tensors

03-26-2018 / hadrienj | linear-algebra python numpy deep-learning-book

This introduction to scalars, vectors, matrices and tensors presents Python/Numpy code and drawings to build a better intuition behind these linear algebra basics. An example of a scalar, a vector, a matrix and a tensor Difference between a scalar, a vector, a matrix and a tensor

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Deep Learning Book Series · Introduction

03-26-2018 / hadrienj | linear-algebra deep-learning machine-learning

I'd like to introduce a series of blog posts and their corresponding Python Notebooks gathering notes on the Deep Learning Book from Ian Goodfellow, Yoshua Bengio, and Aaron Courville (2016). The aim of these notebooks is to help beginners/advanced beginners... Cover of the deep learning book by Goodfellow, Bengio and Courville The Deep Learning Book - Goodfellow, I., Bengio, Y., and Courville, A. (2016)

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