Computers or Machines only recognize quantities. And certain numbers require to be described and treated in a system that allows machines to determine problems by acquiring from the data instead of learning from predefined instructions in the case of programming.
All kinds of programming use computation at some level. Machine Learning knowledge involves programming data to determine the function that best represents the data.
The obstacle (or method) of finding the best parameters of a function using data is called model training in machine learning.
Accordingly, in a nutshell, machine learning is programming to enhance the best feasible solution – and we have a requirement of math to understand how that complication can be solved.
Learning linear algebra is the first step toward learning Math for Machine Learning.
The mathematical foundation explains the difficulty of rendering data furthermore computing in machine learning models that are known as Linear Algebra.
In the Machine Learning link, all principal phases of explaining a model have linear algebra running on the backend.
Important sections of statement that are approved by linear algebra are:
- Word Embeddings
- Dimensionality Reduction
- Data and learned Model Representation
Data Representation
The combustible of machine learning models, that is data, needs to be transformed into arrays where you can maintain it in your models. The estimates presented on certain arrays involve procedures like mold multiplication. This addition records the output that is also represented as a transformed matrix/tensor of numbers.
Word embeddings
Don’t worry about the technology here – it is just about characterizing large-dimensional data (estimate of a large number of variables in your data) with a smaller dimensional vector.
Natural Language Processing (NLP) bargains with textual data. Dealing with text means understanding the meaning of a huge corpus of words. Every word describes various meanings which might be related to different words. Vector embeddings in linear algebra permit us to represent these words more accurately.
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Tensors Flowing Through a Neural Network- Deep Learning
We can understand linear algebra in activity across all the major credentials today. Samples include viewpoint analysis on a Twitter or a Linked post (embeddings), identifying a type of lung disease from X-ray images (computer vision), or any speech-to-text bot (NLP).
All of these data types are interpreted by numbers in tensors. We run vectorized procedures to learn models from them working on a neural network. It then outputs a processed tensor which in turn is decoded to generate the final conclusion of the model.
Every state operates mathematical operations on those data arrays.
Vector Space Transformation-Dimensionality Reduction
When it continues to embed, you can principally think of an n-dimensional vector importing displaced with a complex vector that correlates to a lower-dimensional space. This is very important and it’s the one that succeeds in computational complexities.
For example, here is a three-dimensional vector that is displaced by a two-dimensional space. But you can extrapolate it to a real-world situation wherever you have a very huge number of dimensions. Decreasing dimensions doesn’t mean separating articles from the data. Alternatively, it’s about finding new features that are linear functions of the original features and preserving the variance of the original features.
Getting new variables (features) decodes to finding the principal elements(PCs). This then unites solving eigenvectors and eigenvalues problems.
Linear Algebra is used in which Industries
Presently, I hope you are convinced that Linear algebra is encouraging Machine Learning actions in a gathering of areas today.
Here is a list below to name a few:
- Chemical Physics
- Statistics
- Robotics
- Quantum Physics
- Genomics
- Image Processing
- Word Embeddings — neural networks/deep learning
What should we know in Linear algebra before starting ML/DL?
Now, the relevant question is how you can acquire skills to program these concepts of linear algebra. The information is you don’t have to reinvent the hoop, you just need to understand the fundamentals of vector algebra computationally and you then study to program those concepts using NumPy.
NumPy is a specific computation package that gives us entrance to all the underlying concepts of linear algebra. It is secure and fast as it runs compiled C code and it has a vast number of mathematical and scientific functions that we can use.
What does math have to do with machine learning?
1. All programming involves math at some level.
2. Machine learning is programming by optimization.
3. We need math to understand that optimization.
Mathematics and programming and computers have been tied together since the inception of computer science and programming. ML in particular though is programming by optimization the way that we program computers to do things in ML is through optimization. And in order to understand optimization and what we are optimizing and why that works we need mathematics and this is what makes machine learning such a more mathematical discipline of programming. Linear algebra will help us understand the objects being optimized in calculus which will help us understand how we optimize those things and then probability and stats will help us understand what that thing is that we are optimizing we are making better.
Why do we care about Linear Algebra?
The core operation in linear algebra is matrix multiplication here are some examples of matrix multiplication in action
-{Dot,scalar, inner }product
-Discrete Fourier transform
-Correlation Covariance -pagerank
-Linear Regression
-Hidden layers of neural nets
-Logistic Regression
-Convolutions
-Principal components analysis
-Newton L-bfgs
