![]() Algorithms written in standard 'for-loop' notation can be reformulated as matrix equations providing significant gains in computational efficiency. Linear algebra provides the first steps into vectorisation, presenting a deeper way of thinking about parallelisation of certain operations. This will not only allow reproduction and verification of existing models, but will allow extensions and new developments that can subsequently be deployed in trading strategies. Being able to 'read the language' of linear algebra will open up the ability to understand textbooks, web posts and research papers that contain more complex model descriptions. Even the most elementary machine learning models such as linear regression are optimised with these linear algebra techniques.Ī key topic in linear algebra is that of vector and matrix notation. These partial derivatives are often grouped together-in matrices-to allow more straightforward calculation. In particular it requires the concept of a partial derivative, which specifies how the loss function is altered through individual changes in each parameter. This immediately motivates calculus-the elementary topic in mathematics which describes changes of quantities with respect to another. To carry this out requires some notion of how the loss function changes as the parameters of the model are varied. ![]() Many supervised machine learning and deep learning algorithms largely entail optimising a loss function by adjusting model parameters. Learning these topics will provide a deeper understanding of the underlying algorithmic mechanics and allow development of new algorithms, which can ultimately be deployed as more sophisticated quantitative trading strategies. ![]() Linear algebra, probability and calculus are the 'languages' in which machine learning is written. ![]() Please note that the outline of linear algebra presented in this article series closely follows the notation and excellent treatments of Goodfellow et al (2016), Blyth and Robertson (2002) and Strang (2016). Instead the focus will be on selected topics that are relevant to deep learning practitioners from diverse backgrounds. Hence the set and function notation presented here may be initially unfamiliar.įor this reason the discussion presented in this article series will omit the usual "theorem and proof" approach of an undergraduate mathematics textbook. The computer scientist, software developer or retail discretionary trader however may only have gained exposure to mathematics through subjects such as graph theory or combinatorics-topics found within discrete mathematics. The mathematician, physicist, engineer and quant will likely be familiar with continuous mathematics through the study of differential equations, which are used to model many physical and financial phenomena. Linear algebra is a branch of continuous, rather than discrete mathematics. Hence it is crucial for the deep learning practitioner to understand the core ideas. It also forms the backbone of many machine learning algorithms. Linear algebra is a fundamental topic in the subject of mathematics and is extremely pervasive in the physical sciences. Reading these papers is absolutely crucial to find the best quantitative trading methods and as such it helps to speak the language! It is intended to get you up to scratch in some of the basic ideas and notation that will be found in the more advanced deep learning textbooks and research papers. This article is the first in the series of posts on the topic of Linear Algebra for Deep Learning. Since deep learning is going to be a big part of this year's content we thought it would be worthwhile to write some beginner tutorials on the key mathematical topics-linear algebra, calculus and probability-that are necessary to really understand deep learning for quant trading. Back in March we ran a content survey and found that many of you were interested in a refresher course for the key mathematical topics needed to understand deep learning and quant finance in general.
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