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Mathematics for Data Science
Mathematics is very important in the field of data science as concepts within mathematics aid in identifying patterns and assist in creating algorithms. The understanding of various notions of Statistics and Probability Theory are key for the implementation of such algorithms in data science.
Beyond the basics of calculus, linear algebra, and probability, there is a certain kind of mathematical thinking that comes up pretty often when you’re trying to understand data. It involves quantifying something you want to measure, then understanding how the quantification works in mathematical terms. The interesting part is not usually doing the math, but figuring out what math to do.
Most of the mathematics required for Data Science lie within the realms of statistics and algebra,
Statistics, in particular, is at the very foundation of Data Science, and is the collection of tools which helps us separate significance from randomness. Algebra is quite often at the heart of the analysis itself. The further quantitative skills facilitate intuition, which is essential in analytics.
Data-scientist should have a knowldge about one or more of this topics :
Linear algebraDiscrete mathDifferential equationsTheory of statisticsNumerical analysis : numerical linear algebra and quadratureAbstract algebraNumber theoryReal analysisComplex analysisIntermediate analysisProbability and StatisticsLinear AlgebraMatrix Theory Calculus Set theory
👉 Here are some of the Useful resources to improve your Math skills & Data Science Expertise-
MUST READ Books
1) The Elements of Statistical Learning(Springer Series)
2) Introduction to Linear Algebra by Gilbert Strang.
3) Naked Statistics by Charles Wheelan.
4) An Introduction to Statistical Learning: with Applications in R.
5) Pattern Recognition and Machine Learning by Christopher M. Bishop.
6) Pattern Classification ((A Wiley-Interscience publication).
7) Introduction to Statistical Learning
8) Introduction to Bayesian Statistics
Must Know Algorithms for Data Scientist
AlgorithmsLibraryTutorialPrincipal
Component Analysis(PCA)/SVDhttps://docs.scipy.org/doc/scipy/reference/generated/scipy.linalg.svd.html
http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html https://arxiv.org/pdf/1404.1100.pdfLeast Squares
and Polynomial Fittinghttps://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.lstsq.htmlhttps://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.polyfit.htmlhttps://lagunita.stanford.edu/c4x/HumanitiesScience/StatLearning/asset/linear_regression.pdfConstrained
Linear Regressionhttp://scikit-learn.org/stable/modules/linear_model.htmlhttps://www.youtube.com/watch?v=5asL5Eq2x0A
https://www.youtube.com/watch?v=jbwSCwoT51M K means
Clusteringhttp://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.htmlhttps://www.youtube.com/watch?v=hDmNF9JG3lo
https://www.datascience.com/blog/k-means-clusteringLogistic
Regressionhttp://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.htmlhttps://www.youtube.com/watch?v=-la3q9d7AKQSVM (Support
Vector Machines)http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.htmlhttps://www.youtube.com/watch?v=eHsErlPJWUUFeedforward
Neural Networkshttp://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPClassifier.html#sklearn.neural_network.MLPClassifier
http://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPRegressor.html
https://github.com/keras-team/keras/blob/master/examples/reuters_mlp_relu_vs_selu.pyhttp://www.deeplearningbook.org/contents/mlp.html
http://www.deeplearningbook.org/contents/autoencoders.html
http://www.deeplearningbook.org/contents/representation.htmlConvolutional
Neural Networks (Convnets)https://developer.nvidia.com/digits
https://github.com/kuangliu/torchcv
https://github.com/chainer/chainercv
https://keras.io/applications/http://cs231n.github.io/
https://adeshpande3.github.io/A-Beginner%27s-Guide-To-Understanding-Convolutional-Neural-Networks/Recurrent
Neural Networks (RNNs)https://github.com/tensorflow/models
https://github.com/wabyking/TextClassificationBenchmark
http://opennmt.net/http://cs224d.stanford.edu/
http://www.wildml.com/category/neural-networks/recurrent-neural-networks/
http://colah.github.io/posts/2015-08-Understanding-LSTMs/Conditional
Random Fields (CRFs)https://sklearn-crfsuite.readthedocs.io/en/latest/http://blog.echen.me/2012/01/03/introduction-to-conditional-random-fields/
https://www.youtube.com/watch?v=GF3iSJkgPbADecision
Treeshttp://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestClassifier.html
http://scikit-learn.org/stable/modules/generated/sklearn.ensemble.GradientBoostingClassifier.html
http://xgboost.readthedocs.io/en/latest/
https://catboost.yandex/http://xgboost.readthedocs.io/en/latest/model.html
https://arxiv.org/abs/1511.05741
https://arxiv.org/abs/1407.7502
http://education.parrotprediction.teachable.com/p/practical-xgboost-in-pythonTD
Algorithms https://github.com/keras-rl/keras-rl
https://github.com/tensorflow/minigohttps://web2.qatar.cmu.edu/~gdicaro/15381/additional/SuttonBarto-RL-5Nov17.pdf
https://www.youtube.com/watch?v=2pWv7GOvuf0
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