Lagrangians are a tool for constrained optimization problems. Have a look at the video for an intuitive explanation: 

[www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/lagrange-multipliers-and-constrained-optimization/v/the-lagrangian](https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/lagrange-multipliers-and-constrained-optimization/v/the-lagrangian) 

University of Michigan - Ann Arbor

When we beginning to kernelize the SVM, we have just got to do some calculus. When solving the soft-margin optimization problem we rely on something called a *Lagrangian*. Watch the despicably helpful khan academy video cited, take a look at the proof, convince yourself of it, then accept the new, *dual* formulation for the soft margin problem:

$$\max_{\alpha} - \frac{1}{2} 
\sum_{i,j=1}^n\alpha_i\alpha_jy^iy^j\vec{x}^i\cdot\vec{x}^j + \sum_{i=1}^n\alpha_i$$
$$\text{subject to } \alpha_i \geq 0 \ \ \forall i \\ \text{ and } \sum_{i=1}^n\alpha_iy^i = 0$$


Dual Formulation

This node can be used to share links to online articles and websites that are beneficial for learning and are references for other nodes. 

Helpful Data Science Online Articles

Using the Dual formulation of SVM, we can define an implicit feature mapping with kernels. 

Lets talk about what a kernel is, then give a couple examples of popular kernels.

Kernelization

Lagrangian Khan Academy Video

 [statisticsbyjim.com](https://statisticsbyjim.com/) 

Helpful Statistics Blog 

Assumptions Of Linear Regression Algorithm. Gomathi Tamilselvam. (2019, May 24). Retrieved from [towardsdatascience.com/assumptions-of-linear-regression-algorithm-ed9ea32224e1](https://towardsdatascience.com/assumptions-of-linear-regression-algorithm-ed9ea32224e1) 

Assumptions Of Linear Regression Algorithm and Scikit-learn Visualizations

https://www.r-bloggers.com/how-to-detect-heteroscedasticity-and-rectify-it/

Test for Heteroscadasticity in R

LOGISTIC REGRESSION. Maheshwari, Vineet. (2018, December). Retrieved from
[medium.com/datadriveninvestor/logistic-regression-18afd48779ce](https://medium.com/datadriveninvestor/logistic-regression-18afd48779ce) 

Logistic Regression

How Good is Your Model? — Intro to Resampling Methods. Peixeiro, Marco. (2019, January). Retrieved from [towardsdatascience.com/how-good-is-your-model-intro-to-resampling-methods-2831e832042a](https://towardsdatascience.com/how-good-is-your-model-intro-to-resampling-methods-2831e832042a) 

Intro to Resampling Methods

Dhiraj, K. (2019, August 29). Difference between K-Nearest Neighbor(K-NN) and K-Means Clustering. Medium. [medium.com/@dhiraj8899/difference-between-k-nearest-neighbor-k-nn-and-k-means-clustering-d9a44859182f](https://medium.com/@dhiraj8899/difference-between-k-nearest-neighbor-k-nn-and-k-means-clustering-d9a44859182f) 

Medium: Difference between K-Means and KNN

Data Set. Wikipedia. (2020, February 17). Retrieved from [en.wikipedia.org/wiki/Data_set](https://en.wikipedia.org/wiki/Data_set) 

Data Set

Amir Azimi. Is ‘Computer Science’ and ‘Information Systems’ the same subject? (2017, May 9). Retrieved from [medium.com/@HazzAzimi/is-computer-science-and-information-systems-the-same-subject-4e214292426e](https://medium.com/@HazzAzimi/is-computer-science-and-information-systems-the-same-subject-4e214292426e) 

Is ‘Computer Science’ and ‘Information Systems’ the same subject?

DelSole, Michael. (2018, April 24). *What is One Hot Encoding and How to Do It*. Medium. Retrieved from [medium.com/@michaeldelsole/what-is-one-hot-encoding-and-how-to-do-it-f0ae272f1179](https://medium.com/@michaeldelsole/what-is-one-hot-encoding-and-how-to-do-it-f0ae272f1179) 

What is One Hot Encoding and How to Do It

https://www.dataquest.io/blog/15-python-libraries-for-data-science/

Python Libraries for Data Science

Ph.D., Benjamin Obi Tayo. “Data Scientist Coding Exercise.” Medium, Towards AI - Multidisciplinary Science Journal, 11 June 2020. Retrieved from:  

https://medium.com/towards-artificial-intelligence/data-scientist-coding-exercise-e62f4de7df9e  



Data Scientist Coding Excercise

https://realpython.com/invalid-syntax-python/

Invalid Syntax in Python: Common Reasons for SyntaxError

Matplotlib Documentations

The Big Data Landscape is an annual article written by VC Matt Turck that provides an extremely granular view of companies within the Data Science space along with high and lowlights of the year. 

The Big Data Landscape can be accessed here: http://mattturck.com/wp-content/uploads/2019/07/2019_Matt_Turck_Big_Data_Landscape_Final_Fullsize.png



The Big Data Landscape of 2019

Sætra, Henrik Skaug. “Science as a Vocation in the Era of Big Data: The Philosophy of Science behind Big Data and Humanity’s Continued Part in Science.” Integrative Psychological & Behavioral Science, vol. 52, no. 4, Springer Science and Business Media LLC, 2018, pp. 508–22, doi:10.1007/s12124-018-9447-5.

https://search.lib.umich.edu/articles/record/FETCH-LOGICAL-14812-c1be5f7dc43257eb09516e3b08ea65e044c89b4fb42722c847b69ff64de0a37a3

Science as a Vocation in the Era of Big Data: the Philosophy of Science behind Big Data and humanity’s Continued Part in Science

Hicks, Stephanie C, and Irizarry, Rafael A. “A Guide to Teaching Data Science.” The American Statistician, vol. 72, no. 4, Informa UK Limited, 2017, pp. 382–91, doi:10.1080/00031305.2017.1356747.

https://search.lib.umich.edu/articles/record/FETCH-LOGICAL-14293-bb9dfa170b88df65690f79b02776e19ee338a692c0f0dcb1cc77fe06383a319c3

A Guide to Teaching Data Science

Van Horn, John, et al. “Advancing the International Data Science Workforce through Shared Training and Education.” F1000 Research, vol. 8, F1000 ( Faculty of 1000 Ltd), 2019, p. 251, doi:10.12688/f1000research.18357.1.

https://search.lib.umich.edu/articles/record/FETCH-LOGICAL-12021-e001cfa097b5c4e10c0722b63c521b8f3bc87c6c4a2fbc69395ee643b76403783

Advancing the international data science workforce through shared training and education


https://www.datamation.com/big-data/structured-vs-unstructured-data.html

Structured Data vs. Unstructured Data

An interesting article that looks at Baye's theorem from three different perspective: https://slackprop.wordpress.com/2016/08/28/the-three-faces-of-bayes/

The Three Faces of Bayes

https://www.unofficialgoogledatascience.com/2016/10/practical-advice-for-analysis-of-large.html

Practical advice for analysis of large, complex data sets

"Decision intelligence is the discipline of turning information into better actions at any scale." This article explores this idea: https://towardsdatascience.com/introduction-to-decision-intelligence-5d147ddab767

Introduction to Decision Intelligence

https://www.stradigi.ai/blog/thinking-green-ai-for-earth/

Technology has been enemy #1 to most environmentalists for a number of reasons: the manufacturing industry creates a tremendous amount of dangerous waste, machinery technology has increased development projects which has led to the extinction of many plants, birds and animals and our excessive power consumption is one of the leading causes of greenhouse gas emissions.

It isn’t all doom and gloom though, because as it turns out, AI has a green thumb and it’s been used to develop technology that can help prevent and in some cases even restore the damage we have done.

If human beings continue to refine technology and make a serious stand in protecting the environment, AI will become the planet’s biggest ally in our goal to become a more eco friendly planet.

How Artificial Intelligence will save the environment

Business intelligence (BI) systems have steadily grown faster, simpler to use, more accurate at processing massive amounts of internal and external data, as well as identifying patterns that were previously undetected, or even undetectable, by human users. And yet, some of the more popular BI systems on the market do little more than repackage and distil existing data about past performance, albeit in a visually palatable format. A new approach to mining and deciphering unstructured data using algorithms and automated machine learning (AutoML) to forecast changes in the business landscape before they happen has quite rightly been hailed as the next big thing in artificial intelligence. Here’s how next-generation business platforms that leverage these predictive capabilities put you in a better position than traditional BI.

https://www.stradigi.ai/blog/5-ways-advanced-predictive-analytics-outshine-bi/

How advanced predictive analytics is outpacing old school business intelligence

Maintaining Data Privacy in Association Rule Mining. (2002, August). Retrieved from https://www.sciencedirect.com/science/article/pii/B9781558608696500664

Maintaining Data Privacy in Association Rule Mining

Nonnegative Matrix Factorization: An Analytical and Interpretive Tool in Computational Biology. (2008, July) Retrieved from
https://www.researchgate.net/publication/51427894_Nonnegative_Matrix_Factorization_An_Analytical_and_Interpretive_Tool_in_Computational_Biology

Nonnegative Matrix Factorization

Esbroeck, A. & Chia, C.-C & Syed, Z.. (2012). Heart rate topic models. 2. 1635-1641.  Retrieved from https://www.researchgate.net/publication/290032961_Heart_rate_topic_models

Heart Rate Topic Models

Daniel Gruhl, R. Guha, Ravi Kumar, Jasmine Novak, and Andrew Tomkins. 2005. The predictive power of online chatter. In Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining (KDD '05). Association for Computing Machinery, New York, NY, USA, 78–87. DOI:https://doi.org/10.1145/1081870.1081883

The Predictive Power of Online Chatter

Ver Steeg, Greg & Galstyan, Aram. (2011). Information Transfer in Social Media. 10.1145/2187836.2187906. Retrieved from https://www.researchgate.net/publication/51944496_Information_Transfer_in_Social_Media

Information Transfer in Social Media

Danescu-Niculescu-Mizil, Cristian & Sudhof, Moritz & Jurafsky, Dan & Leskovec, Jure & Potts, Christopher. (2013). A computational approach to politeness with application to social factors. ACL 2013 - 51st Annual Meeting of the Association for Computational Linguistics, Proceedings of the Conference. 1.  Retrieved from  https://www.researchgate.net/publication/239522833_A_computational_approach_to_politeness_with_application_to_social_factors

A computational approach to politeness with application to social factors

Aniruddha Bhandari, (2020). AUC-ROC Curve in Machine Learning Clearly Explained. Retrieved from https://www.analyticsvidhya.com/blog/2020/06/auc-roc-curve-machine-learning/

AUC-ROC Curve in Machine Learning

Ritter, Alan & Mausam, Mausam & Etzioni, Oren & Clark, Sam. (2012). Open domain event extraction from Twitter. Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 1104-1112. 10.1145/2339530.2339704. Retrieved from https://www.researchgate.net/publication/254464301_Open_domain_event_extraction_from_Twitter

Open Domain Event Extraction from Twitter

Gui, Tao & Huang, Haoran & Peng, Minlong & Huang, Xuanjing. (2017). Part-of-Speech Tagging for Twitter with Adversarial Neural Networks. 2411-2420. 10.18653/v1/D17-1256. Retrieved from https://www.researchgate.net/publication/322587060_Part-of-Speech_Tagging_for_Twitter_with_Adversarial_Neural_Networks

Part-of-Speech Tagging for Twitter with Adversarial Neural Networks

Derczynski, Leon & Ritter, Alan & Clark, Sam & Bontcheva, Kalina. (2013). Twitter Part-of-Speech Tagging for All: Overcoming Sparse and Noisy Data. International Conference Recent Advances in Natural Language Processing, RANLP. Retrieved from https://www.aclweb.org/anthology/R13-1026.pdf

Twitter Part-of-Speech Tagging for All: Overcoming Sparse and Noisy Data

https://towardsdatascience.com/probability-and-statistics-for-data-science-part-1-3eed6051c40d

Probability and Statistics for Data Science

https://towardsdatascience.com/how-fast-numpy-really-is-e9111df44347gi=2448916cc6c0#:~:text=As%20the%20array%20size%20increase,also%20frees%20the%20memory%20faster

How Fast Numpy Really is and Why?

https://towardsdatascience.com/types-of-data-sets-in-data-science-data-mining-machine-learning-eb47c80af7a

Types of Data Sets in Data Science, Data Mining & Machine Learning

Kong, Lingpeng & Schneider, Nathan & Swayamdipta, Swabha & Bhatia, Archna & Dyer, Chris & Smith, Noah. (2014). A Dependency Parser for Tweets. 10.3115/v1/D14-1108. Retrieved from https://www.aclweb.org/anthology/D14-1108.pdf

A Dependency Parser for Tweets

Hale, John & Kuncoro, Adhiguna & Hall, Keith & Dyer, Chris & Brennan, Jonathan. (2019). Text Genre and Training Data Size in Human-like Parsing. 5849-5855. 10.18653/v1/D19-1594.  Retrieved from https://www.aclweb.org/anthology/D19-1594.pdf

Text Genre and Training Data Size in Human-Like Parsing

Röder, Michael & Both, Andreas & Hinneburg, Alexander. (2015). Exploring the Space of Topic Coherence Measures. WSDM 2015 - Proceedings of the 8th ACM International Conference on Web Search and Data Mining. 399-408. 10.1145/2684822.2685324. 

Exploring the Space of Topic Coherence Measures

Derczynski, Leon & Chester, Sean. (2016). Generalised Brown Clustering and Roll-up Feature Generation. 

Generalised Brown Clustering and Roll-Up Feature Generation

https://machinelearning.wtf/terms/symmetry-breaking/#:~:text=Symmetry%20breaking%20refer%20to%20a,This%20is%20the%20%E2%80%9Csymmetry%E2%80%9D.

Symmetry breaking


Thắng, Lương & Sutskever, Ilya & Le, Quoc & Vinyals, Oriol & Zaremba, Wojciech. (2014). Addressing the Rare Word Problem in Neural Machine Translation. 10.3115/v1/P15-1002. Retrieved from https://arxiv.org/pdf/1410.8206.pdf

Addressing the Rare Word Problem in Neural Machine Translation

Weston, Jason & Dinan, Emily & Miller, Alexander. (2018). Retrieve and Refine: Improved Sequence Generation Models For Dialogue. 87-92. 10.18653/v1/W18-5713. Retrieved from https://arxiv.org/pdf/1808.04776.pdf.

Retrieve and Refine: Improved Sequence Generation Models For Dialogue

https://towardsdatascience.com/text-classification-with-hugging-face-transformers-in-tensorflow-2-without-tears-ee50e4f3e7ed#:~:text=The%20Hugging%20Face%20transformers%20package,2%20is%20supported%20as%20well.

Text Classification with Hugging Face Transformers in TensorFlow 2 (Without Tears)

https://towardsdatascience.com/introduction-to-logistic-regression-66248243c148


Introduction to Logistic Regression

https://towardsdatascience.com/introduction-to-logistic-regression-66248243c148

https://towardsdatascience.com/support-vector-machines-a-brief-overview-37e018ae310f



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