Quriosity volume 8 issue 7

Autoregressive integrated moving average Quant Guru – Calyampuri Radhakrishna Rao Intern Dairies – Agrocel & JPMC Artificial Neural Networks Quantertainment - Quincunx Quriosity Job Corner

SEPTEMBER 2017

VOLUME 08 EDITION 07

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Editor’s Note Welcome to the latest issue of Quriosity, the monthly newsletter of Quantinuum!

Many current data analysis techniques are beyond the reach of most people. Obscure maths and daunting algorithms have created a chasm for problem solvers and decision makers. Quriosity is trying to bridge these gaps by giving appropriate inputs to our students and readers who are the future managers.

The objective of Quriosity is to publish up-to-date articles on data analytics, alongside relevant and insightful news. This way the magazine aspires to be vibrant, engaging and accessible, and at the same time integrative.

The cover story is based on Artificial Neural Networks by Aditya Sharma. An Artificial Neural Network is a simulation of the human brain created by a computer.

The other story is based on ARIMA, written by V V S Anudeep. ARIMA or Autoregressive Integrated Moving Average model fits to time series data to predict future points in the series.

We are happy to include the new section- Quriosity Job corner with this edition which is aimed to provide information to the Alumni about the existing job opportunities and also give the students an idea about what are the skill sets which are on the lookout in the current industry scenario.

Needless to say, any articles that you wish to submit, either individually or collaboratively, are much appreciated and will make a substantial contribution to the development and success of the magazine.

Thank you and Happy Reading!

Editorial Team Quantinuum

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Contents TOPIC

PAGE NO

Cover Story on Artificial Neural Networks

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by Aditya Sharma

ARIMA by V V S Anudeep

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Quant Guru – Calyampuri Radhakrishna Rao by Rupal Doshi

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Intern Dairies – Agrocel & JPMC by Amod

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Quriosity Updates by Kapil Gupta

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News Digest by Akshay Nagpal

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Quantertainment by Anjali Tiwari

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Quriosity Job Corner by Nikki Gandhi

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Quant Fun

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Quant Connect

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Kulkarni and Sulabh Chokhani

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Cover Story Artificial Neural Networks If the research in the field of Artificial Intelligence continues to thrive at current pace, experts believe that AI will achieve 50% of human intelligence by 2050 and 90% by 2075. Programmers are progressively trying to build highly intelligent machines which are capable of learning on their own. These codes would not only optimize the way things are done, but would also find answers to world’s biggest unsolved problems, such as Global Warming or Cancer. Yes, there’s more to AI than just sci-fi terminator films!

The key to the future of AI lies with the domain of Machine Learning, and the programmers have already come up with some very efficient and smart learning algorithms. Artificial Neural Network, one such omniscient computational model, is widely known to be a universal function approximator. Inspired by biological brain, Warren McCulloch and Walter Pitts, in early 1940s laid the foundation to this increasingly important model in the domain of Machine Learning.

A human brain consists of billions of neurons interconnected with each other through Dendrites. The output information from the neuron is carried away through Axon. Artificial Neural Networks are a computer simulation of biological brain. So, which Neural Network do you think, is faster? A biological brain is based on energy generated from chemical reactions whereas a semiconductor works on electrical signals which are a million times faster than chemical reactions. But the true power of a biological brain lies in its humongous interconnection. There are over a thousand billion neurons and each neuron is connected to over 10,000 others. Imitating such an enormous interconnection on a computer is pragmatically impossible, as today’s computational capabilities are limited.

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An ANN is made of various layers of Neurons, and the neurons of each layer are connected to the neurons in the next layer. The output of the final layer neuron is the output of the ANN. The intermediate layers between input and output layers are called hidden layers. The link between two neurons carries some weight, represented by w. At the core of each neuron is an activation function and the information flows from the input layer to the output layer. The activation function can be unipolar or bipolar sigmoidal, tan hyperbolic or Gaussian. The sum-product of weights and inputs from previous layer neurons is fed to the activation function whose output becomes an input to further layer neurons. This is a typical feed forward network as the output of one layer is fed to the next layer. Based on the application, the architecture and activation function of the ANN varies.

Now comes the question, how does an ANN actually work? Basically, an ANN is just a bunch of code which is used to find relationship between a number of input variables and output variables. For example, let there be three variables, x, y and z, where z is a function of x and y, but the actual relation is unknown. To train the ANN, we provide it with a set of values of x and y (called training set), and the output thus observed is compared with the target value of z. Based on the difference between the target output and the observed output, changes in the value of weights are made. This whole process is iterated multiple times for the same training set and with each iteration the difference between the target and desired output diminishes. Eventually, the ANN internally figures out the relationship between the three variables. Now we only provide ANN with the input variables i.e. x and y, which it has never seen before, and it accurately predicts the value of z.

There are two ways of training a Neural Net, one is Supervised learning and the other one is Unsupervised learning. The above-mentioned example incorporates supervised learning, in which the input and output both are provided to the model and the ANN adjusts its weights based on the feedback provided by the difference between the target and observed output. Just like a child learns from the feedback given by an elder. The major application of supervised learning is in the field of predictive analytics. Whereas, in case of unsupervised learning, the algorithm strengthens its weights based on the inputs only. Its biggest application is in the field of cluster analysis. Artificial Neural Network has found its way into numerous applications such as Cluster analysis, Image compression, Character recognition, Stock Market Prediction, etc.

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Unlike Linear regression models, ANN works on high degree polynomials which provide it a high success rate in the applications of classification and prediction.

Conclusively, an ANN can be seen as a model which can be used to map various variables with each other when the relationship between them is unknown. Fix an ANN between input variables and output variables and voila, the ANN will work as the function between them! This is exactly why it is known as a universal function approximator. Based on the utility, a good combination of architecture, activation function and learning algorithm should be implemented. And the model should be further fine-tuned using parameters such learning rate, momentum, R-value, RMSE, etc. There are various tools such as MATLAB, which are readily available and easy to use. One can use these tools to skip the pain of coding the whole thing and enjoy the jaw-dropping accuracy of ANN right away!

Source:- https://link.springer.com/chapter/10.1007/978-1-4615-0377-4_5 https://www.analyticsvidhya.com/blog/2014/10/ann-work-simplified/

By Aditya Sharma PGDM-FS (2017-19)

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Sub Article ARIMA In general, human beings are inquisitive about future-one of the primary reasons that explains high demand of soothsayers & fortune tellers. How does business establishments and scientists predict future! Time is an important aspect in a successful business. What if we can see ahead of time! No! Let us be practical here, I am not suggesting time machine. I was referring to scientific and statistical way of prediction and forecasting. ARIMA’ (autoregressive integrated moving average) is such a model of time series modelling that does this job.

Where is ARIMA used?

It is used to predict sales for upcoming financial year, website peak hour identification and much more.

As the name indicates the technique is not very intuitive and easy to grasp but finds applications effectively in areas like forecasting of daily peak demands of electricity& public transportation, forecasting stock returns or complex entities like oil prices. Over the next paragraphs I hope to make clear some fundamental concepts regarding ARIMA. Why is ARIMA not intuitive?

Everybody in their primary schools would have played with colours. In fact, one of my favourite hobbies was mixing of colours to generate a new colour like mixing a bottle of blue colour and a bottle of yellow colour gives two shares of green shaded paint. This is where things get interesting. What If I was asked to recreate my original yellow and blue from my green paint?! It is easy to mix things but it is difficult (sometimes impossible) to extract the originals. Typically, entities such as demand and prices as explained in the below figure compromise of the individual aspects in real time.

Trend component- Overall direction of series i.e upwards/down wards Seasonality – Monthly/Quarterly patterns Remainder/error component– Random noise/error left after extraction of components Now, the question is why decompose the original time series into components?!

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It is much easier to predict and grasp the constituent patterns of time series than the actual series. This is similar to forecasting the individual series instead of the final pattern which will be product of these series.

ARIMA and sugar cane juice Sugarcane juice making has fascinating similarities with ARIMA modelling. As the sugar cane passes through the rollers, a batch of juice comes out. Since all the juice cannot be extracted in the first pass, the sugar cane is passed between rollers one more time and another batch of juice comes out. We can imagine the time series to be the sugar cane and processes 1, 2 and 3 can be differencing, auto regressive model extraction and moving average model extraction. ARIMA is a combination of 3 parts i.e. AR (Autoregressive), I (Integrated), and MA (Moving Average). A more convincing notation for ARIMA model is ARIMA (p,d,q).Here p,d, and q are the levels/order for each of the AR, I, and MA models respectively. For example, if the current period has a strong correlation with 2 years old data then order of the time series becomes two.

1. First pass of ARIMA to juicer/Integrated pass We will now try and develop an understanding over these terms and understand the characteristics associated with these models. But before we start, you should remember, AR or MA is not applicable for non-stationary series. (Non-stationary series-series in which the mean, variance covariance of the series is a function of time rather changes with time). If you have a non-stationary series, you first need to make the series stationary (by taking difference / transformation) and then proceed to the next stages.

2. a Second pass of ARIMA to juicer/Autoregressive pass Autoregressive model- extracts the influence of previous period’s values on the current period. This can be achieved by developing a simple multiple linear regression model with the previous period values as independent or predictor variables. ’p’ values refer to the order of the AR model.

2. b Third pass of ARIMA to juicer/moving average pass Moving Average (MA) – Last step of ARIMA juicer- extract the influence of the previous periods error terms on the current periods error. Moving Average (MA) part of ARIMA is developed with the following simple multiple linear regression value with the older error values as independent or predictor variables. ’q’ values refer to the order of the MA model.

3. Finding out the order of the components to build ARIMA The parameters p,d,q which decides the order of the AR and MA models can be found using ACF(Auto correlation function) and PACF(partial correlation function) plots. An addition to this approach is can be, if both ACF and PACF decreases gradually, it indicates that we need to make the time series stationary and introduce a value to “d”.

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4. Build ARIMA model With the parameters in hand, we can now try to build ARIMA model. The value found in the earlier section might be an estimate and thus we need to explore more (p,d,q) combinations for more closer estimates.

Now ARIMA model is built, the predictions can be made with components and can be compared with real time data. Based on the actual vs forecasted results, the model can be smoothened out for future references. With these analogies and concept flow, I hope ARIMA will not be a black box kind of software for all of us.

Sources: Selection of Best ARIMA Model for Forecasting Average Daily Share Price Index of Pharmaceutical Companies in

Bangladesh: A Case Study on Square Pharmaceutical Ltd. By Dr. Jiban Chandra Paul, Md. Shahidul Hoque Mohammad Morshedur Rahma ARIMA Modeling To Forecast Future Oil Prices - The United States Oil ETF, LP (NYSEARCA:USO)

By V V S Anudeep PGDM (2017-19)

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QuantGuru Calyampuri Radhakrishna Rao C.R. Rao was born on 10 September, 1920 in Huvanna Hadagali, now in Karnataka State. He studied in schools at Gudur, Nuzvid, Nandigama and Visakhapatnam, in Andhra Pradesh and completed his M.A. degree in mathematics at the Andhra University in Waltair, Andhra Pradesh. He did his M.A. degree in statistics from Calcutta University in Kolkata, West Bengal.

C. Radhakrishna Rao is among the world leaders in statistical science over the last six decades. His research, scholarship, and professional services have had a profound influence on theory and applications of statistics.

Technical terms such as, Cramer-Rao inequality, Rao-Blackwellization, Rao’s Score Test, Fisher-Rao and Rao Theorems on second order efficiency of an estimator, Rao metric and distance, Analysis of Dispersion (MANOVA) and Canonical Variate analysis and G-inverse of matrices appear in all standard books on statistics. Cramer-Rao Bound and Rao-Blackwellization are the most frequently quoted key words in statistical and engineering literature. Special uses of Cramer-Rao Bound under the technical term, Quantum Cramer- Rao Bound have appeared in Quantum Physics. RaoBlackwellization has found applications in adaptive sampling, particle filtering in high-dimensional state spaces, dynamic Bayesian networks etc. These results have led to contributions of strategic significance to signal detection, tracking of non-friendly planes and recognition of objects by shape.

Other technical terms bearing his name appearing in specialized books are Rao’s F and U tests in multivariate analysis, Rao’s Quadratic Entropy, Cross Entropy and Rao-Rubin, Lau-Rao, Lau-RaoShanbhag and Kagan-Linnik-Rao theorems on characterization of probability distributions.

Two of his papers, one on estimation leading to many technical terms and key words and another on score test which had a high impact on the development of statistical theory appear in the book Breakthroughs in Statistics: 1889-1990.

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Rao has made some significant contributions to combinatorial mathematics for use in design of experiments, the most important of which is Orthogonal arrays (OA).The basic paper on the subject appeared in Proc. Edinburgh Math. Soc. (the referee of the paper reported that it is a fresh and original piece of work). The Japanese Quality Control Expert, G.Taguchi made extensive use of OA’s (described

by Forbes Magazine as “new mantra” for industries), in industrial experimentation.

Rao defined a generalized inverse (g-inverse) of a matrix (singular or rectangular) and demonstrated its usefulness in the study of linear models and singular multivariate normal distributions.

He is the author of 14 books and about 350 research papers. Three of his books have been translated into several European and Chinese and Japanese languages.

C.R. Rao worked in India at the Indian Statistical Institute for 40 years before he took mandatory retirement at the age of 60. He moved to USA and worked for another 25 years at the University of Pittsburgh and the Pennsylvania State University. In reply to a query put to him as to what particular achievement he is most proud of, C.R. Rao replied, “it is the outstanding contributions my students are making to statistical theory and practice.” He is still active at the age of 87 as the Director of the Center for Multivariate Analysis at Pennsylvania State University.

Source: http://www-history.mcs.st-andrews.ac.uk/Biographies/Rao.html http://www.crraoaimscs.org/about-c-r-rao/

By Rupal Doshi PGDM FS (2016-18)

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Intern Diaries AGROCEL I did my summer internship at Agrocel in Mumbai. Agrocel Industries Pvt. Ltd. (Agrocel) is a part of the Excel Group of Companies. The objective of the internship was to map and analyze the recovered bromine market by conducting a market survey of various bromine compounds in the application of agrochemicals and pharmaceuticals.

The methodology to be followed included primary research of recovered bromine companies which are indirect competitors of Agrocel – a manufacturer of virgin bromine. This was carried out by visiting the concerned manufacturing plants mainly in Maharashtra and Gujarat and understanding their processes and techniques.

Market survey was conducted to map the potential of the recovered bromine market in terms of quantity, price and applications. A detailed analysis was done based on the primary research data and data collected during visits to the plants.

Key Learnings from the internship were as follows:   

Learning about product pricing, demand and supply, and distribution Getting an in-depth understanding about market competition and dynamics Tact and understanding in working with third parties Importance of in-depth analysis for an organization with respect to an industry

By Amod Kulkarni MMS (2016-18)

JP Morgan Chase & Co. The 2 month Internship duration was a very well structured programme by the Organization with various tasks and activities aligned during the internship calendar. It started off with a one day induction program where we were assigned our respective departments and teams. In the initial period, a lot of on-desk training sessions were held by the team to get familiar with the tools and applications of our project.

The first part of my project involved preparing Business Requirement Documents (BRD) for automating daily tasks done by the Operations team. This required thorough understanding of the process followed by the operations team and the requirements of the robotics team. The second part was concerned with performing reconciliations on Fund Manager and JPMorgan returns. And the last part was to on-board a new client for fund manager reconciliations.

We had to also work in teams on an Innovation Challenge, where we had to find a solution to a business problem existing in JP Morgan and present it to the different department heads. Our team made it to the finals in this challenge.

Overall these session were quite motivation for us and the entire internship period though a short was a great learning experience

By Sulabh Chokhani MMS (2016-18) 12

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Quriosity Updates Curiosity Climbing Toward Ridge Top NASA's Mars rover Curiosity has begun the steep ascent of an iron-oxide-bearing ridge that's grabbed scientists' attention since before the car-sized rover's 2012 landing. It will allow the scientists to access the layers which they have studied from below.

"Vera Rubin Ridge" stands prominently on the northwestern flank of Mount Sharp, resisting erosion better than the less-steep portions of the mountain below and above it. The ridge, also called "Hematite Ridge," was informally named earlier this year in honor of pioneering astrophysicist Vera Rubin.

Using data from orbiters and their own approach imaging, the team has chosen places to pause for more extensive studies on the way up, such as where the rock layers show changes in appearance or composition. But the campaign plan will evolve as they examine the rocks in detail. As always, it's a mix of planning and discovery.

In orbital spectrometer observations, the iron-oxide mineral hematite shows up more strongly at the ridge top than elsewhere on lower Mount Sharp, including locations where Curiosity has already found hematite. Researchers seek to gain better understanding about why the ridge resists erosion, what concentrated its hematite, whether those factors are related, and what the rocks of the ridge can reveal about ancient Martian environmental conditions.

During the first year after its landing near the base of Mount Sharp, the Curiosity mission accomplished a major goal by determining that billions of years ago, a Martian Lake offered conditions that would have been favorable for microbial life. Curiosity has since traversed through a diversity of environments where both water and wind have left their imprint. Vera Rubin Ridge and layers above it that contain clay and sulfate minerals provide tempting opportunities to learn even more about the history and habitability of ancient Mars.

Source: https://www.jpl.nasa.gov/news/

By Kapil Gupta PGDM (2017-19)

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News Digest IIT & Robert Bosch Centre set up to improve AI, big data research in India A new research center in collaboration between Robert Bosch Engineering and Business Solutions (RBEI) and the IIT, Madras will be established in order to improve foundational research in areas of data science and artificial intelligence in India. “This partnership is to accelerate research for societal impact, taking a long-term view. It will set a precedent in the way big-data is used to improve our problemsolving capability in the industry. At the same time, the collaboration will result in shared outcomes for the benefit of society,” said Vijay Ratnaparkhe, Managing Director, Robert Bosch.

Jaguar uses Artificial Intelligence in ‘Sayer’, the steering wheel of the future With all big automobile companies venturing into autonomous cars, the steering wheel was on the verge of becoming obsolete, until Jaguar Land Rover decided to give it a bright future. Jaguar revealed, Sayer (named after influential designer Malcolm Sayer), the steering wheel of the future — the first voiceactivated, artificial intelligence steering wheel that will be able to carry out hundreds of tasks and follow you from car to car.

Google building an Artificial Intelligence workforce in China Despite having no presence in China, Google Inc.’s parent company Alphabet has floated plans to open an artificial intelligence lab in Beijing. According to several reports, Google is recruiting machine learning engineers and cloud machine learning engineers in Beijing and preparing for the new AI lab, said industry sources and websites including LinkedIn.At least 20 positions based in Beijing are advertised on the company’s careers site, spanning engineering and marketing to product managers. Multiple listings are shown in the field of machine learning and artificial intelligence.

Country to lead Artificial Intelligence will rule world, says Russian President Vladimir Putin Russian President Vladimir Putin has the answer to who will rule the world in the times to come.

According to him, the country, which reaches a breakthrough in developing artificial intelligence will dominate the world. The Russian leader predicted that future wars will be fought by drones, and “when one party’s drones are destroyed by drones of another, it will have no other choice but to surrender.” On the occasion, he also discussed space, medicine and the capacity of the human brain.

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CIA set to be run by AI, has 137 pilot projects in place The CIA currently has 137 pilot projects directly related to artificial intelligence, Dawn Meyerriecks, the CIA’s deputy director for science and technology, told the Intelligence and National Security Summit in downtown DC, according to a report published in Defense One. According to the report, the agency has a “punch list” of different artificial intelligence problems that it wants the private sector to work on. The CIA is already coordinating this work with In-Q-Tel, the agency’s venture capital firm, Meyerriecks said.

Facebook trains AI to understand human reactions by watching Skype conversation videos Facebook has come up with yet another development in robotics and AI. The researchers at Facebook’s AI lab have now developed an expressive bot, the animations of which are controlled by an artificially intelligent algorithm. The algorithm that has been trained by making it watch hundreds of videos of Skype conversation could now mimic the way humans adjust their expressions while talking.

Source: http://analyticsindiamag.com/

By Akshay Nagpal PGDM (2017-19)

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Quantertainment Quincunx A Quincunx, also called as “Galton Board� is a triangular array of pegs arranged one over the other.

Balls are dropped onto the top peg and then bounce their way down to the bottom where they are collected in little bins. Each time a ball hits one of the pegs, it bounces either to left or right.

Allow 100-150 balls to drop down and you will notice that the number of balls collected in each bin form a bell shaped curve, also known as normal distribution.

So what is the probability of a ball being collected in kth bin from the right?

Let’s assume that a quincunx has n rows and the probability of a ball to bounce left is p and to the right is (1-p).

It is generally 50% but it could be 60%-40% etc.

A ball can have k bounces to the left and (n-k) bounces to the right. And the probability for the same would be pk and (1-p)(n-k) respectively.

The total probability of such path would be pk(1-p)(n-k).

But there can be many such paths where a ball takes left turn after hitting 1st and 3rd peg or 1st and 4th peg. The paths could be like LLRRR.., LRLRR.., LRRL..) and ball follows one of these paths.

The number of ways of distributing k things in a sequence of n is given as C(n,k) i.e,

đ??§! đ??§! (đ??§ − đ??¤)!

So, the total probability of ball falling on kth bin from right is

đ??§! đ??§!(đ??§âˆ’đ??¤)!

pk(1-p)(n-k).

When I played the game and the probability was 0.5, the balls collected in the bin formed a bell-shaped curve of the normal distribution. When the probability was not equal to 0.5, the balls collected formed a skewed curve.

By Anjali Tiwari PGDM (2017-19)

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Quriosity Job Corner Analytics Vidhya Role: Analytics Specialist Job Description: Analyze & interpret data and communicate results to clients, design and build dashboards, knowledge if SQL, SAS, python, excellent critical thinking and communication skills.

Experience: 2-4 years. Must have hands on experience with R Click here to apply: Link Location: Mumbai

TATA Motors Role: Business Analyst Job Description: Advanced Excel and Access skills and strong knowledge of SAP, financial accounting skills, work closely with Corporate/ Plant Business Planning and functions Experience: 2+ years of experience in MIS Analysis, budgeting, costing, variance analysis.

Click here to apply: Link Location: Mumbai, Kolkata, Nagpur, Telangana

Bajaj Finsery Role: Senior Manager - BFS Direct, Analytics Job Description: Pre-acquisition analytics framework, web and mobile data analytics framework, predelinquency analytics and interaction analytics along with early warning systems, supervise analytics team Experience: 2-4 years. Worked on large datasets and Big data systems SQL, Hadoop, Hive, ability to use CART/CHAID technique to solve classification problems and Quantitative Regression using SAS or SPSS or R Personal Attributes.

Click here to apply: Link Location: Pune

Vassist.com Role: Data Scientist Job Description: Filter the data to generate relevant reports in the defined formats, use marketing tools such as Google Analytics to drive business insights, deep-dive into data on an ongoing basis and share key findings and inferences Experience: Minimum of 3-4 years of data analytics experience and ability to use data mining tools, Skilled in Data Analytics, Data Management, Data Visualization, Statistics, Web Analytics.

Click here to apply: Link Location: Mumbai

By Nikki Gandhi MMS (2017-19)

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Quant Fun Sudoko:

Puzzle:

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September 2017 Quantinuum, the Quant forum of KJ Somaiya Institute of Management Studies and Research aims to empower students and professionals alike to organize and understand numbers and, in turn, to make good and rational decisions as future managers. The newsletter published monthly consists of a gamut of articles for readers ranging from beginners to advanced learners so as to further enrich the young minds understand the contributions made to the field of mathematics along with a couple of brain- racking sections of Sudoku to tickle the gray cells.

For any further queries and feedback, please contact the following address: KJ Somaiya Institute of Management Studies and Research, Vidya Nagar, VidyaVihar, Ghatkopar East, Mumbai -400077 or drop us a mail @ newsletter.quantinuum@gmail.com Mentor:

Prof. N.S.Nilakantan (+919820680741)

Email – nilakantan@somaiya.edu Team Leaders:

Vaibhav M (+917708521382) Maheshwaran Kumar (+919566173411) Rishita Shah (+919867290018)

Editorial Team:

Rupal Doshi (+919831427640) Amod Kulkarni (+919833701015) Aditya Gupta (+919621655806) Chaitanya Agarwal (+917009638623) Aditya Sharma (+918302525599) VVS Anudeep (+919441201685) Kapil Gupta (+917727936906) Samoshri Mitra (+918697440265)

Designing Team:

Shreyas Kulkarni (+918600106378) Ashish Mohadik (+919819741018)