option-pricing · GitHub Topics · GitHub

I created a mathematically optimal team generator!

Hi all,

I've been playing FPL for a few years now, and by no means am I an expert. However, I like math and particularly optimization problems. And a few days ago I thought to use my math knowledge for something useful.

My goal was to start from some metric that predicts the amount of points a player will score (either in the next gameweek, or over the whole season). From that metric, I wanted to generate the mathematically optimal team, aka choose the 15 players that will give me the most points, while staying within budget. I realized this is a constrained knapsack problem, which can be solved by dedicated solvers as long as the optimization problem is properly defined. Note that while I make a big assumption by choosing some metric from which I start, the solver actually finds the most optimal team, without any prior assumptions about best formation, budget spread, etc!

(Warning: from this point onward it gets kinda math-y, so turn back or skip ahead to the results if that's not your thing)

MATH

So first, the optimization variable needed to be defined. For this purpose I introduced a binary variable x which is basically a vector of all players in the game, where a value of 1 indicates that player is part of our dream team and a 0 means it's not.

Secondly, an objective function needs to be defined, which is what we want to maximize. In our case, this is the total expected points our dreamteam will score. I included double captain points and reduced points for bench players here. The objective function is linear, which is nice since it is convex (an important property which makes solving the problem much easier, and is even required for most solvers).

Lastly are the constraints. Obviously, there is the 100M budget constraint. Then we also want the required amount of goalkeepers, defenders, midfielders and forwards. Then we need to keep in mind the formation constraints, and lastly are the max 3 players per club constraints. Luckily, these are all linear (so convex) constraints.

I solved this problem using CVX for MATLAB, particularly with the Gurobi solver since it allows mixed integer programs. It tries to find the optimal variable x* which maximizes the objective function while staying within the constraints. And amazingly, it actually comes up with solutions!

RESULTS
So like I said before, I need to start from some metric that indicates how many points a player will score (if you have any recommendations, let me know!). For a lack of better options, I chose two different metrics:

  1. The total points scored by the player last year
  2. The expected points scored by the player in the next gameweek (ep_next in the FPL API, for fellow nerds)

Obviously, both metrics are not perfect. The first one doesn't take into account transfers, promoted teams, injuries, fixtures, position changes etc. However, it should work decent for making a set-and-forget team with proven PL players.

The second metric seems to have a problem with overrating bench players of top PL teams such as Ozil, Minamino, etc. I'm not really sure why, but it's a metric taken directly from FPL with undisclosed underlying math so it's not my problem. Also, keep in mind that since the first gameweek does not feature City/Utd/Burnley/Villa players, this metric predicts them to score 0 points so they won't feature in the optimal team.

Team 1: Last year's dreamteam
Bench:

Team 2: Next week's dreamteam
Bench:

Both teams cost exactly 100M.

At first glance, there are some obvious flaws with both teams, but most of them are because the metric used as input is flawed, as I explained before. Lundstram is obviously a much worse choice this year due to various reasons, and Team 2 has some top 6 players which are very much not nailed.

However. What I think is interesting is that both teams have only 2 starting midfielders. This despite the trend of people stacking premium midfielders. On the other hand, premium defenders seem to be very good value, and the importance of TAA and Robertson is underlined. Similarly, near-premium forwards in the 7.5-10 price range seem to be a good choice.

CONCLUSION
I'm quite content with my optimal team generator. Using it, I don't need to use vague value metrics such as VAPM. The input can be any metric which relates simply to how many points a player will score. Choices about relative value of e.g. defenders against midfielders, formation, budget spread etc. are all taken out of my hands with this team generator. The team that is generated is only as good as the metric used as input. But given a certain input metric, you can be sure that the generated team is optimal.

I would gladly share my MATLAB code if there is any interest. Also, I'm open to suggestions on how to extend it. EDIT: Here it is.


(Tiny disclaimer: Remember when I said: "without any prior assumptions"? That is a lie. There is one tiny assumption I made, which is how often bench players are subbed on. I guesstimated this to happen approximately 10% of the time.)
submitted by nectri42 to FantasyPL [link] [comments]

How a Danish university dependent on corporate America fosters corporate loyalty in students

Students of Roskilde University ("RUC") have no choice but to accept, become dependent on, and support these corporations:
At RUC there is no escape from Microsoft. Mathworks is only avoided by students who avoid taking statistics.

E-mail service that establishes trust in Microsoft (and how it evolves into loyalty)

RUC has outsourced e-mail service to Microsoft. Students are obligated to access their Microsoft-served e-mail in order to receive official correspondence from school staff. There is no opt-out mechanism.
Regular exposure to MS corporate branding in the student's UI establishes brand awareness using freemium. Students become accustomed to the look and feel of the Outlook UI, making them more likely to develop trust and cling to that interface more in the future. It's through repeated forced bonding with Microsoft's UI that leads ultimately to fostered loyalty.
The loyalty is deepened further when the student grapples with idiosyncrasies like booking a room because the struggle leads to the user acquiring vendor-specific knowledge. The user is rewarded when their skill with the tool advances as they become more efficient with overcoming flaws and anti-features; as if they filled up a Starbucks loyalty card and got a payout. Unlike a loyalty card these advancements continue rewarding the user as long as they keep using the tool. When the user faces the decision to use an alternate tool they are less inclined to give up the vendor-specific knowledge that has accumulated.
So overcoming non-intuitive aspects of a UI actually leads to more loyalty. The university sharpens this effect by trapping the student on the tool. Whereas being outside an organization includes freedom to switch tools anytime a use-case becomes non-intuitive.
RUC has disabled IMAP access, thereby crippling students who would prefer a vendor-neutral standards-complying mail user agent ("MUA") or an MUA of a different vendor. Forcing Microsoft's non-standard protocols and favoring Microsoft UIs creates biases that raise the barrier to exit. Diligent motivated users who install Evolution or hack together a davmail proxy can escape -- but these users are a small minority and ultimately still forced to share their email contents with Microsoft and to feed Microsoft's bottom line.
And what about independence? If the university can't handle being independent from corporations itself aren't students therefore conditioned to lack confidence in overcoming corporate dependency?
When a self-sufficient student or outsider who runs their own residential mail server tries to send an email to an outlook.com/ruc.dk recipient, they are blocked. Microsoft has configured their mail servers to force individuals to be dependent on a corporation for email delivery. RUC has aligned with a corporation who pushes corporate loyalty even beyond the school, dragging outsiders into the Microsoft loyalty program and causing collateral damage to those who don't comply with Microsoft-dictated policy on how email must be transmitted in order for MS to accept it.

Document preparation: Office 365 or Google Docs (LaTeX discouraged)

Students are free to choose their document preparation tool, but professors and supervisors discourage the use of LaTeX. Scientific papers are produced within group projects with supervisors serving as mentors. Some supervisors are reluctant to learn LaTeX or review LaTeX code. Consequently professors urge students to avoid LaTeX to accommodate limitations of supervisors.
RUC equips students with MS Onedrive accounts and one writing tool: MS Word, which is supplied with gratis copies of Office 365. This implies that using MS Word with its co-authoring feature and Onedrive is the only approach on which students can expect official school support. Note that Office 365 is unavailable to Linux users who are therefore limited to the feature-poor in-browser Word app should a Linux user end up in a Microsoft-aligned group.
Some groups opt for LaTeX (vendor-neutral) and use Overleaf (a service of Writelatex Limited) for collaboration, but this choice comes with risk. If just one student in the group opposes the steep learning curve that LaTeX entails, that student likely already has vendor loyalties that they developed in post-secondary school and they will fight hard to avoid the effort of learning something new. RUC basically has the back of students who resist LaTeX, which bends groups in the direction of a corporate solution that builds vendor loyalty.
Google Docs is seemingly the most popular choice. The school discourages use of the most suitable vendor-neutral technology so students gravitate toward Google Docs.
All realtime collaboration options (msword, gdocs, latex) have stumbling blocks and idiosyncrasies. The LaTeX variety of issues lead students to learn something useful about the language or text editor, which furthers their knowledge of technology in a generic way that can be useful in the future. The MS Word and Google Docs varieties of issues lead students to learn about workarounds for specific flaws and limitations of those particular tools. This vendor-specific knowledge is not generally portable to other tools. It's without foundation and does not generally form a basis for building more knowledge. It's knowledge that bonds the user to the tool. The increased efficiency of knowing workarounds for vendor-specific tools serve to heighten vendor loyalty. The user becomes less inclined to migrate to a competing tool later because it entails wasting the knowledge that has no other applicability while inviting new issues to tackle.

Proprietary software labeled as "Free Software" helps propagate brand loyalty

RUC distributes gratis copies of licensed proprietary software under the heading "Free Software". "Free" has two meanings in English: freedom and gratis. The software industry specifically assigns "free software" special meaning: software that gives the user freedom. The software offered by RUC under this heading is quite the opposite of the industry-accepted term. Microsoft Office 365 and Matlab are commercial proprietary binary blobs that deny students the academic freedom of looking at the source code. The distinction between gratis and freedom when discussing software is paramount. RUC's use of the term misinforms the students they are tasked with educating.
Use of the word "free" has a bigger problem: it's one of the most powerful forces in neuromarketing used to manipulate consumers according to Dan Ariely's study published in Predictably Irrational. RUC has refused to correct the heading on their English website from "free software" to "gratis proprietary software". RUC is exploiting the persuasion of the word "free" to maximize the number of students who will install software that will induce brand loyalty.

Research material jailed in corporate walled-gardens of Google and CloudFlare

Library research is sacred and central to academic coursework. One of the primary sources of information available to RUC students is Google Scholar ("GS"). GS is a walled-garden that blocks access to full text if the student is not signed on through the school. RUC recently started blocking Tor. So RUC students who opt to use GS have been forced to give up the only mechanism that protects them from website visitor tracking ("WVT") in this instance. Although a RUC user id has always been potentially disclosed to Google Scholar through the callback authentication mechanism, students could previously use to Tor to avoid exposing their IP address and browser print to Google, which Google can use to cross-reference logged-out searches. Now avoiding that privacy abuse requires abandoning Google Scholar.
With conventional web searches we can easily give up Google because there are good decentralized alternatives like Searx. But Google Scholar has weak competition at RUC and librarians encourage its use. Simply getting the list of database alternatives first requires executing javascript from microsoft.com. Once Microsoft is trusted (not that it should be), a database list is populated and "REX" is available.
REX is rich in search results and makes it viable to avoid Google Scholar. However, REX does not contain the full text of articles and REX does not serve as a proxy either. REX supplies students a link directly to the external resource that has the full text. These external sources are often dominated by privacy abusers, most notably CloudFlare Inc (an adversary of the Tor community). A substantial number of REX-indexed articles are served by Proquest, who currently subjects users to CloudFlare's IP logging in violation of the GDPR.
Privacy is not the focus of this article, but it's related to the loyalty problem. Because CloudFlare is a privacy abuser, ethical informed students may opt to boycott CloudFlare. Students should not be forced to patronize a privacy abuser who surreptitiously collects their IP addresses and who has taken centralized control of over 10% of the web while undermining network neutrality. When Copenhagen Library leads students to a CloudFlare-controlled private walled-garden, it creates a conflict of interest between academic research and the ethical need to boycott bad players.
CloudFlare goes unnoticed to most people and students would not be developing any kind of brand awareness or loyalty to them. However, students need not just to be free from loyalty but also need the freedom to be proactively disloyal. Putting CloudFlare in reckless control of our academic resources is a bad idea. When we encounter CloudFlare in the marketplace as consumers, we can simply vote with our feet and take our business elsewhere. But this academic intrusion is not solved by students voting with their feet because while research potential is lost public money is still going toward the detriment of freedom.
Europe's Plan S initiative will require government-funded research to be made available to the public on the date of publication by the year 2020. However, Copenhagen Library is dependent on publishers who will continue to jail scientific journals in the private corporate walled-garden of CloudFlare Inc.

Copenhagen housing crisis and Facebook's role in it

There is an acute housing shortage in the whole Copenhagen region resulting in apartments with waiting lists as long as five years. There is also a shortage of on-campus university-administered student housing that's so severe that Roskilde University has restricted the units exclusively to exchange students. Permanent full-time students are ineligible for these rooms.
The school provides no service to help the 8000+ permanent students secure a place to stay amid the shortage. Students are given no information about how to directly get in contact with owners of apartments in close proximity to the university. RUC publishes a list of commercial profit-driven brokers who charge students a fee for helping with the hunt for housing or roommates. In some cases the fee is not based on placement so a student could pay fees to simply communicate with a prospective roommate or landlord without actually acquiring housing - which is a very likely scenario.
Students are made dependent on a dozen or so private corporations before school even begins. RUC pays a premium to one of them ("Housinganywhere") to give RUC students VIP treatment (which in this case entails answering e-mail from students), and Housinganywhere falls short of responding to e-mail.
These brokers have no obligation to get a student a booking. Students often arrive homeless or become homeless mid-term. This illustrates the inherent problem of outsourcing to private corporations something as essential as student housing particularly when resources are severely limited.
The brokers' objective is to maximize profit not maximize student placements. One of the brokers charges nothing to the students but designed their website to deny service to students who don't have a CPR number (a number that can only be acquired after establishing a residence), so students entering Denmark for the first time are blocked from using the one broker who charges them nothing.
Another corporate artifact is age discrimination. Some buildings try to cater for students and to keep the rentals marketable to students they impose an age limit. Every "dorm" in close proximity to RUC imposes age restrictions so older RUC students are pushed out of the city to suit corporate policy.
RUC and the housing specialists and brokers RUC endorses have come up short. Enter Facebook. Facebook is the hack by which students find housing. Facebook secures student loyalty in this case not by clever marketing but simply by actually serving as a hack to an otherwise ill-served need.

Facebook invasion into official school communications

Of all the corporations RUC fosters loyalty for, Facebook is the most insidious. Facebook is a cocaine addiction compared to others. Copious articles try to help people break away from Facebook. The stranglehold of Facebook loyalty has driven Cornell University to study it.
Facebook is used to make announcements to RUC students and the internal website is littered with Facebook references. In particular, there are social events that are officially school-sanctioned which appear exclusively on Facebook.
Some might say "fair enough" because social events are non-essential and purely for entertainment. However, RUC has organized all the coursework around group projects. A culture of social bonding is considered important enough to justify having school-sanctioned parties on campus. The organizers have gone as far as to strategically separate student parties and to discourage intermingling across the parties so that students form more bonds with the peers they work with academically. Social bonding is a component of the study program.
Announcing these social events exclusively on Facebook creates an irresistible temptation for non-Facebook users to join. It also destroys any hope of existing FB users who want to break away from Facebook from doing so. Students without Facebook accounts are naturally in the dark. Facebook non-patrons may be able to catch ad-hoc hallway chatter about school events but this is a reckless approach.
When the official class schedule is incorrectly published students who discover the error in advance announce it on Facebook. Facebook then stands as the only source of information for schedule corrections, causing Facebook non-patrons to either miss class or show up for a class that doesn't exist.
Unofficial student-led seminars and workshops are sometimes announced exclusively on Facebook. These workshops are optional but academic nonetheless.
Sometimes information exists on the school website and is duplicated on Facebook. The information becomes very well buried on the poorly organized school website because the maintainers are paying more attention to the Facebook publication that they assume everyone is reading. Specifically the study abroad program has two versions of the document that lists all the foreign schools for which there is an exchange program. One version is obsolete showing schools that no longer participate. Both versions appear in different parts of the website. The schedule of study abroad workshops is so buried that a student relying on the school website is unlikely to know that the workshops even exist. Removing the Facebook distraction would perhaps mitigate the website neglect.
RUC does not instruct students to establish Facebook accounts. There is simply a silent expectation that students have them. Some of the above mentioned problems can come as a surprise because Facebook excludes non-members from even viewing the content, so non-patrons don't even have a way to see what kind of information they are missing. There is an immense undercurrent of pressure for RUC students to become addicted patrons of Facebook's corporate walled-garden.

VPN depends on GSM

RUC's VPN service requires two-factor authentication ("2fa), and the possession factor is met exclusively by SMS messages. There is no opportunity to opt-out of 2fa and no possibility to use an alternate mechanism. Phones and service are also not provided. This forces students into the marketplace to buy phone equipment when most phone vendors have a long history of unethical conduct. Many GSM service providers have the same problem.
If a student can manage to find non-controversial hardware and service they are still subject to needless tracking that's inherent in GSM technology while being pushed into establishing loyalty for the corporation, baited by the lower pricing of phones and plans that are marketed with contracts. A student should be able to reject all GSM hardware and service vendors without being denied access to the RUC's VPN service.

Telegram Messanger

The FabLab uses Telegram Messanger. Offering to collaborate through a service like this is an advancement away from corporate dependency in principle because it enables voice communication without GSM service. However, Telegram is centralized and requires users to disclose their mobile phone numbers (which they may not have) just to register for an account even if it's only going to be used on a desktop. Some Telegram competitors have figured out how to offer gratis account registration without imposing GSM service on the user.

Matlab

The statistics class is structured around MATLABtm, which cannot be installed without registering at Mathworks website (under Dynatrace tracking mechanisms), signing click-through agreements, and disclosing an email address. The email address is later used to promote Mathworks' products and to ask students to help Mathworks with product promotion to others.
Students would normally be charged for a MATLAB license but RUC pays a high premium to ensure students pay nothing. This creates a brand awareness using freemium scenario. Mathworks marketing tries to draw students to more Mathworks products. Students have little choice but to become entrenched in acquiring vendor-specific knowledge on MATLAB to get through the class. This creates a bond and potential to manifest into brand loyalty.

Microblogging centralized on Twitter - loyalty required (new section)

RUC uses Twitter exclusively for microblogging. Without a Twitter account students are only permitted to read RUC's timeline and cannot participate in any discussion.
Students must become loyal to Twitter Inc. if they want to participate in RUC's microblog. Twitter registration requires Tor users to have a phone number and to disclose it. This forces students to either expose their IP address to Twitter for their records or to trust Twitter with their phone number. Both situations compromise anonymity and as a consequence chills speech. Students are also forced to agree to Twitter's one-sided non-negotiable terms before they can communicate with RUC.
Twitter is a private corporation with ultimate authority over which students may talk to their school and what they can say. Twitter has a right to refuse service to anyone for any reason, and they use it. My account was locked because (apparently) using an API over Tor is (falsely) treated as robotic use. So here I am among the public with the need to communicate with my public school, and this private corporation has blocked it.
RUC gives Twitter this power.

Freedom-respecting solutions

If RUC wants to foster independence from sketchy corporations and enable students to boycott unethical players:
RUC needs to replace.. with..
outlook.com mail server in-house mail server, IMAP service (perhaps consult UCLA for guidance)
MS Office 365 shell accounts on vendor-neutral OS, version control, emacs+Rudel, Gobby or the like, LaTeX, LyX, Libreoffice
Google Docs Cryptopad
Telegram Messenger Openfire or Jami
Matlab GNU Octave
Facebook, Twitter Diaspora, Friendica, GNU Social and/or Mastodon (ideally in-house nodes)
Google Scholar PeerJ (cough..and Sci-Hub..cough)
REX references to CloudFlared sites non-CloudFlared sources if they exist, otherwise show an apologetic warning of GDPR breach next to the CF link & state where to complain
microsoft.com javascript that renders db list HTML
SMS 2fa code card
"Free Software" website heading "Gratis Proprietary Software"
(†) actually Copenhagen Library needs to do this, not RUC. (‡) RUC does not push students to use Google Docs; inertia brings students there. RUC should guide students away from that particular privacy-hostile walled-garden.

Call to action (update)

Contact the DPA for Denmark:
Datatilsynet Borgergade 28, 5 Tel. +45 33 1932 00 Fax +45 33 19 32 18 email: [email protected] Website: http://www.datatilsynet.dk/ Member: Ms Cristina Angela GULISANO, Director 
submitted by rucrefugee to opensource [link] [comments]

Help choosing Stats courses

I'm going to be a junior in college soon, and I need help choosing between different statistics courses! I'm very much interested in Machine Learning and Data science, but I'm not sure which Statistics courses will help for that, if I decide to attend graduate school. I'm hoping to complete a minor in either Math or Stats, but I'm not too focused on the official title, rather the material I'll learn. Any help is appreciated!! Here's some course sequences I'm deciding between:
  1. Probability and Stochastic Processes (In the Math Department, 3 courses): Basic concepts of random variables, distributions, independence, correlations, moments, limit theorems, conditional probability, Markov chains, gambler's ruin, branching process, birth and death processes, numerical simulations in Matlab. / Exponential distributions, Poisson processes, continuous time Markov chains, renewal theory, insurance ruin and claim problems, numerical simulations in Matlab. / Martingales, Invariance Principle, Brownian motions and applications in option pricing, stationary processes and applications in Wiener filter, numerical simulations in Matlab.
  2. Statistical Methods for Data Analysis (3 courses): Introduction to statistical methods for analyzing data from experiments and surveys. Methods covered include two-sample procedures, analysis of variance, simple and multiple linear regression. / Emphasizes application and understanding of methods for categorical data including contingency tables, logistic and Poisson regression, loglinear models. / Topics covered include survival methods for censored time-to-event data, linear mixed models, non-linear mixed effects models, and generalized estimating equations.
  3. Introduction to Probability and Statistics (3 courses): Introduction to basic principles of probability and statistical inference. Axiomatic definition of probability, random variables, probability distributions, expectation. / Point estimation, interval estimating, and testing hypotheses, Bayesian approaches to inference. / Linear regression, analysis or variance, model checking.
  4. Introduction to Bayesian Data Analysis (1 course): Basic Bayesian concepts and methods with emphasis on data analysis. Special emphasis on specification of prior distributions. Development for one-two samples and on to binary, Poisson, and linear regression. Analyses performed using free OpenBugs software.
  5. Multivariate Statistical Methods (1 course): Theory and application of multivariate statistical methods. Topics include statistical inference for the multivariate normal model and its extensions to multiple samples and regression, use of statistical packages for data visualization and reduction, discriminant analysis, cluster analysis, and factor analysis.
  6. Linear Algebra (2 courses)
  7. Numerical Analysis (2 courses)
  8. Real Analysis (1-3 courses)
submitted by statsthrowaway124 to AskStatistics [link] [comments]

After 9 months of obsession, here is my open source Node.js framework for backtesting forex trading strategies

TL;DR There's lots more to the story. But the code is all open source now. Have at it. I'm too exhausted to continue with this. If you'd like more details, feel free to message me. If you happen to carry on with this project or use any ideas from it, I would greatly appreciate it if you could keep in touch on your findings. If anyone has any insights, please feel free to comment or message me.
I've spent the last nine months working furiously on this. I started a project for backtesting strategies against data I exported from MetaTrader. I had a very powerful computer crunching numbers constantly, trying to find the most optimal configuration of strategy indicator inputs that would results in the highest win rate and profit possible.
Eventually, after talking with a data scientist, I realized my backtesting optimizer was suffering from something called overfitting. He then recommend using the k-fold cross-validation technique. So, I modified things (in the "k-fold" forex-backtesting branch), and in fact it provided very optimistic results when backtested against MetaTrader data (60 - 70% win rate for 3 years). However, I had collected 3 months of data from a trading site (by intercepting their Web Socket data), and when I performed validation tests against that data using the k-fold results created from the MetaTrader data, I only got a ~57% win rate or so. In order to break even with Binary Options trading, you need at least a 58% win rate. So in short, the k-fold optimization results produce a good result when validation tested against data exported from MetaTrader, but they do not produce a good result when validation tested against the trading site's data.
I have two theories on why this ended up not working with the trading site's data:
For the strategy I use the following indicators: SMA (Simple Moving Average), EMA (Exponential Moving Average), RSI (Relative Strength Index), Stochastic Oscillator, and Polynomial Regression Channel. forex-backtesting has an optimizer which tries hundreds of thousands of combinations of values for each of these indicators, combined, and saves the results to a MongoDB database. It can take days to run depending on how many configurations there are.
Basically the strategy tries to detect price reversals and trade with those. So if it "thinks" the price is going to go down within the next five minutes, it places a 5 minutes PUT trade. The Polynomial Regression Channel indicator is the most important indicator; if the price deviates outside the upper or lower value for this indicator (and other indicators meet their criteria for the strategy), then a trade is initiated. The optimizer tries to find the best values for the upper and lower values (standard deviations from the middle regression line).
Additionally, I think it might be best to enter trades at the 59th or 00th second of each minute. So I have used minute tick data for backtesting.
Also, I apologize that some of the code is messy. I tried to keep it clean but ended up hacking some of it in desperation toward the end :)
gulpfile.js is a good place to start as far as figuring out how to use the tools available. Look through the available tasks, and see how various "classes" are used ("classes" in quotes because ES5 doesn't have real class support).
The best branches to look at are "k-fold" and "master", and "validation".
One word of advice: never, ever create an account with Tradorax. They will call you every other day, provide very bad customer support, hang up the phone on you, and they will make it almost impossible to withdraw your money.
submitted by chaddjohnson to algotrading [link] [comments]

Help deciding which Statistics courses to take

X-post from /AskStatistics
I'm going to be a junior in college soon, and I need help choosing between different statistics courses! I'm very much interested in Machine Learning and Data science, but I'm not sure which Statistics courses will help for that, if I decide to attend graduate school. I'm hoping to complete a minor in either Math or Stats, but I'm not too focused on the official title, rather the material I'll learn. Any help is appreciated!! Here's some course sequences I'm deciding between:
  1. Probability and Stochastic Processes (In the Math Department, 3 courses): Basic concepts of random variables, distributions, independence, correlations, moments, limit theorems, conditional probability, Markov chains, gambler's ruin, branching process, birth and death processes, numerical simulations in Matlab. / Exponential distributions, Poisson processes, continuous time Markov chains, renewal theory, insurance ruin and claim problems, numerical simulations in Matlab. / Martingales, Invariance Principle, Brownian motions and applications in option pricing, stationary processes and applications in Wiener filter, numerical simulations in Matlab.
  2. Statistical Methods for Data Analysis (3 courses): Introduction to statistical methods for analyzing data from experiments and surveys. Methods covered include two-sample procedures, analysis of variance, simple and multiple linear regression. / Emphasizes application and understanding of methods for categorical data including contingency tables, logistic and Poisson regression, loglinear models. / Topics covered include survival methods for censored time-to-event data, linear mixed models, non-linear mixed effects models, and generalized estimating equations.
  3. Introduction to Probability and Statistics (3 courses): Introduction to basic principles of probability and statistical inference. Axiomatic definition of probability, random variables, probability distributions, expectation. / Point estimation, interval estimating, and testing hypotheses, Bayesian approaches to inference. / Linear regression, analysis or variance, model checking.
  4. Introduction to Bayesian Data Analysis (1 course): Basic Bayesian concepts and methods with emphasis on data analysis. Special emphasis on specification of prior distributions. Development for one-two samples and on to binary, Poisson, and linear regression. Analyses performed using free OpenBugs software.
  5. Multivariate Statistical Methods (1 course): Theory and application of multivariate statistical methods. Topics include statistical inference for the multivariate normal model and its extensions to multiple samples and regression, use of statistical packages for data visualization and reduction, discriminant analysis, cluster analysis, and factor analysis.
  6. Linear Algebra (2 courses)
  7. Numerical Analysis (2 courses)
  8. Real Analysis (1-3 courses)
submitted by statsthrowaway124 to learnmachinelearning [link] [comments]

Optimization of an array with intlinprog

Hello.
URL of .jpg that will be helpful.
For an educational assignment, I had to come up with a optimization problem and then implement it in Matlab, using one of the algorithms we covered in our course. My idea was to put myself in the position of some kind of social department of a company, that has to maximize the amount of "joy" that they can provide to their coworkers by taking them to a cinema. I created a structure of 10 employees, of which everyone was assigned with a couple of characteristics. The most important one is their "film preferences" which is a vector of how they feel about 10 films I picked for them, in a rate of 0-10, assuming they have 10 "points" to spare on all 10 movies. So, for example, employee Jack has [0,1,1,0,0,0,8,0,0,0] on him.
Another structure is obviously the structure of films, they are distinguishable by IMDB rating, the price of a ticket (some of those 10 are 3D movies, some are not, that doesn't really matter though) and some other values.
The idea is: having a specific budget for each employee (I made this stupid assumption just for the case of the exercise), couple of other constraints I had to implement (like the fact that everyone has to go to one movie and one movie only and that cost of a movie can't go beyond the budget) and an array ("1" in the attached .jpg), that is filled with numbers describing how different employees feel about certain movie (based on their preferences, mentioned IMDB rating and some other things), I have to optimize the effort of this fictional department of a company using algorithm built in Matlab, called intlinprog. The result is meant to be a binary 10x10 array with one "1" in a line and nine "0", where "1" represents the movie that is picked for the exact employee.
The problem is: once I did 90% of what I imagined this whole program is going to be, I realized I have no idea how to put it together. The syntax of intlinprog is:
X = intlinprog(f,intcon,A,b,Aeq,beq,LB,UB,OPTIONS)
And: X is going to be my array number 2, my array number 1 is probably going to be "f" in it, my constraints - "A" and "b", and from what I remember "Aeq" and "beq" are meant to be zeros and ones. But I struggle with choosing the right size of every one of these variables, because in most cases we covered, f was a vector, not an array. I asked my teacher about it, but he doesn't really seem to know what he's doing and I don't have the time to come up with another, easier optimization problem, so I have to go with this one. He only mentioned something about the function "trace", but I only thought I knew what he meant by that.
SUMMARY:
I HAVE: an array (1) 10x10 with numbers describing willingness of employees to see a specific movie, couple of constraints A, b in form of functions (because the course is called "methods of optimization" or "optimization of systems" and that's one of the key points of it).
I WANT TO HAVE: a binary 10x10 array (2), being an effect of an action of intlingprog, presenting what movie each employee is going to see.
I HAVE TROUBLES WITH: putting it all together.
Please, /matlab help me once again, because not making this work will put me in a really miserable situation. I am aware I probably described the whole thing quite poorly, so feel free to ask questions. Love you and thank you.
UPDATE:
I managed to get the algorithm working, using:
[x,flag] = intlinprog(f,1:L10,A,b,zeros(L,L10),ones(L,1));
where f is an array (1) loaded from the other function and A, b are my constraints also put together from other functions. Unfortunately, Matlab returns me this statement:
Intlinprog stopped because no point satisfies the constraints.
Is that 100% matter of constraints not being designed properly? Because when I put [] in places of A and b, I get the same statement from Matlab.
submitted by pilarenko to matlab [link] [comments]

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