Posted on Categories Finance, Mathematics, Opinion, TutorialsTags , , 6 Comments on What is a good Sharpe ratio?

What is a good Sharpe ratio?

We have previously written that we like the investment performance summary called the Sharpe ratio (though it does have some limits).

What the Sharpe ratio does is: give you a dimensionless score to compare similar investments that may vary both in riskiness and returns without needing to know the investor’s risk tolerance. It does this by separating the task of valuing an investment (which can be made independent of the investor’s risk tolerance) from the task of allocating/valuing a portfolio (which must depend on the investor’s preferences).

But what we have noticed is nobody is willing to honestly say what a good value for this number is. We will use the R analysis suite and Yahoo finance data to produce some example real Sharpe ratios here so you can get a qualitative sense of the metric. Continue reading What is a good Sharpe ratio?

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Win-Vector LLC is a consultancy founded in 2007 that specializes in research, algorithms, data-science, and training. (The name is an attempt at a mathematical pun.)

Win-Vector LLC can complete your high value project quickly (some examples), and train your data science team to work much more effectively. Our consultants include the authors of Practical Data Science with R and also the video course Introduction to Data Science. We now offer on site custom master classes in data science and R.

Please reach out to us at contact@win-vector.com for research, consulting, or training.

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Why does designing a simple A/B test seem so complicated?

Why does planning something as simple as an A/B test always end up feeling so complicated?

An A/B test is a very simple controlled experiment where one group is subject to a new treatment (often group “B”) and the other group (often group “A”) is considered a control group. The classic example is attempting to compare defect rates of two production processes (the current process, and perhaps a new machine).

Illustration: Boris Artzybasheff
(photo James Vaughan, some rights reserved)
In our time an A/B test typically compares the conversion to sales rate of different web-traffic sources or different web-advertising creatives (like industrial defects, a low rate process). An A/B test uses a randomized “at the same time” test design to help mitigate the impact of any possible interfering or omitted variables. So you do not run “A” on Monday and then “B” on Tuesday, but instead continuously route a fraction of your customers to each treatment. Roughly a complete “test design” is: how much traffic to route to A, how much traffic to route to B, and how to chose A versus B after the results are available.

A/B testing is one of the simplest controlled experimental design problems possible (and one of the simplest examples of a Markov decision process). And that is part of the problem: it is likely the first time a person will need to truly worry about:

• Power/Significance
• Design of experiments
• Defining utility
• Priors or beliefs
• Efficiency of inference

All of these are technical terms we will touch on in this article. However, we argue the biggest sticking point of A/B testing is: it requires a lot more communication between the business partner (sponsoring the test) and the analyst (designing and implementing the test) than a statistician or data scientist would care to admit. In this first article of a new series called “statistics as it should be” (in partnership with Revolution Analytics) we will discuss some of the essential issues in planning A/B tests. Continue reading Why does designing a simple A/B test seem so complicated?

Posted on Categories Computers, math programming, Tutorials

Neural net image salad again (with code)

Alexander Mordvintsev, Christopher Olah, and Mike Tyka, recently posted a great research blog article where they tried to visualize what a image classification neural net “wants to see.” They achieve this by optimizing the input to correspond to a fixed pattern of neural net internal node activation. This generated truly beautiful and fascinating phantasmagorical images (or an “image salad” by analogy to word salad). It is sort of like a search for eigenfaces (but a lot more fun).

A number of researchers had previously done this (many cited in their references), but the authors added more good ideas:

• Enforce a “natural image constraint” through insisting on near-pixel correlations.
• Start the search from another real image. For example: if the net is internal activation is constrained to recognize buildings and you start the image optimization from a cloud you can get a cloud with building structures. This is a great way to force interesting pareidolia like effects.
• They then “apply the algorithm iteratively on its own outputs and apply some zooming after each iteration.” This gives them wonderful fractal architecture with repeating motifs and beautiful interpolations.
• Freeze the activation pattern on intermediate layers of the neural network.
• (not claimed, but plausible given the look of the results) Use the access to the scoring gradient for final image polish (likely cleans up edges and improves resolution).

From Michael Tyka’s Inceptionism gallery

Likely this used a lot of GPU cycles. The question is, can we play with some of the ideas on our own (and on the cheap)? The answer is yes.

I share complete instructions, and complete code for a baby (couple of evenings) version of related effects. Continue reading Neural net image salad again (with code)

Posted on Categories math programming, Opinion, Quantitative Finance, Tutorials1 Comment on Betting with their money

Betting with their money

The recent The Atlantic article “The Man Who Broke Atlantic City” tells the story of Don Johnson who won millions of dollars in private room custom rules high stakes blackjack. The method Mr. Johnson reportedly used is, surprisingly, not card counting (as made famous by professor Edward O. Thorp in Beat the Dealer). It is instead likely an amazingly simple process I will call a martingale money pump. Naturally the Atlantic wouldn’t want to go into the math, but we can do that here.

Blackjack Wikimedia
Continue reading Betting with their money

Posted on Categories Opinion, Rants, StatisticsTags 2 Comments on I do not believe Google invented the term A/B test

I do not believe Google invented the term A/B test

The June 4, 2015 Wikipedia entry on A/B Testing claims Google data scientists were the origin of the term “A/B test”:

Google data scientists ran their first A/B test at the turn of the millennium to determine the optimum number of results to display on a search engine results page.[citation needed] While this was the origin of the term, very similar methods had been used by marketers long before “A/B test” was coined. Common terms used before the internet era were “split test” and “bucket test”.

It is very unlikely Google data scientists were the first to use the informal shorthand “A/B test.” Test groups have been routinely called “A” and “B” at least as early as the 1940s. So it would be natural for any working group to informally call their test comparing abstract groups “A” and “B” an “A/B test” from time to time. Statisticians are famous for using the names of variables (merely chosen by convention) as formal names of procedures (p-values, t-tests, and many more).

Even if other terms were dominant in earlier writing, it is likely A/B test was used in speech. And writings of our time are sufficiently informal (or like speech) that they should be compared to earlier speech, not just earlier formal writing.

That being said, a quick search yields some examples of previous use. We list but a few below. Continue reading I do not believe Google invented the term A/B test

Posted on 9 Comments on Wanted: A Perfect Scatterplot (with Marginals)

Wanted: A Perfect Scatterplot (with Marginals)

We saw this scatterplot with marginal densities the other day, in a blog post by Thomas Wiecki:

The graph was produced in Python, using the seaborn package. Seaborn calls it a “jointplot;” it’s called a “scatterhist” in Matlab, apparently. The seaborn version also shows the strength of the linear relationship between the x and y variables. Nice.

I like this plot a lot, but we’re mostly an R shop here at Win-Vector. So we asked: can we make this plot in ggplot2? Natively, ggplot2 can add rugs to a scatterplot, but doesn’t immediately offer marginals, as above.

However, you can use Dean Attali’s ggExtra package. Here’s an example using the same data as the seaborn jointplot above; you can download the dataset here.

``` library(ggplot2) library(ggExtra) frm = read.csv("tips.csv") plot_center = ggplot(frm, aes(x=total_bill,y=tip)) + geom_point() + geom_smooth(method="lm") # default: type="density" ggMarginal(plot_center, type="histogram") ```

I didn’t bother to add the internal annotation for the goodness of the linear fit, though I could.

The `ggMarginal()` function goes to heroic effort to line up the coordinate axes of all the graphs, and is probably the best way to do a scatterplot-plus-marginals in ggplot (you can also do it in base graphics, of course). Still, we were curious how close we could get to the seaborn version: marginal density and histograms together, along with annotations. Below is our version of the graph; we report the linear fit’s R-squared, rather than the Pearson correlation.

``` # our own (very beta) plot package: details later library(WVPlots) frm = read.csv("tips.csv") ScatterHist(frm, "total_bill", "tip", smoothmethod="lm", annot_size=3, title="Tips vs. Total Bill") ```

You can see that (at the moment) we’ve resorted to padding the axis labels with underbars to force the x-coordinates of the top marginal plot and the scatterplot to align; white space gets trimmed. This is profoundly unsatisfying, and less robust than the `ggMarginal` version. If you’re curious, the code is here. It relies on some functions in the file `sharedFunctions.R` in the same repository. Our more general version will do either a linear or lowess/spline smooth, and you can also adjust the histogram and density plot parameters.

Thanks to Slawa Rokicki’s excellent ggplot2: Cheatsheet for Visualizing Distributions for our basic approach. Check out the graph at the bottom of her post — and while you’re at it, check out the rest of her blog too.

Posted on Categories Opinion, ProgrammingTags , , 4 Comments on R in a 64 bit world

R in a 64 bit world

32 bit data structures (pointers, integer representations, single precision floating point) have been past their “best before date” for quite some time. R itself moved to a 64 bit memory model some time ago, but still has only 32 bit integers. This is going to get more and more awkward going forward. What is R doing to work around this limitation?

We discuss this in this article, the first of a new series of articles discussing aspects of “R as it is” that we are publishing with cooperation from Revolution Analytics. Continue reading R in a 64 bit world