Choquet Integral A Choquet integral is a subadditive or superadditive integral created by the French mathematician Gustave Choquet in 1953. It was initially used in statistical mechanics and potential theory, but found its way into decision theory in the 1980s, where it is used as a way of measuring the expected utility of an uncertain event. It is applied specifically to membership functions and capacities. In imprecise probability theory, the Choquet integral is also used to calculate the lower expectation induced by a 2-monotone lower probability, or the upper expectation induced by a 2-alternating upper probability. Using the Choquet integral to denote the expected utility of belief functions measured with capacities is a way to reconcile the Ellsberg paradox and the Allais paradox. http://…/Ayub_Khan_2009.pdf …

In the previous post https://statcompute.wordpress.com/2018/07/29/co-integration-and-pairs-trading, it was shown how to identify two co-integrated stocks in the pair trade. In the example below, I will show how to form a mean reverting portfolio with three or more stocks, e.g. stocks with co-integration, and also how to find the linear combination that is stationary for these stocks.

While developing the RcppDynProg R package I took a little extra time to port the core algorithm from C++ to both R and Python.

In these small tutorials to follow over the next 3 weeks, I go through the steps of using an AWS AMI Rstudio instance to run a toy machine learning example on a large AWS instance. I have to admit that you have to know a little bit about AWS to follow the next couple of steps, but be assured it doesn’t take too much googling to find your way if you get confused at any stage by some of the jargon.

gganimate hits CRAN –

2018 brought more volatility to the markets, which so far has spilled into 2019. Let’s take a look at the long term volatility history picture using the Dow Jones Industrial Average:

Stackelberg GAN We study the problem of alleviating the instability issue in the GAN training procedure via new architecture design. The discrepancy between the minimax and maximin objective values could serve as a proxy for the difficulties that the alternating gradient descent encounters in the optimization of GANs. In this work, we give new results on the benefits of multi-generator architecture of GANs. We show that the minimax gap shrinks to $\epsilon$ as the number of generators increases with rate $\widetilde{O}(1/\epsilon)$. This improves over the best-known result of $\widetilde{O}(1/\epsilon^2)$. At the core of our techniques is a novel application of Shapley-Folkman lemma to the generic minimax problem, where in the literature the technique was only known to work when the objective function is restricted to the Lagrangian function of a constraint optimization problem. Our proposed Stackelberg GAN performs well experimentally in both synthetic and real-world datasets, improving Fr\’echet Inception Distance by $14.61\%$ over the previous multi-generator GANs on the benchmark datasets. …

2018 was very different than 2017. The stock market already made the headlines, registering its first down year in a while.

“A lot of existing Big Data techniques require you to really get your hands dirty; I don’t think that most Big Data software is as mature as it needs to be in order to be accessible to business users at most enterprises. So if you’re not Google or LinkedIn or Facebook, and you don’t have thousands of engineers to work with Big Data, it can be difficult to find business answers in the information.” Paul Kent

Gartners Ethics related Predicts for 2019