Computer science and Algorithms

How long does this sorting program run? It possibly takes a very long time on large inputs (that is many strings) until the program has completed its work and gives a sign of life again. Sometimes it makes sense to be able to estimate the running time beforestarting a program. Nobody wants to wait for a sorted phone book for years! Obviously, the running time depends on the number n of the strings to be sorted. Can we find a formula for the running time which depends on n?

Having a close look at the program we notice that it consists of two nested for-loops. In both loops the variables run from 0 to n, but the inner variable starts right from where the outer one just stands. An if with a comparison and some assignments not necessarily executed reside inside the two loops. A good measure for the running time is the number of executed comparisons.[11] In the first iteration n comparisons take place, in the second n-1, then n-2, then n-3 etc. So 1+2+...+n comparisons are performed altogether. According to the well known Gaussian sum formula these are exactly 1/2·(n-1)·n comparisons. Figure 2.8 illustrates this. The screened area corresponds to the number of comparisons executed. It apparently corresponds approx. to half of the area of a square with a side length of n. So it amounts to approx. 1/2·n2.

If you followed the Prize competition, you might be wondering what happened with the final Grand Prize ensemble that won the $1M two years later. This is a truly impressive compilation and culmination of years of work, blending hundreds of predictive models to finally cross the finish line. We evaluated some of the new methods offline but the additional accuracy gains that we measured did not seem to justify the engineering effort needed to bring them into a production environment. Also, our focus on improving Netflix personalization had shifted to the next level by then. In the remainder of this post we will explain how and why it has shifted.

Overview

• Collaborative filtering
  A very brief introduction, its virtues and its flaws.
• Content-based recommendation
  What to do when no usage data is available.
• Predicting listening preferences with deep learning
  Music recommendation based on audio signals.
• Scaling up
  Some details about the convnets I’ve been training at Spotify.
• Analysis: what is it learning?
  A look at what the convnets learn about music, with lots of audio examples, yay!
• What will this be used for?
  Some potential applications of my work.
• Future work
• Conclusion