Lokad’s first major breakthrough was the use of highly atypical types of forecasts for supply chain purposes, specifically quantile forecasts. At Lokad, quantile forecasts were the precursors to probabilistic forecasts. Quantiles marked Lokad’s first significant departure from what is still considered the ‘mainstream’ supply chain theory. This breakthrough was associated with the work of Lokad’s first employee, Benoit Patra. (As the CEO and founder, I didn’t join my own company’s payroll until much later.)

Fifteen years later, much to my horror, I realized that the manuscripts from the multiple PhDs conducted at Lokad had never been published on our website. So, better late than never, let’s republish this manuscript!

Author: Benoit Patra

Date: March 2012

Large Scale Learning Abstract
Large Scale Learning Figure


The subjects addressed in this thesis manuscript are inspired from research problems encountered by the company Lokad, which are summarized in the first chapter. Chapter 2 deals with a nonparametric method for forecasting the quantiles of a real-valued time series. In particular, we establish a consistency result for this technique under minimal assumptions. The remainder of the dissertation is devoted to the analysis of distributed asynchronous clustering algorithms (DALVQ). Chapter 3 first proposes a mathematical description of the models and then offers a theoretical analysis, where the existence of an asymptotical consensus and the almost sure convergence towards critical points of the distortion are proved. In the next chapter, we propose a thorough discussion as well as some experiments on parallelization schemes to be implemented for a practical deployment of DALVQ algorithms. Finally, Chapter 5 contains an effective implementation of DALVQ on the Cloud Computing platform Microsoft Windows Azure. We study, among other topics, the speed ups brought by the algorithm with more parallel computing resources, and we compare this algorithm with the so-called Lloyd’s method, which is also distributed and deployed on Windows Azure.

Fun fact: The abstract mentions ‘Windows Azure’, which was indeed the commercial name of Microsoft Azure in the early years.


Large Scale Learning Jury

Download the thesis (PDF)