Learning network structure from node behavior

Understanding the network structure connecting a group of entities is of interest in applications such as predicting stock prices and making recommendations to customers. The network structure is usually not directly observable. However, due to improvements in technology and the ever-increasing use of the Internet, large amounts of data about individual node behavior is becoming more easily available. Thus, an interesting problem is to devise algorithms to infer network structure from node behavior data. Since network sizes are enormous in typical applications, the learning problem is not tractable for general network topology. In this thesis, we focus on three models with simplifying assumptions on the underlying network. The first model represents the network as a Markov random field, where each node in the network is viewed as a random variable and the conditional independence relations among them is encoded by a graph. The simplifying assumption is that the underlying graph is loosely connected: the number of short paths between any pair of nodes is small. We point out that many previously studied models are examples of this family. Given i.i.d. samples from the joint distribution, we present a natural low complexity algorithm for learning the structure of loosely connected Markov random fields. In particular, our algorithm learns the graph correctly with high probability using $n = O(\log p)$ samples, where $p$ is the size of the graph. If there are at most $D_1$ short paths between non-neighbor nodes and $D_2$ non-direct short paths between neighboring nodes, the running time of our algorithm is $O(np^{D_1+D_2+2})$. The second model arises from the recommender systems where users give ratings to items. We make the assumption that both users and items form clusters and users in the same cluster give the same binary rating to items in the same cluster. The goal is to recover the user and item clusters by observing only a small fraction of noisy entries. We first derive a lower bound on the minimum number of observations needed for exact cluster recovery. Then, we study three algorithms with different running time and compare the number of observations needed for successful cluster recovery. Our analytical results show smooth time-data trade-offs: one can gradually reduce the computational complexity when increasingly more observations are available. The third model considers a similar scenario as the previous one: instead of giving binary ratings, users give pairwise comparisons to items. We assume the users form clusters where users in the same cluster share the same score vector for the items, and the pairwise comparisons obtained from each user are generated according to the Bradley-Terry model with his/her score vector. We propose a two-step algorithm for estimating the score vectors: first cluster the users using projected comparison vectors and then estimate a score vector separately for each cluster by the maximum likelihood estimation for the classical Bradley-Terry model. The key observation is that, though each user is represented by a high-dimensional comparison vector, the corresponding expected comparison vector is determined by only a small number of parameters and it lies close to a low-dimensional linear subspace. When projecting the comparison vectors onto this subspace, it significantly reduces the noise and improves the clustering performance. Moreover, we show that the maximum likelihood estimation is robust to clustering errors

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

SIS 2017. Statistics and Data Science: new challenges, new generations

The 2017 SIS Conference aims to highlight the crucial role of the Statistics in Data Science. In this new domain of ‘meaning’ extracted from the data, the increasing amount of produced and available data in databases, nowadays, has brought new challenges. That involves different fields of statistics, machine learning, information and computer science, optimization, pattern recognition. These afford together a considerable contribute in the analysis of ‘Big data’, open data, relational and complex data, structured and no-structured. The interest is to collect the contributes which provide from the different domains of Statistics, in the high dimensional data quality validation, sampling extraction, dimensional reduction, pattern selection, data modelling, testing hypotheses and confirming conclusions drawn from the data

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described