Intermediate integer programming representations using value disjunctions

We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by creating a new binary variable for each generated value. Initial experiments show that the extended formulation can have a more compact complete description than the original formulation. We prove that, using this reformulation technique, the facet description decomposes into one ``linking polyhedron'' per block and the ``aggregated polyhedron''. Each of these polyhedra can be analyzed separately. For the case of identical coefficients in a block, we provide a complete description of the linking polyhedron and a polynomial-time separation algorithm. Applied to the knapsack with a fixed number of distinct coefficients, this theorem provides a complete description in an extended space with a polynomial number of variables.Comment: 26 pages, 5 figure

Three dimensional fixed charge bi-criterion indefinite quadratic transportation problem

The three-dimensional fixed charge transportation problem is an extension of the classical three-dimensional transportation problem in which a fixed cost is incurred for every origin. In the present paper three-dimensional fixed charge bi-criterion indefinite quadratic transportation problem, giving the same priority to cost as well as time, is studied. An algorithm to find the efficient cost-time trade off pairs in a three dimensional fixed charge bi-criterion indefinite quadratic transportation problem is developed. The algorithm is illustrated with the help of a numerical example

Fidelity-Weighted Learning

Training deep neural networks requires many training samples, but in practice training labels are expensive to obtain and may be of varying quality, as some may be from trusted expert labelers while others might be from heuristics or other sources of weak supervision such as crowd-sourcing. This creates a fundamental quality versus-quantity trade-off in the learning process. Do we learn from the small amount of high-quality data or the potentially large amount of weakly-labeled data? We argue that if the learner could somehow know and take the label-quality into account when learning the data representation, we could get the best of both worlds. To this end, we propose "fidelity-weighted learning" (FWL), a semi-supervised student-teacher approach for training deep neural networks using weakly-labeled data. FWL modulates the parameter updates to a student network (trained on the task we care about) on a per-sample basis according to the posterior confidence of its label-quality estimated by a teacher (who has access to the high-quality labels). Both student and teacher are learned from the data. We evaluate FWL on two tasks in information retrieval and natural language processing where we outperform state-of-the-art alternative semi-supervised methods, indicating that our approach makes better use of strong and weak labels, and leads to better task-dependent data representations.Comment: Published as a conference paper at ICLR 201

The sleekest link algorithm

How does Google decide which web sites are important? It uses an ingenious algorithm that exploits the structure of the web and is resistant to hacking. Here, we describe this PageRank algorithm, illustrate it by example, and show how it can be interpreted as a Jacobi iteration and a teleporting random walk. We also ask the algorithm to rank the undergraduate mathematics classes offered at the University of Strathclyde. PageRank draws upon ideas from linear algebra, graph theory and stochastic processes, and it throws up research-level challenges in scientific computing. It thus forms an exciting and modern application area that could brighten up many a mathematics class syllabus

Why Imposing New Tolls on Third-Party Content and Applications Threatens Innovation and Will Not Improve Broadband Providers’ Investment

While some broadband providers have called Internet content and application providers free riders on their infrastructure, this is incorrect and misguided. End-users pay for their residential broadband providers for access to the Internet, and content providers pay their own ISPs for connectivity as well. However, content providers need not pay residential broadband providers’ ISPs in order to reach their customers. This feature of the Internet has been one key factor that has allowed innovation to prosper and kept barriers to entry low, as the network transport market for content and application providers functions relatively efficiently. In this paper, I consider the impact of a departure from this current system. I examine the possible impact of last-mile broadband providers’ imposing “termination fees” on third-party content providers or application providers to reach end-users. Broadband providers would engage in paid prioritization arrangements – that is, application and content providers could pay the broadband provider to have their traffic prioritized over competitors’ services. I argue that these arrangements would create inefficiency in the market and harm innovation. Because the last mile access broadband market is concentrated and consumers face switching costs, these concerns are particularly significant. Broadband providers insist that imposing these new charges will greatly improve network investment, and thus these charges are beneficial. I argue that this is not the case. Possible higher revenues from discrimination may simply be returned to shareholders and not invested. Additionally, evidence suggests networks invest more under non-discrimination requirements, and paid prioritization schemes would divert money towards managing scarcity instead of expanding capacity. Paid prioritization could even create an incentive for broadband providers to create congestion to increase the price of prioritized service.