Fast and exact search for the partition with minimal information loss

In analysis of multi-component complex systems, such as neural systems, identifying groups of units that share similar functionality will aid understanding of the underlying structures of the system. To find such a grouping, it is useful to evaluate to what extent the units of the system are separable. Separability or inseparability can be evaluated by quantifying how much information would be lost if the system were partitioned into subsystems, and the interactions between the subsystems were hypothetically removed. A system of two independent subsystems are completely separable without any loss of information while a system of strongly interacted subsystems cannot be separated without a large loss of information. Among all the possible partitions of a system, the partition that minimizes the loss of information, called the Minimum Information Partition (MIP), can be considered as the optimal partition for characterizing the underlying structures of the system. Although the MIP would reveal novel characteristics of the neural system, an exhaustive search for the MIP is numerically intractable due to the combinatorial explosion of possible partitions. Here, we propose a computationally efficient search to precisely identify the MIP among all possible partitions by exploiting the submodularity of the measure of information loss. Mutual information is one such submodular information loss functions, and is a natural choice for measuring the degree of statistical dependence between paired sets of random variables. By using mutual information as a loss function, we show that the search for MIP can be performed in a practical order of computational time for a reasonably large system. We also demonstrate that MIP search allows for the detection of underlying global structures in a network of nonlinear oscillators

Clustering clinical departments for wards to achieve a prespecified blocking probability

When the number of available beds in a hospital is limited and fixed, it can be beneficial to cluster several clinical departments such that the probability of not being able to admit a patient is acceptably small. The clusters are then assigned to the available wards such that enough beds are available to guarantee a blocking probability below a prespecified value. We first give an exact formulation of the problem to be able to achieve optimal solutions. To reduce computation times, we also introduce two heuristic solution methods. The first heuristic is similar to the exact solution method, however, the number of beds needed is approximated by a linear function. The second heuristic uses a local search approach to determine the assignment of clinical departments to clusters and a restricted version of the exact solution method to determine the assignment of clusters to wards

Visual Search at eBay

In this paper, we propose a novel end-to-end approach for scalable visual search infrastructure. We discuss the challenges we faced for a massive volatile inventory like at eBay and present our solution to overcome those. We harness the availability of large image collection of eBay listings and state-of-the-art deep learning techniques to perform visual search at scale. Supervised approach for optimized search limited to top predicted categories and also for compact binary signature are key to scale up without compromising accuracy and precision. Both use a common deep neural network requiring only a single forward inference. The system architecture is presented with in-depth discussions of its basic components and optimizations for a trade-off between search relevance and latency. This solution is currently deployed in a distributed cloud infrastructure and fuels visual search in eBay ShopBot and Close5. We show benchmark on ImageNet dataset on which our approach is faster and more accurate than several unsupervised baselines. We share our learnings with the hope that visual search becomes a first class citizen for all large scale search engines rather than an afterthought.Comment: To appear in 23rd SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), 2017. A demonstration video can be found at https://youtu.be/iYtjs32vh4

Segmentation of the Poisson and negative binomial rate models: a penalized estimator

We consider the segmentation problem of Poisson and negative binomial (i.e. overdispersed Poisson) rate distributions. In segmentation, an important issue remains the choice of the number of segments. To this end, we propose a penalized log-likelihood estimator where the penalty function is constructed in a non-asymptotic context following the works of L. Birg\'e and P. Massart. The resulting estimator is proved to satisfy an oracle inequality. The performances of our criterion is assessed using simulated and real datasets in the RNA-seq data analysis context