Deep Metric Learning with Chance Constraints

Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding image. We relate DML to feasibility problem of finite chance constraints. We show that minimizer of proxy-based DML satisfies certain chance constraints, and that the worst case generalization performance of the proxy-based methods can be characterized by the radius of the smallest ball around a class proxy to cover the entire domain of the corresponding class samples, suggesting multiple proxies per class helps performance. To provide a scalable algorithm as well as exploiting more proxies, we consider the chance constraints implied by the minimizers of proxy-based DML instances and reformulate DML as finding a feasible point in intersection of such constraints, resulting in a problem to be approximately solved by iterative projections. Simply put, we repeatedly train a regularized proxy-based loss and re-initialize the proxies with the embeddings of the deliberately selected new samples. We apply our method with the well-accepted losses and evaluate on four popular benchmark datasets for image retrieval. Outperforming state-of-the-art, our method consistently improves the performance of the applied losses. Code is available at: https://github.com/yetigurbuz/ccp-dmlComment: Under review at IEEE Transactions on Neural Networks and Learning System

An adaptivity hierarchy theorem for property testing

Adaptivity is known to play a crucial role in property testing. In particular, there exist properties for which there is an exponential gap between the power of adaptive testing algorithms, wherein each query may be determined by the answers received to prior queries, and their non-adaptive counterparts, in which all queries are independent of answers obtained from previous queries. In this work, we investigate the role of adaptivity in property testing at a finer level. We first quantify the degree of adaptivity of a testing algorithm by considering the number of "rounds of adaptivity" it uses. More accurately, we say that a tester is k-(round) adaptive if it makes queries in k+1 rounds, where the queries in the i'th round may depend on the answers obtained in the previous i-1 rounds. Then, we ask the following question: Does the power of testing algorithms smoothly grow with the number of rounds of adaptivity? We provide a positive answer to the foregoing question by proving an adaptivity hierarchy theorem for property testing. Specifically, our main result shows that for every n in N and 0 <= k <= n^{0.99} there exists a property Pi_{n,k} of functions for which (1) there exists a k-adaptive tester for Pi_{n,k} with query complexity tilde O(k), yet (2) any (k-1)-adaptive tester for Pi_{n,k} must make Omega(n) queries. In addition, we show that such a qualitative adaptivity hierarchy can be witnessed for testing natural properties of graphs

Survey of scientific programming techniques for the management of data-intensive engineering environments

The present paper introduces and reviews existing technology and research works in the field of scientific programming methods and techniques in data-intensive engineering environments. More specifically, this survey aims to collect those relevant approaches that have faced the challenge of delivering more advanced and intelligent methods taking advantage of the existing large datasets. Although existing tools and techniques have demonstrated their ability to manage complex engineering processes for the development and operation of safety-critical systems, there is an emerging need to know how existing computational science methods will behave to manage large amounts of data. That is why, authors review both existing open issues in the context of engineering with special focus on scientific programming techniques and hybrid approaches. 1193 journal papers have been found as the representative in these areas screening 935 to finally make a full review of 122. Afterwards, a comprehensive mapping between techniques and engineering and nonengineering domains has been conducted to classify and perform a meta-analysis of the current state of the art. As the main result of this work, a set of 10 challenges for future data-intensive engineering environments have been outlined.The current work has been partially supported by the Research Agreement between the RTVE (the Spanish Radio and Television Corporation) and the UC3M to boost research in the field of Big Data, Linked Data, Complex Network Analysis, and Natural Language. It has also received the support of the Tecnologico Nacional de Mexico (TECNM), National Council of Science and Technology (CONACYT), and the Public Education Secretary (SEP) through PRODEP