We study the problem usually referred to as group testing in the context of COVID-19. Given n samples collected from patients, how should we select and test mixtures of samples to maximize information and minimize the number of tests? Group testing is a well-studied problem with several appealing solutions, but recent biological studies impose practical constraints for COVID-19 that are incompatible with traditional methods. Furthermore, existing methods use unnecessarily restrictive solutions, which were devised for settings with more memory and compute constraints than the problem at hand. This results in poor utility. In the new setting, we obtain strong solutions for small values of n using evolutionary strategies. We then develop a new method combining Bloom filters with belief propagation to scale to larger values of n (more than 100) with good empirical results. We also present a more accurate decoding algorithm that is tailored for specific COVID-19 settings. This work demonstrates the practical gap between dedicated algorithms and well-known generic solutions. Our efforts results in a new and practical multiplex method yielding strong empirical performance without mixing more than a chosen number of patients into the same probe. Finally, we briefly discuss adaptive methods, casting them into the framework of adaptive sub-modularity.

DGL is platform-agnostic so that it can easily be integrated with tensor-oriented frameworks like PyTorch and MXNet. It is an open-source project under active development. Appendix A summarizes the models released in DGL repository. In this paper, we compare DGL against the state-of- the-art library on multiple standard GNN setups and show the improvement of training speed and memory efficiency. 2 F RAMEWORK REQUIREMENTS OF D EEP L EARNING ON G RAPHS Message passing paradigm. Formally, we define a graph G(V,E). V is the set of nodes with v i being the feature vector associated with each node. E is the set of the edge tuples (e k,r k,s k), where s k r k represents the edge from node s k to r k, and e k is feature vector associated with the edge. DGNs are defined by the following edgewise and node-wise computation: Edgewise: m (t) k φ e (e ( t 1) k, v ( t 1) r k, v ( t 1) s k), Node-wise: v ( t) i φ v (v (t 1) i, null k s.t.

In this paper, we study the problem of designing objective functions for machine learning problems defined on finite \emph{sets}. In contrast to traditional objective functions defined for machine learning problems operating on finite dimensional vectors, the new objective functions we propose are operating on finite sets and are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics \citep{poczos13aistats}, via anomaly detection in piezometer data of embankment dams \citep{Jung15Exploration}, to cosmology \citep{Ntampaka16Dynamical,Ravanbakhsh16ICML1}. Our main theorem characterizes the permutation invariant objective functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and image tagging.

Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are unique to tensors. We develop novel methods for randomized computation of tensor contractions via FFTs, without explicitly forming the tensors. Such tensor contractions are encountered in decomposition methods such as tensor power iterations and alternating least squares. We also design novel colliding hashes for symmetric tensors to further save time in computing the sketches. We then combine these sketching ideas with existing whitening and tensor power iterative techniques to obtain the fastest algorithm on both sparse and dense tensors. The quality of approximation under our method does not depend on properties such as sparsity, uniformity of elements, etc. We apply the method for topic modeling and obtain competitive results.

Web page ranking and collaborative filtering require the optimization of sophisticated performance measures. Current Support Vector approaches are unable to optimize them directly and focus on pairwise comparisons instead. We present a new approach which allows direct optimization of the relevant loss functions. This is achieved via structured estimation in Hilbert spaces. It is most related to Max-Margin-Markov networks optimization of multivariate performance measures. Key to our approach is that during training the ranking problem can be viewed as a linear assignment problem, which can be solved by the Hungarian Marriage algorithm. At test time, a sort operation is sufficient, as our algorithm assigns a relevance score to every (document, query) pair. Experiments show that the our algorithm is fast and that it works very well.