This paper proposes a new approach for testing Granger non-causality on panel data. Instead of aggregating panel member statistics, we aggregate their corresponding p-values and show that the resulting p-value approximately bounds the type I error by the chosen significance level even if the panel members are dependent. We compare our approach against the most widely used Granger causality algorithm on panel data and show that our approach yields lower FDR at the same power for large sample sizes and panels with cross sectional dependencies. Finally, we examine COVID-19 data about confirmed cases and deaths measured in countries/regions worldwide and show that our approach is able to discover the true causal relation between confirmed cases and deaths while state-of-the-art approaches fail.

Since out-of-distribution generalization is a generally ill-posed problem, various proxy targets (e.g., calibration, adversarial robustness, algorithmic corruptions, invariance across shifts) were studied across different research programs resulting in different recommendations. While sharing the same aspirational goal, these approaches have never been tested under the same experimental conditions on real data. In this paper, we take a unified view of previous work, highlighting message discrepancies that we address empirically, and providing recommendations on how to measure the robustness of a model and how to improve it. To this end, we collect 172 publicly available dataset pairs for training and out-of-distribution evaluation of accuracy, calibration error, adversarial attacks, environment invariance, and synthetic corruptions. We fine-tune over 31k networks, from nine different architectures in the many- and few-shot setting. Our findings confirm that in- and out-of-distribution accuracies tend to increase jointly, but show that their relation is largely dataset-dependent, and in general more nuanced and more complex than posited by previous, smaller scale studies.

Since data sizes of analytical applications are continuously growing, many data scientists are switching from customized micro-solutions to scalable alternatives, such as statistical and scientific databases. However, many algorithms in data mining and science are expressed in terms of linear algebra, which is barely supported by major database vendors and big data solutions. On the other side, conventional linear algebra algorithms and legacy matrix representations are often not suitable for very large matrices. We propose a strategy for large matrix processing on modern multicore systems that is based on a novel, adaptive tile matrix representation (AT MATRIX). Our solution utilizes multiple techniques inspired from database technology, such as multidimensional data partitioning, cardinality estimation, indexing, dynamic rewrites, and many more in order to optimize the execution time. Based thereon we present a matrix multiplication operator ATMULT, which outperforms alternative approaches. The aim of our solution is to overcome the burden for data scientists of selecting appropriate algorithms and matrix storage representations. We evaluated AT MATRIX together with ATMULT on several real-world and synthetic random matrices.

Abstract: In order to confirm their theoretical assumptions, physicists employ Monte-Carlo generators to produce millions of simulated particle collision events and compare them with the results of the detector experiments. The traditional, static analysis workflow of physicists involves creating and compiling a C++ program for each study, and loading large data files for every run of their program. To make this process more interactive and agile, we created an application that loads the data into the relational in-memory column store DBMS SAP HANA, exposes raw particle data as database views and offers an interactive web interface to explore this data. We expressed common particle physics analysis algorithms using SQL queries to benefit from the inherent scalability and parallelization of the DBMS. In this paper we compare the two approaches, i.e. manual analysis with C++ programs and interactive analysis with SAP HANA. We demonstrate the tuning of the physical database schema and the SQL queries used for the application. Moreover, we show the web-based interface that allows for interactive analysis of the simulation data generated by the EPOS Monte-Carlo generator, which is developed in conjunction with the ALICE experiment at the Large Hadron Collider (LHC), CERN. 1

In the age of statistical and scientific databases, there is an emerging trend of integrating analytical algorithms into database systems. Many of these algorithms are based on linear algebra with large, sparse matrices. However, linear algebra expressions often contain multiplications of more then two matrices. The execution of sparse matrix chains is nontrivial, since the runtime depends on the parenthesization and on physical properties of intermediate results. Our approach targets to overcome the burden for data scientists of selecting appropriate algorithms, matrix storage representations, and execution paths. In this paper, we present a sparse matrix chain optimizer (SpMachO) that creates an execution plan, which is composed of multiplication operators and transformations between sparse and dense matrix storage representations. We introduce a comprehensive cost model for sparse-, dense- and hybrid multiplication kernels. Moreover, we propose a sparse matrix product density estimator (SpProdest) for intermediate result matrices. We evaluated SpMachO and SpProdest using real-world matrices and random matrix chains.

Scientific computations and analytical business applications are often based on linear algebra operations on large, sparse matrices. With the hardware shift of the primary storage from disc into memory it is now feasible to execute linear algebra queries directly in the database engine. This paper presents and compares different approaches of storing sparse matrices in an in-memory column-oriented database system. We show that a system layout derived from the compressed sparse row representation integrates well with a columnar database design and that the resulting architecture is moreover amenable to a wide range of non-numerical use cases when dictionary encoding is used. Dynamic matrix manipulation operations, like online insertion or deletion of elements, are not covered by most linear algebra frameworks. Therefore, we present a hybrid architecture that consists of a read-optimized main and a write-optimized delta structure and evaluate the performance for dynamic sparse matrix workloads by applying workflows of nuclear science and network graphs.