In this paper, we propose a way to combine two acceleration techniques for the @math -regularized least squares problem: safe screening tests, which allow to eliminate useless dictionary atoms, and the use of fast structured approximations of the dictionary matrix. To do so, we introduce a new family of screening tests, termed stable screening, which can cope with approximation errors on the dictionary atoms while keeping the safety of the test (i.e. zero risk of rejecting atoms belonging to the solution support). Some of the main existing screening tests are extended to this new framework. The proposed algorithm consists in using a coarser (but faster) approximation of the dictionary at the initial iterations and then switching to better approximations until eventually adopting the original dictionary. A systematic switching criterion based on the duality gap saturation and the screening ratio is derived.Simulation results show significant reductions in both computational complexity and execution times for a wide range of tested scenarios.
Joint screening @cite_32 allows to screen many atoms which lie close together in one single test, reducing the number of required tests for a given dictionary. Interestingly, the resulting tests share many similarities and mathematical connections to the stable screening tests introduced here, despite arising from an essentially different premise.
@cite_32
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This paper focusses on “safe” screening techniques for the LASSO problem. Motivated by the need for low-complexity algorithms, we propose a new approach, dubbed “joint screening test”, allowing to screen a set of atoms by carrying out one single test. The approach is particularized to two different sets of atoms, respectively expressed as sphere and dome regions. After presenting the mathematical derivations of the tests, we elaborate on their relative effectiveness and discuss the practical use of such procedures. Data association is a fundamental problem in multisensor fusion, tracking, and localization. The joint compatibility test is commonly regarded as the true solution to the problem. However, traditional joint compatibility tests are computationally expensive, are sensitive to linearization errors, and require the knowledge of the full covariance matrix of state variables. The paper proposes a posterior-based joint compatibility test scheme to conquer the three problems mentioned above. The posterior-based test naturally separates the test of state variables from the test of observations. Therefore, through the introduction of the robot movement and proper approximation, the joint test process is sequentialized to the sum of individual tests; therefore, the test has O(n) complexity (compared with O(n2) for traditional tests), where n denotes the total number of related observations. At the same time, the sequentialized test neither requires the knowledge to the full covariance matrix of state variables nor is sensitive to linearization errors caused by poor pose estimates. The paper also shows how to apply the proposed method to various simultaneous localization and mapping (SLAM) algorithms. Theoretical analysis and experiments on both simulated data and popular datasets show the proposed method outperforms some classical algorithms, including sequential compatibility nearest neighbor (SCNN), random sample consensus (RANSAC), and joint compatibility branch and bound (JCBB), on precision, efficiency, and robustness. Recent advances in software testing introduced parameterized unit tests (PUT), which accept parameters, unlike conventional unit tests (CUT), which do not accept parameters. PUTs are more beneficial than CUTs with regards to fault-detection capability, since PUTs help describe the behaviors of methods under test for all test arguments. In general, existing applications often include manually written CUTs. With the existence of these CUTs, natural questions that arise are whether these CUTs can be retrofitted as PUTs to leverage the benefits of PUTs, and what are the cost and benefits involved in retrofitting CUTs as PUTs. To address these questions, in this paper, we conduct an empirical study to investigate whether existing CUTs can be retrofitted as PUTs with feasible effort and achieve the benefits of PUTs in terms of additional fault-detection capability and code coverage. We also propose a methodology, called test generalization, that helps in systematically retrofitting existing CUTs as PUTs. Our results on three real-world open-source applications (≈ 4.6 KLOC) show that the retrofitted PUTs detect 19 new defects that are not detected by existing CUTs, and also increase branch coverage by 4 on average (with maximum increase of 52 for one class under test and 10 for one application under analysis) with feasible effort. In this work, we address the problem of robust data association for feature cloud matching. For matching two feature clouds observed at two different poses, we discover that the covariance matrix of the measurement prediction error can be written as the sum of a low rank matrix and a block diagonal matrix, if we assume that the features are observed independently at each pose. This special structure of the covariance matrix allows us to compute its inverse analytically and efficiently. Together with a good bookkeeping strategy, the complexity of the Joint Compatibility (JC) test is reduced to O(1). Contrary to the approximated JC test, ours is both exact and fast. Based on the efficient JC test algorithm and a branch and bound search procedure, we devise an algorithm, called Fast Joint Compatibility Branch and Bound (FastJCBB), to quickly obtain robust data association. The FastJCBB algorithm is essentially modified from the conventional Joint Compatibility Branch and Bound (JCBB) algorithm and both of these algorithms are able to produce exactly the same data association results. However, with the substantial improvement in the efficiency of JC tests, our FastJCBB algorithm is much faster than the conventional JCBB, especially when matching two large feature clouds. It is reported that our FastJCBB algorithm is more than 740 times faster than the conventional JCBB in carrying out one million JC tests when matching two clouds with about 100 features each. Since both FastJCBB and JCBB share the same branch and bound procedure in exploring the interpretation tree, the search complexity remains exponential. Our main contribution is the significant improvement in the efficiency of exploring each node of the interpretation tree.