Georg Hahn

Kyle Henke, Elijah Pelofske, Georg Hahn et al.

We consider the problem of computing a sparse binary representation of an image. To be precise, given an image and an overcomplete, non-orthonormal basis, we aim to find a sparse binary vector indicating the minimal set of basis vectors that when added together best reconstruct the given input. We formulate this problem with an $L_2$ loss on the reconstruction error, and an $L_0$ (or, equivalently, an $L_1$) loss on the binary vector enforcing sparsity. This yields a so-called Quadratic Unconstrained Binary Optimization (QUBO) problem, whose solution is generally NP-hard to find. The contribution of this work is twofold. First, the method of unsupervised and unnormalized dictionary feature learning for a desired sparsity level to best match the data is presented. Second, the binary sparse coding problem is then solved on the Loihi 1 neuromorphic chip by the use of stochastic networks of neurons to traverse the non-convex energy landscape. The solutions are benchmarked against the classical heuristic simulated annealing. We demonstrate neuromorphic computing is suitable for sampling low energy solutions of binary sparse coding QUBO models, and although Loihi 1 is capable of sampling very sparse solutions of the QUBO models, there needs to be improvement in the implementation in order to be competitive with simulated annealing.

Rebecca M. Hurwitz, Georg Hahn

Principal components computed via PCA (principal component analysis) are traditionally used to reduce dimensionality in genomic data or to correct for population stratification. In this paper, we explore the penalized eigenvalue problem (PEP) which reformulates the computation of the first eigenvector as an optimization problem and adds an $L_1$ penalty constraint to enforce sparseness of the solution. The contribution of our article is threefold. First, we extend PEP by applying smoothing to the original LASSO-type $L_1$ penalty. This allows one to compute analytical gradients which enable faster and more efficient minimization of the objective function associated with the optimization problem. Second, we demonstrate how higher order eigenvectors can be calculated with PEP using established results from singular value decomposition (SVD). Third, we present four experimental studies to demonstrate the usefulness of the smoothed penalized eigenvectors. Using data from the 1000 Genomes Project dataset, we empirically demonstrate that our proposed smoothed PEP allows one to increase numerical stability and obtain meaningful eigenvectors. We also employ the penalized eigenvector approach in two additional real data applications (computation of a polygenic risk score and clustering), demonstrating that exchanging the penalized eigenvectors for their smoothed counterparts can increase prediction accuracy in polygenic risk scores and enhance discernibility of clusterings. Moreover, we compare our proposed smoothed PEP to seven state-of-the-art algorithms for sparse PCA and evaluate the accuracy of the obtained eigenvectors, their support recovery, and their runtime.

Shirley V Wang, Georg Hahn, Sushama Kattinakere Sreedhara et al.

Background: One of the ways to enhance analyses conducted with large claims databases is by validating the measurement characteristics of code-based algorithms used to identify health outcomes or other key study parameters of interest. These metrics can be used in quantitative bias analyses to assess the robustness of results for an inferential study given potential bias from outcome misclassification. However, extensive time and resource allocation are typically re-quired to create reference-standard labels through manual chart review of free-text notes from linked electronic health records. Methods: We describe an expedited process that introduces efficiency in a validation study us-ing two distinct mechanisms: 1) use of natural language processing (NLP) to reduce time spent by human reviewers to review each chart, and 2) a multi-wave adaptive sampling approach with pre-defined criteria to stop the validation study once performance characteristics are identified with sufficient precision. We illustrate this process in a case study that validates the performance of a claims-based outcome algorithm for intentional self-harm in patients with obesity. Results: We empirically demonstrate that the NLP-assisted annotation process reduced the time spent on review per chart by 40% and use of the pre-defined stopping rule with multi-wave samples would have prevented review of 77% of patient charts with limited compromise to precision in derived measurement characteristics. Conclusion: This approach could facilitate more routine validation of code-based algorithms used to define key study parameters, ultimately enhancing understanding of the reliability of find-ings derived from database studies.

Muhammad Ali Siddiqi, Georg Hahn, Said Hamdioui et al.

A Medical Body Area Network (MBAN) is an ensemble of collaborating, potentially heterogeneous, medical devices located inside, on the surface of or around the human body with the objective of tackling one or multiple medical conditions of the MBAN host. These devices -- which are a special category of Wireless Body Area Networks (WBANs) -- collect, process and transfer medical data outside of the network, while in some cases they also administer medical treatment autonomously. Since communication is so pivotal to their operation, the newfangled IEEE 802.15.6 standard is aimed at the communication aspects of WBANs. It places a set of physical and communication constraints while it also includes association/disassociation protocols and security services that WBAN applications need to comply with. However, the security specifications put forward by the standard can be easily shown to be insufficient when considering realistic MBAN use cases and need further enhancements. The present work addresses these shortcomings by, first, providing a structured analysis of the IEEE 802.15.6 security features and, afterwards, proposing comprehensive and tangible recommendations on improving the standard's security.

Aaron Barbosa, Elijah Pelofske, Georg Hahn et al.

Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a way to compute solutions of NP-hard problems that can be expressed in Ising or QUBO (quadratic unconstrained binary optimization) form. Although such solutions are typically of very high quality, problem instances are usually not solved to optimality due to imperfections of the current generations quantum annealers. In this contribution, we aim to understand some of the factors contributing to the hardness of a problem instance, and to use machine learning models to predict the accuracy of the D-Wave 2000Q annealer for solving specific problems. We focus on the Maximum Clique problem, a classic NP-hard problem with important applications in network analysis, bioinformatics, and computational chemistry. By training a machine learning classification model on basic problem characteristics such as the number of edges in the graph, or annealing parameters such as D-Wave's chain strength, we are able to rank certain features in the order of their contribution to the solution hardness, and present a simple decision tree which allows to predict whether a problem will be solvable to optimality with the D-Wave 2000Q. We extend these results by training a machine learning regression model that predicts the clique size found by D-Wave.

Aaron Barbosa, Elijah Pelofske, Georg Hahn et al.

Quantum annealers have been designed to propose near-optimal solutions to NP-hard optimization problems. However, the accuracy of current annealers such as the ones of D-Wave Systems, Inc., is limited by environmental noise and hardware biases. One way to deal with these imperfections and to improve the quality of the annealing results is to apply a variety of pre-processing techniques such as spin reversal (SR), anneal offsets (AO), or chain weights (CW). Maximizing the effectiveness of these techniques involves performing optimizations over a large number of parameters, which would be too costly if needed to be done for each new problem instance. In this work, we show that the aforementioned parameter optimization can be done for an entire class of problems, given each instance uses a previously chosen fixed embedding. Specifically, in the training phase, we fix an embedding E of a complete graph onto the hardware of the annealer, and then run an optimization algorithm to tune the following set of parameter values: the set of bits to be flipped for SR, the specific qubit offsets for AO, and the distribution of chain weights, optimized over a set of training graphs randomly chosen from that class, where the graphs are embedded onto the hardware using E. In the testing phase, we estimate how well the parameters computed during the training phase work on a random selection of other graphs from that class. We investigate graph instances of varying densities for the Maximum Clique, Maximum Cut, and Graph Partitioning problems. Our results indicate that, compared to their default behavior, substantial improvements of the annealing results can be achieved by using the optimized parameters for SR, AO, and CW.