arXiv subjects

Georg Hahn

Publications and source records attributed to Georg Hahn.

At least 19 recordsLinked to original sources

arXiv2025

A chart review process aided by natural language processing and multi-wave adaptive sampling to expedite validation of code-based algorithms for large database studies

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.

cs.CL↗

arXiv2025

Undersmoothed LASSO Models for Propensity Score Weighting and Synthetic Negative Control Exposures for Bias Detection

The propensity score (PS) is often used to control for large numbers of covariates in high-dimensional healthcare database studies. The least absolute shrinkage and selection operator (LASSO) has become the most widely used tool for fitting large-scale PS models in these settings. LASSO uses L1 regularized regression to prevent overfitting by shrinking coefficients toward zero (setting some exactly to zero). The degree of regularization is typically selected using cross-validation to minimize out-of-sample prediction error. Both theory and simulations have shown, however, that when using LASSO models for PS weighting, less regularization is needed to minimize bias in PS weighted estimators. This is referred to as undersmoothing the LASSO model, where the optimal degree of undersmoothing can be derived from the target causal parameter's efficient influence function. In many settings, however, the efficient influence function is unknown or difficult to derive. Here, we consider the use of balance metrics as a simple and generally applicable approach to select the degree of undersmoothing when the efficient influence function is unknown. Because LASSO models that are tuned using balance metrics alone are not assured to minimize bias in PS weighted estimators -- as such metrics are blind to the efficient influence function -- we propose a framework to generate synthetic negative control exposures for bias detection. We show that synthetic negative control exposures can identify analyses that likely violate partial exchangeability due to lack of control for measured confounding. Finally, we use a series of numerical studies to investigate the finite sample performance of using balance criteria to undersmooth LASSO PS-weighted estimators, and the use of synthetic negative control exposures to detect biased analyses.

stat.ME↗

arXiv2025

Parameter Estimation and Inference in a Continuous Piecewise Linear Regression Model

The estimation of regression parameters in one dimensional broken stick models is a research area of statistics with an extensive literature. We are interested in extending such models by aiming to recover two or more intersecting (hyper)planes in multiple dimensions. In contrast to approaches aiming to recover a given number of piecewise linear components using either a grid search or local smoothing around the change points, we show how to use Nesterov smoothing to obtain a smooth and everywhere differentiable approximation to a piecewise linear regression model with a uniform error bound. The parameters of the smoothed approximation are then efficiently found by minimizing a least squares objective function using a quasi-Newton algorithm. Our main contribution is threefold: We show that the estimates of the Nesterov smoothed approximation of the broken plane model are also $\sqrt{n}$ consistent and asymptotically normal, where $n$ is the number of data points on the two planes. Moreover, we show that as the degree of smoothing goes to zero, the smoothed estimates converge to the unsmoothed estimates and present an algorithm to perform parameter estimation. We conclude by presenting simulation results on simulated data together with some guidance on suitable parameter choices for practical applications.

stat.ME↗

arXiv2025

Adaptive multi-wave sampling for efficient chart validation

Computable phenotypes are used to characterize patients and identify outcomes in studies conducted using healthcare claims and electronic health record data. Chart review studies establish reference labels against which computable phenotypes are compared to understand their measurement characteristics, the quantity of interest, for instance the positive predictive value. We describe a method to adaptively evaluate a quantity of interest over sequential samples of charts, with the goal to minimize the number of charts reviewed. With the help of a simultaneous confidence band, we stop the reviewing once the confidence band meets a pre-specified stopping threshold. The contribution of this article is threefold. First, we tested the use of an adaptive approach called Neyman's sampling of charts versus random or stratified random sampling. Second, we propose frequentist confidence bands and Bayesian credible intervals to sequentially evaluate the quantity of interest. Third, we propose a tool to predict the stopping time (defined as the number of charts reviewed) at which the chart review would be complete. We observe that Bayesian credible intervals proved to be tighter than its frequentist confidence band counterparts. Moreover, we observe that simple random sampling is often performing similarly to Neyman's sampling.

stat.AP↗

arXiv2024

Scalable computation of the maximum flow in large brain connectivity networks

We are interested in computing an approximation of the maximum flow in large (brain) connectivity networks. The maximum flow in such networks is of interest in order to better understand the routing of information in the human brain. However, the runtime of $O(|V||E|^2)$ for the classic Edmonds-Karp algorithm renders computations of the maximum flow on networks with millions of vertices infeasible, where $V$ is the set of vertices and $E$ is the set of edges. In this contribution, we propose a new Monte Carlo algorithm which is capable of computing an approximation of the maximum flow in networks with millions of vertices via subsampling. Apart from giving a point estimate of the maximum flow, our algorithm also returns valid confidence bounds for the true maximum flow. Importantly, its runtime only scales as $O(B \cdot |\tilde{V}| |\tilde{E}|^2)$, where $B$ is the number of Monte Carlo samples, $\tilde{V}$ is the set of subsampled vertices, and $\tilde{E}$ is the edge set induced by $\tilde{V}$. Choosing $B \in O(|V|)$ and $|\tilde{V}| \in O(\sqrt{|V|})$ (implying $|\tilde{E}| \in O(|V|)$) yields an algorithm with runtime $O(|V|^{3.5})$ while still guaranteeing the usual "root-n" convergence of the confidence interval of the maximum flow estimate. We evaluate our proposed algorithm with respect to both accuracy and runtime on simulated graphs as well as graphs downloaded from the Brain Networks Data Repository (https://networkrepository.com).

stat.ME↗

arXiv2024

Increasing the Hardness of Posiform Planting Using Random QUBOs for Programmable Quantum Annealer Benchmarking

Posiform planting is a method for constructing QUBO problems with a single unique planted solution that can be tailored to arbitrary connectivity graphs. In this study we investigate making posiform planted QUBOs computationally harder by fusing many smaller random discrete coefficient spin-glass Ising models, whose global minimum energy is computed classically using classical binary integer programming optimization software, with posiform-planted QUBOs. The single unique ground-state solution of the resulting QUBO problem is the concatenation of (exactly one of) the ground-states of each of the smaller problems. We apply these modified posiform planted QUBOs to the task of benchmarking programmable D-Wave quantum annealers. The proposed method enables generating binary variable combinatorial optimization problems that cover the entire quantum annealing processor hardware graph, have a unique solution, are entirely hardware-graph-native, and can have tunable computational hardness. We benchmark the capabilities of three D-Wave superconducting qubit quantum annealing processors, having from 563 up to 5627 qubits, to sample the optimal unique planted solution of problems generated by our proposed method and compare them against simulated annealing and Gurobi. We find that the D-Wave QPU ground-state sampling success rate does not change with respect to the size of the random QUBOs we employ. Surprisingly, we find that some of these classes of QUBOs are solved at very high success rates at short annealing times compared to longer annealing times for the Zephyr connectivity graph QPUs.

quant-ph↗

arXiv2024

An efficient heuristic for approximate maximum flow computations

Several concepts borrowed from graph theory are routinely used to better understand the inner workings of the (human) brain. To this end, a connectivity network of the brain is built first, which then allows one to assess quantities such as information flow and information routing via shortest path and maximum flow computations. Since brain networks typically contain several thousand nodes and edges, computational scaling is a key research area. In this contribution, we focus on approximate maximum flow computations in large brain networks. By combining graph partitioning with maximum flow computations, we propose a new approximation algorithm for the computation of the maximum flow with runtime O(|V||E|^2/k^2) compared to the usual runtime of O(|V||E|^2) for the Edmonds-Karp algorithm, where $V$ is the set of vertices, $E$ is the set of edges, and $k$ is the number of partitions. We assess both accuracy and runtime of the proposed algorithm on simulated graphs as well as on graphs downloaded from the Brain Networks Data Repository (https://networkrepository.com).

cs.DS↗

arXiv2024

Comparing Quantum Annealing and Spiking Neuromorphic Computing for Sampling Binary Sparse Coding QUBO Problems

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 quadratic unconstrained binary optimization problem (QUBO), whose optimal solution(s) in general is NP-hard to find. The contribution of this work is twofold. First, we solve the sparse representation QUBOs by solving them both on a D-Wave quantum annealer with Pegasus chip connectivity via minor embedding, as well as on the Intel Loihi 2 spiking neuromorphic processor using a stochastic Non-equilibrium Boltzmann Machine (NEBM). Second, we deploy Quantum Evolution Monte Carlo with Reverse Annealing and iterated warm starting on Loihi 2 to evolve the solution quality from the respective machines. The solutions are benchmarked against simulated annealing, a classical heuristic, and the optimal solutions are computed using CPLEX. Iterated reverse quantum annealing performs similarly to simulated annealing, although simulated annealing is always able to sample the optimal solution whereas quantum annealing was not always able to. The Loihi 2 solutions that are sampled are on average more sparse than the solutions from any of the other methods. We demonstrate that both quantum annealing and neuromorphic computing are suitable for binary sparse coding QUBOs, and that Loihi 2 outperforms a D-Wave quantum annealer standard linear-schedule anneal, while iterated reverse quantum annealing performs much better than both unmodified linear-schedule quantum annealing and iterated warm starting on Loihi 2.

cs.ET↗

arXiv2023

Penalized Principal Component Analysis Using Smoothing

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.

stat.AP↗

arXiv2023

Posiform Planting: Generating QUBO Instances for Benchmarking

We are interested in benchmarking both quantum annealing and classical algorithms for minimizing Quadratic Unconstrained Binary Optimization (QUBO) problems. Such problems are NP-hard in general, implying that the exact minima of randomly generated instances are hard to find and thus typically unknown. While brute forcing smaller instances is possible, such instances are typically not interesting due to being too easy for both quantum and classical algorithms. In this contribution, we propose a novel method, called posiform planting, for generating random QUBO instances of arbitrary size with known optimal solutions, and use those instances to benchmark the sampling quality of four D-Wave quantum annealers utilizing different interconnection structures (Chimera, Pegasus, and Zephyr hardware graphs) as well as the simulated annealing algorithm. Posiform planting differs from many existing methods in two key ways. It ensures the uniqueness of the planted optimal solution, thus avoiding groundstate degeneracy, and it enables the generation of QUBOs that are tailored to a given hardware connectivity structure, provided that the connectivity is not too sparse. Posiform planted QUBOs are a type of 2-SAT boolean satisfiability combinatorial optimization problems. Our experiments demonstrate the capability of the D-Wave quantum annealers to sample the optimal planted solution of combinatorial optimization problems with up to $5627$ qubits.

quant-ph↗

arXiv2023

Sampling binary sparse coding QUBO models using a spiking neuromorphic processor

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.

cs.NE↗

arXiv2023

Initial State Encoding via Reverse Quantum Annealing and h-gain Features

Quantum annealing is a specialized type of quantum computation that aims to use quantum fluctuations in order to obtain global minimum solutions of combinatorial optimization problems. Programmable D-Wave quantum annealers are available as cloud computing resources which allow users low level access to quantum annealing control features. In this paper, we are interested in improving the quality of the solutions returned by a quantum annealer by encoding an initial state into the annealing process. We explore two D-Wave features allowing one to encode such an initial state: the reverse annealing and the h-gain features. Reverse annealing (RA) aims to refine a known solution following an anneal path starting with a classical state representing a good solution, going backwards to a point where a transverse field is present, and then finishing the annealing process with a forward anneal. The h-gain (HG) feature allows one to put a time-dependent weighting scheme on linear ($h$) biases of the Hamiltonian, and we demonstrate that this feature likewise can be used to bias the annealing to start from an initial state. We also consider a hybrid method consisting of a backward phase resembling RA, and a forward phase using the HG initial state encoding. Importantly, we investigate the idea of iteratively applying RA and HG to a problem, with the goal of monotonically improving on an initial state that is not optimal. The HG encoding technique is evaluated on a variety of input problems including the edge-weighted Maximum Cut problem and the vertex-weighted Maximum Clique problem, demonstrating that the HG technique is a viable alternative to RA for some problems. We also investigate how the iterative procedures perform for both RA and HG initial state encoding on random whole-chip spin glasses with the native hardware connectivity of the D-Wave Chimera and Pegasus chips.

quant-ph↗

arXiv2022

Noise Dynamics of Quantum Annealers: Estimating the Effective Noise Using Idle Qubits

Quantum annealing is a type of analog computation that aims to use quantum mechanical fluctuations in search of optimal solutions of QUBO (quadratic unconstrained binary optimization) or, equivalently, Ising problems. Since NP-hard problems can in general be mapped to Ising and QUBO formulations, the quantum annealing paradigm has the potential to help solve various NP-hard problems. Current quantum annealers, such as those manufactured by D-Wave Systems, Inc., have various practical limitations including the size (number of qubits) of the problem that can be solved, the qubit connectivity, and error due to the environment or system calibration, which can reduce the quality of the solutions. Typically, for an arbitrary problem instance, the corresponding QUBO (or Ising) structure will not natively embed onto the available qubit architecture on the quantum chip. Thus, in these cases, a minor embedding of the problem structure onto the device is necessary. However, minor embeddings on these devices do not always make use of the full sparse chip hardware graph, and a large portion of the available qubits stay unused during quantum annealing. In this work, we embed a disjoint random QUBO on the unused parts of the chip alongside the QUBO to be solved, which acts as an indicator of the solution quality of the device over time. Using experiments on three different D-Wave quantum annealers, we demonstrate that (i) long term trends in solution quality exist on the D-Wave device, and (ii) the unused qubits can be used to measure the current level of noise of the quantum system.

quant-ph↗

arXiv2022

Solving Larger Maximum Clique Problems Using Parallel Quantum Annealing

Quantum annealing has the potential to find low energy solutions of NP-hard problems that can be expressed as quadratic unconstrained binary optimization problems. However, the hardware of the quantum annealer manufactured by D-Wave Systems, which we consider in this work, is sparsely connected and moderately sized (on the order of thousands of qubits), thus necessitating a minor-embedding of a logical problem onto the physical qubit hardware. The combination of relatively small hardware sizes and the necessity of a minor-embedding can mean that solving large optimization problems is not possible on current quantum annealers. In this research, we show that a hybrid approach combining parallel quantum annealing with graph decomposition allows one to solve larger optimization problem accurately. We apply the approach on the Maximum Clique problem on graphs with up to 120 nodes and 6395 edges.

quant-ph↗

arXiv2022

Improving the Security of the IEEE 802.15.6 Standard for Medical BANs

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.

cs.CR↗

arXiv2021

Parallel Quantum Annealing

Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute high quality solutions of NP-hard problems. This is done by mapping a problem onto the physical qubits of the quantum chip, from which a solution is obtained after quantum annealing. However, since the connectivity of the physical qubits on the chip is limited, a minor embedding of the problem structure onto the chip is required. In this process, and especially for smaller problems, many qubits will stay unused. We propose a novel method, called parallel quantum annealing, to make better use of available qubits, wherein either the same or several independent problems are solved in the same annealing cycle of a quantum annealer, assuming enough physical qubits are available to embed more than one problem. Although the individual solution quality may be slightly decreased when solving several problems in parallel (as opposed to solving each problem separately), we demonstrate that our method may give dramatic speed-ups in terms of Time-to-Solution (TTS) for solving instances of the Maximum Clique problem when compared to solving each problem sequentially on the quantum annealer. Additionally, we show that solving a single Maximum Clique problem using parallel quantum annealing reduces the TTS significantly.

quant-ph↗

arXiv2021

Quantum Annealing Algorithms for Boolean Tensor Networks

Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., {0, 1}) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called \textit{parallel quantum annealing}, we demonstrate that tensor with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.

quant-ph↗

arXiv2021

Using machine learning for quantum annealing accuracy prediction

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.

quant-ph↗