Regularized Maximum Likelihood Research Articles

Using multiobjective optimization to reconstruct interferometric data

Context. In very long baseline interferometry (VLBI), signals recorded at multiple antennas are combined to form a sparsely sampled virtual aperture with an effective diameter set by the largest separation between the antennas. Due to the sparsity of the sampled aperture, VLBI imaging constitutes an ill-posed inverse problem. Various algorithms have been employed to deal with the VLBI imaging, including the recently proposed multiobjective evolutionary algorithm by decomposition (MOEA/D) described in the first paper of this series. Aims. Among the approaches to the reconstruction of the image features in total intensity from sparsely sampled visibilities, extensions to the polarimetric and the temporal domain are of great interest for the VLBI community in general and the Event Horizon Telescope Collabroration (EHTC) in particular. Based on the success of MOEA/D in presenting an alternative claim of the image structure in a unique, fast, and largely unsupervised way, we study the extension of MOEA/D to polarimetric and time dynamic reconstructions in this paper. Methods. To this end, we utilized the multiobjective, evolutionary framework introduced for MOEA/D, but added the various penalty terms specific to total intensity imaging time-variable and polarimetric variants, respectively. We computed the Pareto front (the sample of all non-dominated solutions) and identified clusters of close proximities. Results. We tested MOEA/D with synthetic data sets that are representative for the main science targets and instrumental configuration of the EHTC and its possible successors. We successfully recovered the polarimetric and time-dynamic signature of the ground truth movie (even with relative sparsity) and a set of realistic data corruptions. Conclusions. MOEA/D has been successfully extended to polarimetric and time-dynamic reconstructions and, specifically, in a setting that would be expected for the EHTC. It offers a unique alternative and independent claim to the already existing methods, along with a number of additional benefits, namely: it is the first method that effectively explores the problem globally and compared to regularized maximum likelihood (RML) methods. Thus, it waives the need for parameter surveys. Hence, MOEA/D is a novel, useful tool to characterize the polarimetric and dynamic signatures in a VLBI data set robustly with a minimal set of user-based choices. In a consecutive work, we will address the last remaining limitation for MOEA/D (the number of pixels and numerical performance), so that MOEA/D can firmly solidify its place within the VLBI data reduction pipeline.

Algorithm XXX: Sparse Precision Matrix Estimation With SQUIC

We present SQUIC , a fast and scalable package for sparse precision matrix estimation. The algorithm employs a second-order method to solve the \(\ell_{1}\) -regularized maximum likelihood problem, utilizing highly optimized linear algebra subroutines. In comparative tests using synthetic datasets, we demonstrate that SQUIC not only scales to datasets of up to a million random variables but also consistently delivers run times that are significantly faster than other well-established sparse precision matrix estimation packages. Furthermore, we showcase the application of the introduced package in classifying microarray gene expressions. We demonstrate that by utilizing a matrix form of the tuning parameter (also known as the regularization parameter), SQUIC can effectively incorporate prior information into the estimation procedure, resulting in improved application results with minimal computational overhead.

Regularized maximum likelihood estimation for radio interferometric imaging in the presence of radiofrequency interferences

We consider a regularized Maximum Likelihood Estimation (MLE) framework to produce images in the context of radio interferometric measurements. Specifically, we consider the class of compound Gaussian distributions to model the additive noise in the presence of radiofrequency interferences. In most cases, direct maximization of the likelihood is not tractable. To overcome this issue, we propose a generic expectation–maximization (EM) algorithm in the presence of a compound Gaussian noise. In addition, we leverage an approximation of the forward radio interferometric operator to derive an original latent data space that allows the use of the FFT in the maximization step, leading to an accelerated extension of the proposed imaging algorithm. The proposed approaches are evaluated on simulated and real data and show a significant improvement in the robustness to the presence of radiofrequency interferences (RFI) in the measurement.

Using multiobjective optimization to reconstruct interferometric data. Part I

Context. Imaging in radioastronomy is an ill-posed inverse problem. However, with increasing sensitivity and capabilities of telescopes, several strategies have been developed in order to solve this challenging problem. In particular, novel algorithms have recently been proposed using (constrained) nonlinear optimization and Bayesian inference. Aims. The Event Horizon Telescope (EHT) Collaboration convincingly investigated the fidelity of their image reconstructions with large surveys, solving the image reconstruction problem with different optimization parameters. This strategy faces a limitation for the existing methods when imaging active galactic nuclei: Large and expensive surveys solving the problem with different optimization parameters are time-consuming. We present a novel nonconvex, multiobjective optimization modeling approach that gives a different type of claim and may provide a pathway to overcome this limitation. Methods. To this end, we use a multiobjective version of the genetic algorithm (GA): the Multiobjective Evolutionary Algorithm Based on Decomposition, or MOEA/D. The GA strategies explore the objective function by evolutionary operations to find the different local minima and to avoid becoming trapped in saddle points. Results. First, we tested our algorithm (MOEA/D) using synthetic data based on the 2017 EHT array and a possible EHT plus next-generation EHT configuration. We successfully recover a fully evolved Pareto front of nondominated solutions for these examples. The Pareto front divides into clusters of image morphologies representing the full set of locally optimal solutions. We discuss approaches to find the most natural guess among these solutions and demonstrate its performance on synthetic data. Finally, we apply MOEA/D to observations of the black hole shadow in Messier 87 with the EHT data in 2017. Conclusions. The MOEA/D is very flexible and faster than any other Bayesian method, and it explores more solutions than regularized maximum likelihood methods. We have written two papers to present this new algorithm. In the first, we explain the basic idea behind multiobjective optimization and MOEA/D, and we use MOEA/D to recover static images. In the second paper, we extend the algorithm to allow dynamic and (static and dynamic) polarimetric reconstructions.

Regularized Maximum Likelihood Image Synthesis and Validation for ALMA Continuum Observations of Protoplanetary Disks

Regularized Maximum Likelihood (RML) techniques are a class of image synthesis methods that achieve better angular resolution and image fidelity than traditional methods like CLEAN for sub-mm interferometric observations. To identify best practices for RML imaging, we used the GPU-accelerated open source Python package MPoL, a machine learning-based RML approach, to explore the influence of common RML regularizers (maximum entropy, sparsity, total variation, and total squared variation) on images reconstructed from real and synthetic Atacama Large millimeter/submillimeter Array (ALMA) continuum observations of protoplanetary disks. We tested two different cross-validation (CV) procedures to characterize their performance and determine optimal prior strengths, and found that CV over a coarse grid of regularization strengths easily identifies a range of models with comparably strong predictive power. To evaluate the performance of RML techniques against a ground truth image, we used MPoL on a synthetic protoplanetary disk data set and found that RML methods successfully resolve structures at fine spatial scales present in the original simulation. We used ALMA DSHARP observations of the protoplanetary disk around HD 143006 to compare the performance of MPoL and CLEAN, finding that RML imaging improved the spatial resolution of the image by up to a factor of 3 without sacrificing sensitivity. We provide general recommendations for building an RML workflow for image synthesis of ALMA protoplanetary disk observations, including effective use of CV. Using these techniques to improve the imaging resolution of protoplanetary disk observations will enable new science, including the detection of protoplanets embedded in disks.

Model-Robust Estimation of Multiple-Group Structural Equation Models

Structural equation models (SEM) are widely used in the social sciences. They model the relationships between latent variables in structural models, while defining the latent variables by observed variables in measurement models. Frequently, it is of interest to compare particular parameters in an SEM as a function of a discrete grouping variable. Multiple-group SEM is employed to compare structural relationships between groups. In this article, estimation approaches for the multiple-group are reviewed. We focus on comparing different estimation strategies in the presence of local model misspecifications (i.e., model errors). In detail, maximum likelihood and weighted least-squares estimation approaches are compared with a newly proposed robust Lp loss function and regularized maximum likelihood estimation. The latter methods are referred to as model-robust estimators because they show some resistance to model errors. In particular, we focus on the performance of the different estimators in the presence of unmodelled residual error correlations and measurement noninvariance (i.e., group-specific item intercepts). The performance of the different estimators is compared in two simulation studies and an empirical example. It turned out that the robust loss function approach is computationally much less demanding than regularized maximum likelihood estimation but resulted in similar statistical performance.

Abstract 4274: Functional dissection of complex tissue microenvironment using spatial transcriptomics data

Abstract Spatial transcriptomics (ST) data holds enormous potential to provide new perspectives for biologists seeking to understand the tumor tissue microenvironments. Cells in the same microenvironment are always exposed to biochemical conditions displacing specific spatial patterns. To truly dismantle the tissue microenvironment heterogeneity as well as cells’ diverse responses to the variable microenvironment, we rely on spatial information to dissect the tissue into different functional regions, which are spatially dependent and biologically meaningful. We have developed a statistical method, smooth Low Rank approximation and Clustering (smoothLRC) to model the spatial transcriptomic data as its low-rank approximation with spatial smoothness. smoothLRC accomplishes this by extracting the latent low-rank structure of the expression profiles. We present a regularized maximum likelihood estimator approximating the noisy observed expression matrix. This estimator incorporates spatial information and addresses expression dropout. It uses a low-rank Poisson distribution to account for the noise that plagues ST-based gene expression data with severe dropout events and a spatial smoothness penalty to encourage neighboring cells to fall into the same functional region. A dropout is an event where genes expressed in a given cell or region are incorrectly measured as unexpressed. SmoothLRC has the following key features: 1) it is a statistically rigorous method; 2) the spatially smooth low-rank subspace could enable meaningful functional dissection, which is an unprecedented capability; 3) the low-rank structures could be used to recover the original expression, saving many expression values that are not captured. Citation Format: Xinyu Zhou, Alexander White, Tingbo Guo, Pengtao Dang, Yuhui Wei, Xiao Wang, Kaman So, Chi Zhang, Sha Cao. Functional dissection of complex tissue microenvironment using spatial transcriptomics data. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 4274.

Robust construction of differential emission measure profiles using a regularized maximum likelihood method

Context.Extreme-ultraviolet (EUV) observations provide considerable insight into evolving physical conditions in the active solar atmosphere. For a prescribed density and temperature structure, it is straightforward to construct the corresponding differential emission measure profileξ(Τ), such thatξ(Τ) dTis proportional to the emissivity from plasma in the temperature range [T,T+ dT]. Here we study the inverse problem of obtaining a validξ(T) profile from a set of EUV spectral line intensities observed at a pixel within a solar image.Aims.Our goal is to introduce and develop a regularized maximum likelihood (RML) algorithm designed to address the mathematically ill-posed problem of constructing differential emission measure profiles from a discrete set of EUV intensities in specified wavelength bands, specifically those observed by the Atmospheric Imaging Assembly (AIA) on the NASA Solar Dynamics Observatory.Methods.The RML method combines features of maximum likelihood and regularized approaches used by other authors. It is also guaranteed to produce a positive definite differential emission measure profile.Results.We evaluate and compare the effectiveness of the method against other published algorithms, using both simulated data generated from parametric differential emission profile forms, and AIA data from a solar eruptive event on 2010 November 3. Similarities and differences between the differential emission measure profiles and maps reconstructed by the various algorithms are discussed.Conclusions.The RML inversion method is mathematically rigorous, computationally efficient, and produces acceptable measures of performance in the following three key areas: fidelity to the data, accuracy in the reconstruction, and robustness in the presence of data noise. As such, it shows considerable promise for computing differential emission measure profiles from datasets of discrete spectral lines.

Multifrequency Black Hole Imaging for the Next-generation Event Horizon Telescope

The Event Horizon Telescope (EHT) has produced images of the plasma flow around the supermassive black holes in Sgr A* and M87* with a resolution comparable to the projected size of their event horizons. Observations with the next-generation Event Horizon Telescope (ngEHT) will have significantly improved Fourier plane coverage and will be conducted at multiple frequency bands (86, 230, and 345 GHz), each with a wide bandwidth. At these frequencies, both Sgr A* and M87* transition from optically thin to optically thick. Resolved spectral index maps in the near-horizon and jet-launching regions of these supermassive black hole sources can constrain properties of the emitting plasma that are degenerate in single-frequency images. In addition, combining information from data obtained at multiple frequencies is a powerful tool for interferometric image reconstruction, since gaps in spatial scales in single-frequency observations can be filled in with information from other frequencies. Here we present a new method of simultaneously reconstructing interferometric images at multiple frequencies along with their spectral index maps. The method is based on existing regularized maximum likelihood (RML) methods commonly used for EHT imaging and is implemented in the eht-imaging Python software library. We show results of this method on simulated ngEHT data sets as well as on real data from the Very Long Baseline Array and Atacama Large Millimeter/submillimeter Array. These examples demonstrate that simultaneous RML multifrequency image reconstruction produces higher-quality and more scientifically useful results than is possible from combining independent image reconstructions at each frequency.

Super-Resolved Image of M87 Observed with East Asian VLBI Network

Obtaining high-resolution images at centimeter-or-longer wavelengths is vital for understanding the physics of jets. We reconstructed images from the M87 22 GHz data observed with the East Asian VLBI Network (EAVN) by using the regularized maximum likelihood (RML) method, which is different from the conventional imaging method CLEAN. Consequently, a bright core and jet extending about 30 mas to the northwest were detected with a higher resolution than in the CLEAN image. The width of the jet was 0.5 mas at 0.3 mas from the core, consistent with the width measured in the 86 GHz image in the previous study. In addition, three ridges were able to be detected at around 8 mas from the core, even though the peak-to-peak separation was only 1.0 mas. This indicates that the RML image’s spatial resolution is at least 30% higher than that of the CLEAN image. This study is an important step for future multi-frequency and high-cadence observations of the EAVN to discuss the more detailed structure of the jet and its time variability.

Efficient Inference of Spatially-Varying Gaussian Markov Random Fields With Applications in Gene Regulatory Networks.

In this paper, we study the problem of inferring spatially-varying Gaussian Markov random fields (SV-GMRF) where the goal is to learn a network of sparse, context-specific GMRFs representing network relationships between genes. An important application of SV-GMRFs is in inference of gene regulatory networks from spatially-resolved transcriptomics datasets. The current work on inference of SV-GMRFs are based on the regularized maximum likelihood estimation (MLE) and suffer from overwhelmingly high computational cost due to their highly nonlinear nature. To alleviate this challenge, we propose a simple and efficient optimization problem in lieu of MLE that comes equipped with strong statistical and computational guarantees. Our proposed optimization problem is extremely efficient in practice: we can solve instances of SV-GMRFs with more than 2 million variables in less than 2 minutes. We apply the developed framework to study how gene regulatory networks in Glioblastoma are spatially rewired within tissue, and identify prominent activity of the transcription factor HES4 and ribosomal proteins as characterizing the gene expression network in the tumor peri-vascular niche that is known to harbor treatment resistant stem cells.

DoG-HiT: A novel VLBI multiscale imaging approach

Context. Reconstructing images from very long baseline interferometry (VLBI) data with a sparse sampling of the Fourier domain (uv-coverage) constitutes an ill-posed deconvolution problem. It requires application of robust algorithms, maximizing the information extraction from all of the sampled spatial scales, and minimizing the influence of the unsampled scales on image quality. Aims. We develop a new multiscale wavelet deconvolution algorithm, DoG-HiT, for imaging sparsely sampled interferometric data, which combines the difference of Gaussian (DoG) wavelets and hard image thresholding (HiT). Based on DoG-HiT, we propose a multistep imaging pipeline for analysis of interferometric data. Methods. DoG-HiT applies the compressed sensing approach to imaging by employing a flexible DoG wavelet dictionary, which is designed to adapt smoothly to the uv-coverage. It uses closure properties as data fidelity terms only, initially, and performs nonconvex, nonsmooth optimization by an amplitude-conserving and total-flux-conserving, hard thresholding splitting. DoG-HiT calculates a multiresolution support as a side product. The final reconstruction is refined through self-calibration loops and imaging with amplitude and phase information applied for the multiresolution support only. Results. We demonstrate the stability of DoG-HiT, and benchmark its performance against image reconstructions made with the CLEAN and regularized maximum-likelihood (RML) methods using synthetic data. The comparison shows that DoG-HiT matches the super-resolution achieved by the RML reconstructions and surpasses the sensitivity to extended emission reached by CLEAN. Conclusions. The application of regularized maximum likelihood methods, outfitted with flexible multiscale wavelet dictionaries, to imaging of interferometric data, matches the performance of state-of-the art convex optimization imaging algorithms and requires fewer prior and user-defined constraints.

Robust Gaussian process regression with a bias model

This paper presents a new approach to a robust Gaussian process regression, creating a non-parametric Bayesian regression estimate robust to outliers. Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution, such as the Laplace distribution and Student-t distribution. However, the use of a non-Gaussian likelihood would incur the need for a computationally expensive Bayesian approximate computation in the posterior inferences. The proposed approach models an outlier as a noisy and biased observation of an unknown regression function, and accordingly, the likelihood contains bias terms to explain the degree of deviations from the regression function. We introduce two bias models that handle the bias terms differently, treating a bias as an unknown and fixed quantity or treating a bias as a random quantity. We entail how the biases can be estimated accurately with other hyperparameters by a regularized maximum likelihood estimation. Conditioned on the bias estimates, the robust GP regression can be reduced to a standard GP regression problem with analytical forms of the predictive mean and variance estimates. Therefore, the proposed approach is simple and very computationally attractive. It also gives a very robust and accurate GP estimate for many tested scenarios. For the numerical evaluation, we perform a comprehensive simulation study to evaluate the proposed approach with the comparison to the existing robust GP approaches under various simulated scenarios of different outlier proportions and different noise levels. The approach is applied to data from two measurement systems, where the predictors are based on robust environmental parameter measurements and the response variables utilize more complex chemical sensing methods that contain a certain percentage of outliers. The utility of the measurement systems and value of the environmental data are improved through the computationally efficient GP regression and bias model.

Learning Interaction Kernels in Stochastic Systems of Interacting Particles from Multiple Trajectories

We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel, which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of the positions of the particles, in either continuous or discrete time, along multiple independent trajectories. We introduce a nonparametric inference approach to this inverse problem, based on a regularized maximum likelihood estimator constrained to suitable hypothesis spaces adaptive to data. We show that a coercivity condition enables us to control the condition number of this problem and prove the consistency of our estimator, and that in fact it converges at a near-optimal learning rate, equal to the min–max rate of one-dimensional nonparametric regression. In particular, this rate is independent of the dimension of the state space, which is typically very high. We also analyze the discretization errors in the case of discrete-time observations, showing that it is of order 1/2 in terms of the time spacings between observations. This term, when large, dominates the sampling error and the approximation error, preventing convergence of the estimator. Finally, we exhibit an efficient parallel algorithm to construct the estimator from data, and we demonstrate the effectiveness of our algorithm with numerical tests on prototype systems including stochastic opinion dynamics and a Lennard-Jones model.

Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging

Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically focus on recovering a point estimate. This is a serious limitation when working with under-determined imaging systems, where it is conceivable that multiple image modes would be consistent with the measured data. Characterizing the space of probable images that explain the observational data is therefore crucial. In this paper, we propose a variational deep probabilistic imaging approach to quantify reconstruction uncertainty. Deep Probabilistic Imaging (DPI) employs an untrained deep generative model to estimate a posterior distribution of an unobserved image. This approach does not require any training data; instead, it optimizes the weights of a neural network to generate image samples that fit a particular measurement dataset. Once the network weights have been learned, the posterior distribution can be efficiently sampled. We demonstrate this approach in the context of interferometric radio imaging, which is used for black hole imaging with the Event Horizon Telescope, and compressed sensing Magnetic Resonance Imaging (MRI).

Validity limits of the maximum entropy method

Maximum entropy (MAXENT) is a widespread method for recovering unknown probabilities of a random variable Z. The method uses first few (empiric) moments of Z and leads to non-parametric estimators. Here we study MAXENT in a Bayesian set-up assuming that there exists a well-defined Dirichlet density for unknown probabilities. This allows to employ the average Kullback-Leibler (KL) distance in evaluating various MAXENT constraints, and comparing MAXENT with parametric estimators: the regularized maximum likelihood (ML) and the Bayesian estimator. KL distance is singled out among other distances from demanding a weak consistency of MAXENT with respect to a shrinkage. We show that MAXENT applies to sparse data, provided that there are certain types of prior information, e.g. the probabilities of Z are most probably deterministic, or there exist prior conditional rank correlations between Z and its probabilities. In the latter case MAXENT can outperform the optimally regularized ML and produce results that are close to the globally optimal Bayes estimator. Predictions of MAXENT are meaningless (i.e. worse than a random guess) if the needed prior information is absent.

Robust Symbol Detection in Large-Scale Overloaded NOMA Systems

We a framework for the design of low-complexity and high-performance receivers for multidimensional overloaded non-orthogonal multiple access (NOMA) systems. The framework is built upon a novel compressed sensing (CS) regularized maximum likelihood (ML) formulation of the discrete-input detection problem, in which the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -norm is introduced to enforce adherence of the solution to the prescribed discrete symbol constellation. Unlike much of preceding literature,.g., (Assaf et al., 2020, Yeom et al., 2019, Nagahara, 2015, Naderpour and Bizaki, 2020, Hayakawa and Hayashi, 2017, Hayakawa and Hayashi, 2018, and Zeng et al., 2020), the method is not relaxed into the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm, but rather approximated with a continuous and asymptotically exact expression without resorting to parallel interference cancellation (PIC). The objective function of the resulting formulation is thus a sum of concave-over-convex ratios, which is then tightly convexified via the quadratic transform (QT), such that its solution can be obtained via the iteration of a simple closed-form expression that closely resembles that of the classic zero-forcing (ZF) receiver, making the method particularly suitable to large-scale set-ups. By further transforming the aforementioned problem into a quadratically constrained quadratic program with one convex constraint (QCQP-1), the optimal regularization parameter to be used at each step of the iterative algorithm is then shown to be the largest generalized eigenvalue of a pair of matrices which are given in closed-form. The method so obtained, referred to as the Iterative Discrete Least Square (IDLS), is then extended to address several factors of practical relevance, such as noisy conditions, imperfect channel state information (CSI), and hardware impairments, thus yielding the Robust IDLS algorithm. Simulation results show that the proposed art significantly outperforms both classic receivers, such as the linear minimum mean square error (LMMSE), and recent CS-based state-of-the-art (SotA) alternatives, such as the sum-of-absolute-values (SOAV) and the sum of complex sparse regularizers (SCSR) detectors. It is also shown via simulations that the technique can be integrated with existing iterative detection-and-decoding (IDD) methods, resulting in accelerated convergence.

ℓ1-regularized maximum likelihood estimation with focused-spot illumination quadruples the diffraction-limited resolution in fluorescence microscopy.

Super-resolution fluorescence microscopy has proven to be a useful tool in biological studies. To achieve more than two-fold resolution improvement over the diffraction limit, existing methods require exploitation of the physical properties of the fluorophores. Recently, it has been demonstrated that achieving more than two-fold resolution improvement without such exploitation is possible using only a focused illumination spot and numerical post-processing. However, how the achievable resolution is affected by the processing step has not been thoroughly investigated. In this paper, we focus on the processing aspect of this emerging super-resolution microscopy technique. Based on a careful examination of the dominant noise source and the available prior information in the image, we find that if a processing scheme is appropriate for the dominant noise model in the image and can utilize the prior information in the form of sparsity, improved accuracy can be expected. Based on simulation results, we identify an improved processing scheme and apply it in a real-world experiment to super-resolve a known calibration sample. We show an improved super-resolution of 60nm, approximately four times beyond the conventional diffraction-limited resolution.

Abstract PO-029: CliP: A model-based method for subclonal architecture reconstruction using regularized maximum likelihood estimation

Abstract Background Subpopulations of tumor cells characterized by mutation profiles may confer differential fitness to treatment and prognosis across cancers. Understanding subclonal architecture has the potential to provide biological insight into tumor evolution and advance the precision treatment of cancers. Recent methods comprehensively integrate single nucleotide variants (SNVs) and copy number alterations (CNAs) to reconstruct subclonal architecture using whole-genome sequencing (WGS) data from bulk tumor samples. However, most methods follow a Bayesian framework and require extensive computational resources, a prior knowledge of the number of subclones, as well as ad hoc post-analysis data processing. Altogether this creates a bottleneck in processing time in large-scale studies. Objectives The primary objective of this study is to introduce a fast and accurate subclonal architecture reconstruction method, which utilizes a model-based clustering approach and addresses all the limitations above. Methods We introduce a novel model-based clustering method: Clonal structure identification through pairwise penalization (CliP). CliP assumes the number of reads observed with variant alleles follows a binomial model, which is a function of mutation cellular prevalence (CP), copy number aberrations, and tumor purity. We propose to minimize a penalized likelihood of this model with a SCAD penalty on CPs across pairs of mutations. The optimization problem is then efficiently solved via Alternating Direction Method of Multipliers (ADMM). As a subclonal reconstruction algorithm, CliP attempts to infer the population structure of heterogeneous tumors, and is the first method to utilize a regularized maximum likelihood framework in subclonal reconstruction, therefore benefiting from its computational efficiency in parameter estimation. Results Rigorous and extensive simulation results demonstrate that CliP is 100 times faster than MCMC-based algorithms without decreased performance. Unlike previous models, the CliP model is applicable to regions with or without CNAs. Furthermore, CliP generates subclonal structure without prior knowledge or post-processing. In an application to WGS data from Pan-Cancer Analysis of Whole Genomes (PCAWG), it only took 8 hours to process 2,500 tumor samples. Conclusion Since CliP executes quickly, it is ultimately suitable for 1) processing large datasets with thousands of samples and 2) participation in a group of methods to generate consensus calls. As the sizes of datasets continue to grow, CliP represents an important step towards fast and accurate subclonal reconstruction. Citation Format: Yujie Jiang, Kaixian Yu, Hongtu Zhu, Wenyi Wang. CliP: A model-based method for subclonal architecture reconstruction using regularized maximum likelihood estimation [abstract]. In: Proceedings of the AACR Virtual Special Conference on Tumor Heterogeneity: From Single Cells to Clinical Impact; 2020 Sep 17-18. Philadelphia (PA): AACR; Cancer Res 2020;80(21 Suppl):Abstract nr PO-029.

Maximum likelihood reconstruction for grating-based X-ray microscopy.

The combination of grating-based phase-contrast imaging with X-ray microscopy can result in a complicated image formation. Generally, transverse shifts of the interference fringes are nonlinearly dependent on phase differences of the measured wave front. We present an iterative reconstruction scheme based on a regularized maximum likelihood cost function that fully takes this dependency into account. The scheme is validated by numerical simulations. It is particularly advantageous at low photon numbers and when the premises for deconvolution-based reconstructions are not met. Our reconstruction scheme hence enables a broader applicability of X-ray grating interferometry in imaging and wave front sensing.