Superfast Line Spectral Estimation

A number of recent works have proposed to solve the line spectral estimation problem by applying off-the-grid extensions of sparse estimation techniques. These methods are preferable over classical line spectral estimation algorithms because they inherently estimate the model order. However, they all have computation times which grow at least cubically in the problem size, thus limiting their practical applicability in cases with large dimensions. To alleviate this issue, we propose a low-complexity method for line spectral estimation, which also draws on ideas from sparse estimation. Our method is based on a Bayesian view of the problem. The signal covariance matrix is shown to have Toeplitz structure, allowing superfast Toeplitz inversion to be used. We demonstrate that our method achieves estimation accuracy at least as good as current methods and that it does so while being orders of magnitudes faster.Comment: 16 pages, 7 figures, accepted for IEEE Transactions on Signal Processin

Variational Bayesian Inference of Line Spectra

In this paper, we address the fundamental problem of line spectral estimation in a Bayesian framework. We target model order and parameter estimation via variational inference in a probabilistic model in which the frequencies are continuous-valued, i.e., not restricted to a grid; and the coefficients are governed by a Bernoulli-Gaussian prior model turning model order selection into binary sequence detection. Unlike earlier works which retain only point estimates of the frequencies, we undertake a more complete Bayesian treatment by estimating the posterior probability density functions (pdfs) of the frequencies and computing expectations over them. Thus, we additionally capture and operate with the uncertainty of the frequency estimates. Aiming to maximize the model evidence, variational optimization provides analytic approximations of the posterior pdfs and also gives estimates of the additional parameters. We propose an accurate representation of the pdfs of the frequencies by mixtures of von Mises pdfs, which yields closed-form expectations. We define the algorithm VALSE in which the estimates of the pdfs and parameters are iteratively updated. VALSE is a gridless, convergent method, does not require parameter tuning, can easily include prior knowledge about the frequencies and provides approximate posterior pdfs based on which the uncertainty in line spectral estimation can be quantified. Simulation results show that accounting for the uncertainty of frequency estimates, rather than computing just point estimates, significantly improves the performance. The performance of VALSE is superior to that of state-of-the-art methods and closely approaches the Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on Signal Processin

A Fast Interior Point Method for Atomic Norm Soft Thresholding

The atomic norm provides a generalization of the $\ell_1$-norm to continuous parameter spaces. When applied as a sparse regularizer for line spectral estimation the solution can be obtained by solving a convex optimization problem. This problem is known as atomic norm soft thresholding (AST). It can be cast as a semidefinite program and solved by standard methods. In the semidefinite formulation there are $O(N^2)$ dual variables which complicates the implementation of a standard primal-dual interior-point method based on symmetric cones. That has lead researcher to consider alternating direction method of multipliers (ADMM) for the solution of AST, but this method is still somewhat slow for large problem sizes. To obtain a faster algorithm we reformulate AST as a non-symmetric conic program. That has two properties of key importance to its numerical solution: the conic formulation has only $O(N)$ dual variables and the Toeplitz structure inherent to AST is preserved. Based on it we derive FastAST which is a primal-dual interior point method for solving AST. Two variants are considered with the fastest one requiring only $O(N^2)$ flops per iteration. Extensive numerical experiments demonstrate that FastAST solves AST significantly faster than a state-of-the-art solver based on ADMM.Comment: 31 pages, accepted for publication in Elsevier Signal Processin

Processes Underlying Glycemic Deterioration in Type 2 Diabetes: An IMI DIRECT Study

Objective We investigated the processes underlying glycemic deterioration in type 2 diabetes (T2D). Research Design and Methods 732 recently diagnosed T2D patients from the IMI-DIRECT study were extensively phenotyped over three years, including measures of insulin sensitivity (OGIS), β-cell glucose sensitivity (GS) and insulin clearance (CLIm) from mixed meal tests, liver enzymes, lipid profiles, and baseline regional fat from MRI. The associations between the longitudinal metabolic patterns and HbA1c deterioration, adjusted for changes in BMI and in diabetes medications, were assessed via stepwise multivariable linear and logistic regression. Results Faster HbA1c progression was independently associated with faster deterioration of OGIS and GS, and increasing CLIm; visceral or liver fat, HDL-cholesterol and triglycerides had further independent, though weaker, roles (R2=0.38). A subgroup of patients with a markedly higher progression rate (fast progressors) was clearly distinguishable considering these variables only (discrimination capacity from AUROC=0.94). The proportion of fast progressors was reduced from 56% to 8-10% in subgroups in which only one trait among OGIS, GS and CLIm was relatively stable (odds ratios 0.07 to 0.09). T2D polygenic risk score and baseline pancreatic fat, GLP-1, glucagon, diet, and physical activity did not show an independent role. Conclusions Deteriorating insulin sensitivity and β-cell function, increasing insulin clearance, high visceral or liver fat, and worsening of the lipid profile are the crucial factors mediating glycemic deterioration of T2D patients in the initial phase of the disease. Stabilization of a single trait among insulin sensitivity, β-cell function, and insulin clearance may be relevant to prevent progression

Discovery of drug-omics associations in type 2 diabetes with generative deep-learning models.

The application of multiple omics technologies in biomedical cohorts has the potential to reveal patient-level disease characteristics and individualized response to treatment. However, the scale and heterogeneous nature of multi-modal data makes integration and inference a non-trivial task. We developed a deep-learning-based framework, multi-omics variational autoencoders (MOVE), to integrate such data and applied it to a cohort of 789 people with newly diagnosed type 2 diabetes with deep multi-omics phenotyping from the DIRECT consortium. Using in silico perturbations, we identified drug-omics associations across the multi-modal datasets for the 20 most prevalent drugs given to people with type 2 diabetes with substantially higher sensitivity than univariate statistical tests. From these, we among others, identified novel associations between metformin and the gut microbiota as well as opposite molecular responses for the two statins, simvastatin and atorvastatin. We used the associations to quantify drug-drug similarities, assess the degree of polypharmacy and conclude that drug effects are distributed across the multi-omics modalities. [Abstract copyright: © 2023. The Author(s).