We propose a novel graphical model selection scheme for high-dimensional stationary time series or discrete time processes. The method is based on a natural generalization of the graphical LASSO algorithm, introduced originally for the case of i.i.d. samples, and estimates the conditional independence graph of a time series from a finite length observation. The graphical LASSO for time series is defined as the solution of an l₁-regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers. Our approach is nonparametric as we do not assume a finite dimensional parametric model, but only require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails. Numerical experiments demonstrate the ability of our method to recover the correct conditional independence graph from a limited amount of samples.

The automatic and accurate analysis of medical images (e.g., segmentation,detection, classification) are prerequisites for modern disease diagnosis and prognosis. Computer-aided diagnosis (CAD) systems empower accurate and effective detection of various diseases and timely treatment decisions. The past decade witnessed a spur in deep learning (DL)-based CADs showing outstanding performance across many health care applications. Medical imaging is hindered by multiple sources of uncertainty ranging fromnteasurement (aleatoric) errors, physiological variability, and limited medical knowledge (epistemic errors). However, uncertainty quantification (UQ) in most existing DL methods is insufficiently investigated, particularly in medical image analysis. Therefore, to address this gap, in this article, we propose a simple yet novel hierarchical attentive multilevel feature fusion model with an uncertainty-aware module for medical image classification coined Hercules . This approach is tested on several real medical image classification challenges. The proposed Hercules model consists of two main feature fusion blocks, where the former concentrates on attention-based fusion with uncertainty quantification module and the latter uses the raw features. Hercules was evaluated across three medical imaging datasets, i.e., retinal OCT, lung CT, and chest X-ray. Hercules produced the best classification accuracy in retinal OCT (94.21%), lung CT (99.59%), and chest X-ray (96.50%) datasets, respectively, against other state-of-the-art medical image classification methods.

We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity of the dictionary learning (DL) schemes. By casting DL as a classical (or frequentist) estimation problem, the lower bounds on the worst case MSE are derived following an established information-theoretic approach to minimax estimation. The main contribution of this paper is the adaption of these information-theoretic tools to the DL problem in order to derive lower bounds on the worst case MSE of any DL algorithm. We derive three different lower bounds applying to different generative models for the observed signals. The first bound only requires the existence of a covariance matrix of the (unknown) underlying coefficient vector. By specializing this bound to the case of sparse coefficient distributions and assuming the true dictionary satisfies the restricted isometry property, we obtain a lower bound on the worst case MSE of DL methods in terms of the signal-to-noise ratio (SNR). The third bound applies to a more restrictive subclass of coefficient distributions by requiring the non-zero coefficients to be Gaussian. Although the applicability of this bound is the most limited, it is the tightest of the three bounds in the low SNR regime. A particular use of our lower bounds is the derivation of necessary conditions on the required number of observations (sample size), such that DL is feasible, i.e., accurate DL schemes might exist. By comparing these necessary conditions with sufficient conditions on the sample size such that a particular DL technique is successful, we are able to characterize the regimes, where those algorithms are optimal in terms of required sample size.

Interpreting gradient methods as fixed-point iterations, we provide a detailed analysis of those methods for minimizing convex objective functions. Due to their conceptual and algorithmic simplicity, gradient methods are widely used in machine learning for massive datasets (big data). In particular, stochastic gradient methods are considered the defacto standard for training deep neural networks. Studying gradient methods within the realm of fixed-point theory provides us with powerful tools to analyze their convergence properties. In particular, gradient methods using inexact or noisy gradients, such as stochastic gradient descent, can be studied conveniently using well-known results on inexact fixed-point iterations. Moreover, as we demonstrate in this paper, the fixed-point approach allows an elegant derivation of accelerations for basic gradient methods. In particular, we will show how gradient descent can be accelerated by a fixed-point preserving transformation of an operator associated with the objective function.

Strong winds induced by extratropical storms cause a large number of power outages, especially in highly forested countries such as Finland. Thus, predicting the impact of the storms is one of the key challenges for power grid operators. This article introduces a novel method to predict the storm severity for the power grid employing ERA5 reanalysis data combined with forest inventory. We start by identifying storm objects from wind gust and pressure fields by using contour lines of 15 m s⁻¹ and 1000 hPa, respectively. The storm objects are then tracked and characterized with features derived from surface weather parameters and forest vegetation information. Finally, objects are classified with a supervised machine-learning method based on how much damage to the power grid they are expected to cause. Random forest classifiers, support vector classifiers, naïve Bayes processes, Gaussian processes, and multilayer perceptrons were evaluated for the classification task, with support vector classifiers providing the best results.