Mild Traumatic Brain Injury (mTBI) is a significant public health problem. The most troubling symptoms after mTBI are cognitive complaints. Studies show measurable differences between patients with mTBI and healthy controls with respect to tissue microstructure using diffusion MRI. However, it remains unclear which diffusion measures are the most informative with regard to cognitive functions in both the healthy state as well as after injury. In this study, we use diffusion MRI to formulate a predictive model for performance on working memory based on the most relevant MRI features. The key challenge is to identify relevant features over a large feature space with high accuracy in an efficient manner. To tackle this challenge, we propose a novel improvement of the best first search approach with crossover operators inspired by genetic algorithm. Compared against other heuristic feature selection algorithms, the proposed method achieves significantly more accurate predictions and yields clinically interpretable selected features.

Experimental evaluation is a major research methodology for investigating clustering algorithms. For this purpose, a number of benchmark datasets have been widely used in the literature and their quality plays an important role on the value of the research work. However, in most of the existing studies, little attention has been paid to the specific properties of the datasets and they are often regarded as black-box problems. In our work, with the help of advanced visualization and dimension reduction techniques, we show that there are potential issues with some of the popular benchmark datasets used to evaluate clustering algorithms that may seriously compromise the research quality and even may produce completely misleading results. We suggest that significant efforts need to be devoted to improving the current practice of experimental evaluation of clustering algorithms by having a principled analysis of each benchmark dataset of interest.

In this paper we study k-means clustering in the online setting. In the offline setting the main parameters are number of centers, k, and size of the dataset, n. Performance guarantees are given as a function of these parameters. In the online setting new factors come into place: the ordering of the dataset and whether n is known in advance or not. One of the main results of this paper is the discovery that these new factors have dramatic effects on the quality of the clustering algorithms. For example, for constant k: (1) $\Omega(n)$ centers are needed if the order is arbitrary, (2) if the order is random and n is unknown in advance, the number of centers reduces to $\Theta(logn)$, and (3) if n is known, then the number of centers reduces to a constant. For different values of the new factors, we show upper and lower bounds that are exactly the same up to a constant, thus achieving optimal bounds.

Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new insights on deep neural networks for estimating smooth functions in usual settings such as nonparametric regression. In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference. In particular, we highlight the connection between estimation and approximation theories via the classical bias-variance trade-off and show that it leads to near-minimax rates of convergence for H\"older smooth functions. Additionally, we show that the model selection framework over the neural network architecture via ELBO maximization does not overfit and adaptively achieves the optimal rate of convergence.

Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of penalized regression relies crucially on the choice of the tuning parameter, which determines the amount of regularization and hence the sparsity level of the fitted model. The optimal choice of tuning parameter depends on both the structure of the design matrix and the unknown random error distribution (variance, tail behavior, etc). This article reviews the current literature of tuning parameter selection for high-dimensional regression from both theoretical and practical perspectives. We discuss various strategies that choose the tuning parameter to achieve prediction accuracy or support recovery. We also review several recently proposed methods for tuning-free high-dimensional regression.

High entropy alloys (HEAs) have been increasingly attractive as promising next-generation materials due to their various excellent properties. It's necessary to essentially characterize the degree of chemical ordering and identify order-disorder transitions through efficient simulation and modeling of thermodynamics. In this study, a robust data-driven framework based on Bayesian approaches is proposed and demonstrated on the accurate and efficient prediction of configurational energy of high entropy alloys. The proposed effective pair interaction (EPI) model with ensemble sampling is used to map the configuration and its corresponding energy. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. Compared with the arbitrary determination of model complexity, we further conduct a physical feature selection to identify the truncation of coordination shells in EPI model using Bayesian information criterion. The results achieve efficient and robust performance in predicting the configurational energy, particularly given small data. The developed methodology is applied to study a series of refractory HEAs, i.e. NbMoTaW, NbMoTaWV and NbMoTaWTi where it is demonstrated how dataset size affects the confidence we can place in statistical estimates of configurational energy when data are sparse. Introduction As one of the typical multicomponent alloys, high entropy alloys (HEAs) consisting of four or more principal elements have been widely studied due to their exceptional mechanical properties [1, 2, 3, 4].

We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our training objective, based on the Hilbert Schmidt Information Criterion, can be optimized via gradient adaptations on the Stiefel manifold, leading to significant acceleration over spectral methods relying on eigendecompositions. Finally, our trained embedding can be directly applied to out-of-sample data. We show experimentally that our approach outperforms several state-of-the-art deep clustering methods, as well as traditional approaches such as $k$-means and spectral clustering over a broad array of real-life and synthetic datasets.

Human mobility has a significant impact on several layers of society, from infrastructural planning and economics to the spread of diseases and crime. Representing the system as a complex network, in which nodes are assigned to regions (e.g., a city) and links indicate the flow of people between two of them, physics-inspired models have been proposed to quantify the number of people migrating from one city to the other. Despite the advances made by these models, our ability to predict the number of commuters and reconstruct mobility networks remains limited. Here, we propose an alternative approach using machine learning and 22 urban indicators to predict the flow of people and reconstruct the intercity commuters network. Our results reveal that predictions based on machine learning algorithms and urban indicators can reconstruct the commuters network with 90.4% of accuracy and describe 77.6% of the variance observed in the flow of people between cities. We also identify essential features to recover the network structure and the urban indicators mostly related to commuting patterns. As previously reported, distance plays a significant role in commuting, but other indicators, such as Gross Domestic Product (GDP) and unemployment rate, are also driven-forces for people to commute. We believe that our results shed new lights on the modeling of migration and reinforce the role of urban indicators on commuting patterns. Also, because link-prediction and network reconstruction are still open challenges in network science, our results have implications in other areas, like economics, social sciences, and biology, where node attributes can give us information about the existence of links connecting entities in the network.

Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of uncertainty that can enhance decision making, agent exploration and prediction fairness. Markov Chain Monte Carlo (MCMC) methods enable Bayesian inference by generating samples from the posterior distribution over model parameters. Despite the theoretical advantages of Bayesian inference and the similarity between MCMC and optimization methods, the performance of sampling methods has so far lagged behind optimization methods for large scale deep learning tasks. We aim to fill this gap and introduce ATMC, an adaptive noise MCMC algorithm that estimates and is able to sample from the posterior of a neural network. ATMC dynamically adjusts the amount of momentum and noise applied to each parameter update in order to compensate for the use of stochastic gradients. We use a ResNet architecture without batch normalization to test ATMC on the Cifar10 benchmark and the large scale ImageNet benchmark and show that, despite the absence of batch normalization, ATMC outperforms a strong optimization baseline in terms of both classification accuracy and test log-likelihood. We show that ATMC is intrinsically robust to overfitting on the training data and that ATMC provides a better calibrated measure of uncertainty compared to the optimization baseline.

This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-particularly in the high order/ dimension setting-resulting in better performance. We prove that our model is closely related to the Kruskal tensor regression problem, offering interesting theoretical guarantees to our setting. Furthermore, we provide an efficient optimization algorithm based on alternating optimization to solve this model. Finally, we evaluate our algorithm with a large range of experiments, highlighting its advantages and limitations.