LASSO regularization is a popular regression tool to enhance the prediction accuracy of statistical models by performing variable selection through the $\ell_1$ penalty, initially formulated for the linear model and its variants. In this paper, the territory of LASSO is extended to two-layer ReLU neural networks, a fashionable and powerful nonlinear regression model. Specifically, given a neural network whose output $y$ depends only on a small subset of input $\boldsymbol{x}$, denoted by $\mathcal{S}^{\star}$, we prove that the LASSO estimator can stably reconstruct the neural network and identify $\mathcal{S}^{\star}$ when the number of samples scales logarithmically with the input dimension. This challenging regime has been well understood for linear models while barely studied for neural networks. Our theory lies in an extended Restricted Isometry Property (RIP)-based analysis framework for two-layer ReLU neural networks, which may be of independent interest to other LASSO or neural network settings. Based on the result, we advocate a neural network-based variable selection method. Experiments on simulated and real-world datasets show promising performance of the variable selection approach compared with existing techniques.

Time series anomaly detection has been recognized as of critical importance for the reliable and efficient operation of real-world systems. Many anomaly detection methods have been developed based on various assumptions on anomaly characteristics. However, due to the complex nature of real-world data, different anomalies within a time series usually have diverse profiles supporting different anomaly assumptions. This makes it difficult to find a single anomaly detector that can consistently outperform other models. In this work, to harness the benefits of different base models, we propose a reinforcement learning-based model selection framework. Specifically, we first learn a pool of different anomaly detection models, and then utilize reinforcement learning to dynamically select a candidate model from these base models. Experiments on real-world data have demonstrated that the proposed strategy can indeed outplay all baseline models in terms of overall performance.

Background and aim: Image registration and alignment are the main limitations of augmented reality-based knee replacement surgery. This research aims to decrease the registration error, eliminate outcomes that are trapped in local minima to improve the alignment problems, handle the occlusion, and maximize the overlapping parts. Methodology: markerless image registration method was used for Augmented reality-based knee replacement surgery to guide and visualize the surgical operation. While weight least square algorithm was used to enhance stereo camera-based tracking by filling border occlusion in right to left direction and non-border occlusion from left to right direction. Results: This study has improved video precision to 0.57 mm~0.61 mm alignment error. Furthermore, with the use of bidirectional points, for example, forwards and backwards directional cloud point, the iteration on image registration was decreased. This has led to improve the processing time as well. The processing time of video frames was improved to 7.4~11.74 fps. Conclusions: It seems clear that this proposed system has focused on overcoming the misalignment difficulty caused by movement of patient and enhancing the AR visualization during knee replacement surgery. The proposed system was reliable and favorable which helps in eliminating alignment error by ascertaining the optimal rigid transformation between two cloud points and removing the outliers and non-Gaussian noise. The proposed augmented reality system helps in accurate visualization and navigation of anatomy of knee such as femur, tibia, cartilage, blood vessels, etc.

In many machine learning problems the output should not depend on the order of the input. Such "permutation invariant" functions have been studied extensively recently. Here we argue that temporal architectures such as RNNs are highly relevant for such problems, despite the inherent dependence of RNNs on order. We show that RNNs can be regularized towards permutation invariance, and that this can result in compact models, as compared to non-recurrent architectures. We implement this idea via a novel form of stochastic regularization. Existing solutions mostly suggest restricting the learning problem to hypothesis classes which are permutation invariant by design. Our approach of enforcing permutation invariance via regularization gives rise to models which are \textit{semi permutation invariant} (e.g. invariant to some permutations and not to others). We show that our method outperforms other permutation invariant approaches on synthetic and real world datasets.

In identifying infected patients in a population, group testing is an effective method to reduce the number of tests and correct the test errors. In the group testing procedure, tests are performed on pools of specimens collected from patients, where the number of pools is lower than that of patients. The performance of group testing heavily depends on the design of pools and algorithms that are used in inferring the infected patients from the test outcomes. In this paper, an adaptive design method of pools based on the predictive distribution is proposed in the framework of Bayesian inference. The proposed method executed using the belief propagation algorithm results in more accurate identification of the infected patients, as compared to the group testing performed on random pools determined in advance.

Group testing is a method of identifying infected patients by performing tests on a pool of specimens collected from patients. For the case in which the test returns a false result with finite probability, we propose Bayesian inference and a corresponding belief propagation (BP) algorithm to identify the infected patients from the results of tests performed on the pool. We show that the true-positive rate is improved by taking into account the credible interval of a point estimate of each patient. Further, the prevalence and the error probability in the test are estimated by combining an expectation-maximization method with the BP algorithm. As another approach, we introduce a hierarchical Bayes model to identify the infected patients and estimate the prevalence. By comparing these methods, we formulate a guide for practical usage.