Blessing of Nonconvexity in Deep Linear Models: Depth Flattens the Optimization Landscape Around the True Solution

This work characterizes the effect of depth on the optimization landscape of linear regression, showing that, despite their nonconvexity, deeper models have more desirable optimization landscape. We consider a robust and over-parameterized setting, where a subset of measurements are grossly corrupted with noise and the true linear model is captured via an $N$-layer linear neural network. On the negative side, we show that this problem \textit{does not} have a benign landscape: given any $N\geq 1$, with constant probability, there exists a solution corresponding to the ground truth that is neither local nor global minimum. However, on the positive side, we prove that, for any $N$-layer model with $N\geq 2$, a simple sub-gradient method becomes oblivious to such ``problematic'' solutions; instead, it converges to a balanced solution that is not only close to the ground truth but also enjoys a flat local landscape, thereby eschewing the need for "early stopping". Lastly, we empirically verify that the desirable optimization landscape of deeper models extends to other robust learning tasks, including deep matrix recovery and deep ReLU networks with $\ell_1$-loss

Road Crack Detection Using Deep Convolutional Neural Network and Adaptive Thresholding

Crack is one of the most common road distresses which may pose road safety hazards. Generally, crack detection is performed by either certified inspectors or structural engineers. This task is, however, time-consuming, subjective and labor-intensive. In this paper, we propose a novel road crack detection algorithm based on deep learning and adaptive image segmentation. Firstly, a deep convolutional neural network is trained to determine whether an image contains cracks or not. The images containing cracks are then smoothed using bilateral filtering, which greatly minimizes the number of noisy pixels. Finally, we utilize an adaptive thresholding method to extract the cracks from road surface. The experimental results illustrate that our network can classify images with an accuracy of 99.92%, and the cracks can be successfully extracted from the images using our proposed thresholding algorithm.Comment: 6 pages, 8 figures, 2019 IEEE Intelligent Vehicles Symposiu

Robust Sparse Mean Estimation via Incremental Learning

In this paper, we study the problem of robust sparse mean estimation, where the goal is to estimate a $k$-sparse mean from a collection of partially corrupted samples drawn from a heavy-tailed distribution. Existing estimators face two critical challenges in this setting. First, they are limited by a conjectured computational-statistical tradeoff, implying that any computationally efficient algorithm needs $\tilde\Omega(k^2)$ samples, while its statistically-optimal counterpart only requires $\tilde O(k)$ samples. Second, the existing estimators fall short of practical use as they scale poorly with the ambient dimension. This paper presents a simple mean estimator that overcomes both challenges under moderate conditions: it runs in near-linear time and memory (both with respect to the ambient dimension) while requiring only $\tilde O(k)$ samples to recover the true mean. At the core of our method lies an incremental learning phenomenon: we introduce a simple nonconvex framework that can incrementally learn the top-$k$ nonzero elements of the mean while keeping the zero elements arbitrarily small. Unlike existing estimators, our method does not need any prior knowledge of the sparsity level $k$. We prove the optimality of our estimator by providing a matching information-theoretic lower bound. Finally, we conduct a series of simulations to corroborate our theoretical findings. Our code is available at https://github.com/huihui0902/Robust_mean_estimation

Multiple Lane Detection Algorithm Based on Optimised Dense Disparity Map Estimation

Lane detection is very important for self-driving vehicles. In recent years, computer stereo vision has been prevalently used to enhance the accuracy of the lane detection systems. This paper mainly presents a multiple lane detection algorithm developed based on optimised dense disparity map estimation, where the disparity information obtained at time t_{n} is utilised to optimise the process of disparity estimation at time t_{n+1}. This is achieved by estimating the road model at time t_{n} and then controlling the search range for the disparity estimation at time t_{n+1}. The lanes are then detected using our previously published algorithm, where the vanishing point information is used to model the lanes. The experimental results illustrate that the runtime of the disparity estimation is reduced by around 37% and the accuracy of the lane detection is about 99%.Comment: 5 pages, 7 figures, IEEE International Conference on Imaging Systems and Techniques (IST) 201

Prognostic and clinicopathological significance of fatty acid synthase in breast cancer: A systematic review and meta-analysis

BackgroundAberrant expression of fatty acid synthase (FASN) was demonstrated in various tumors including breast cancer. A meta-analysis was conducted to investigate the role of FASN in breast cancer development and its potential prognostic significance.MethodsThe Web of Science, PubMed, Embase, and Cochrane Library databases were searched to identify studies that evaluated the relationship between FASN expression and overall survival (OS), relapse-free survival (RFS), and disease-free survival (DFS) of breast cancer patients. To analyze the clinicopathological and prognostic values of FASN expression in breast cancer, pooled hazard ratios (HRs), odds ratios (ORs), and 95% confidence intervals (CIs) were clustered based on random-effects models. To confirm whether the findings were stable and impartial, a sensitivity analysis was performed, and publication bias was estimated. Data were analyzed using Engauge Digitizer version 5.4 and Stata version 15.0.ResultsFive studies involving 855 participants were included. Patients with higher FASN expression did not have a shorter survival period compared to those with lower FASN expression (summary HR: OS, 0.73 [95% CI, 0.41-1.32; P=0.300]; DFS/RFS, 1.65 [95% CI, 0.61-4.43; P=0.323]). However, increased FASN expression was correlated with large tumor size (OR, 2.04; 95% CI, 1.04-4.00; P=0.038), higher human epidermal growth factor receptor 2 (HER2) positivity (OR, 1.53; 95% CI, 1.05-2.23; P=0.028). No significant associations were observed between FASN expression and histological grade (OR, 0.92; 95% CI, 0.41-2.04; P=0.832), Tumor Node Metastasis (TNM) stage (OR, 1.11; 95% CI, 0.49-2.53; P=0.795), nodal metastasis (OR, 1.42; 95% CI, 0.84-2.38; P=0.183), Ki-67 labelling index (OR, 0.64; 95% CI, 0.15-2.63; P=0.533), estrogen receptor (ER) status (OR, 0.90; 95% CI, 0.61-1.32; P=0.586), or progesterone receptor (PR) status (OR, 0.67; 95% CI, 0.29-1.56; P=0.354).ConclusionFASN is associated with HER2 expression and may contribute to tumor growth, but it has no significant impact on the overall prognosis of breast cancer

A nomogram combining thoracic CT and tumor markers to predict the malignant grade of pulmonary nodules ≤3 cm in diameter

BackgroundWith the popularity of computed tomography (CT) of the thorax, the rate of diagnosis for patients with early-stage lung cancer has increased. However, distinguishing high-risk pulmonary nodules (HRPNs) from low-risk pulmonary nodules (LRPNs) before surgery remains challenging.MethodsA retrospective analysis was performed on 1064 patients with pulmonary nodules (PNs) admitted to the Qilu Hospital of Shandong University from April to December 2021. Randomization of all eligible patients to either the training or validation cohort was performed in a 3:1 ratio. Eighty-three PNs patients who visited Qianfoshan Hospital in the Shandong Province from January through April of 2022 were included as an external validation. Univariable and multivariable logistic regression (forward stepwise regression) were used to identify independent risk factors, and a predictive model and dynamic web nomogram were constructed by integrating these risk factors.ResultsA total of 895 patients were included, with an incidence of HRPNs of 47.3% (423/895). Logistic regression analysis identified four independent risk factors: the size, consolidation tumor ratio, CT value of PNs, and carcinoembryonic antigen levels in blood. The area under the ROC curves was 0.895, 0.936, and 0.812 for the training, internal validation, and external validation cohorts, respectively. The Hosmer-Lemeshow test demonstrated excellent calibration capability, and the fit of the calibration curve was good. DCA has shown the nomogram to be clinically useful.ConclusionThe nomogram performed well in predicting the likelihood of HRPNs. In addition, it identified HRPNs in patients with PNs, achieved accurate treatment with HRPNs, and is expected to promote their rapid recovery