Unlabeled sample compression schemes and corner peelings for ample and maximum classes

We examine connections between combinatorial notions that arise in machine learning and topological notions in cubical/simplicial geometry. These connections enable to export results from geometry to machine learning. Our first main result is based on a geometric construction by Tracy Hall (2004) of a partial shelling of the cross-polytope which can not be extended. We use it to derive a maximum class of VC dimension 3 that has no corners. This refutes several previous works in machine learning from the past 11 years. In particular, it implies that all previous constructions of optimal unlabeled sample compression schemes for maximum classes are erroneous. On the positive side we present a new construction of an unlabeled sample compression scheme for maximum classes. We leave as open whether our unlabeled sample compression scheme extends to ample (a.k.a. lopsided or extremal) classes, which represent a natural and far-reaching generalization of maximum classes. Towards resolving this question, we provide a geometric characterization in terms of unique sink orientations of the 1-skeletons of associated cubical complexes

Unlabeled Sample Compression Schemes and Corner Peelings for Ample and Maximum Classes

We examine connections between combinatorial notions that arise in machine learning and topological notions in cubical/simplicial geometry. These connections enable to export results from geometry to machine learning. Our first main result is based on a geometric construction by H. Tracy Hall (2004) of a partial shelling of the cross-polytope which can not be extended. We use it to derive a maximum class of VC dimension 3 that has no corners. This refutes several previous works in machine learning from the past 11 years. In particular, it implies that the previous constructions of optimal unlabeled compression schemes for maximum classes are erroneous. On the positive side we present a new construction of an optimal unlabeled compression scheme for maximum classes. We leave as open whether our unlabeled compression scheme extends to ample (a.k.a. lopsided or extremal) classes, which represent a natural and far-reaching generalization of maximum classes. Towards resolving this question, we provide a geometric characterization in terms of unique sink orientations of the 1-skeletons of associated cubical complexes

Restricted Minimum Error Entropy Criterion for Robust Classification

The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the literature. The original MEE only focuses on minimizing the Renyi's quadratic entropy of the error probability distribution function (PDF), which could cause failure in noisy classification tasks. To this end, we analyze the optimal error distribution in the presence of outliers for those classifiers with continuous errors, and introduce a simple codebook to restrict MEE so that it drives the error PDF towards the desired case. Half-quadratic based optimization and convergence analysis of the new learning criterion, called restricted MEE (RMEE), are provided. Experimental results with logistic regression and extreme learning machine are presented to verify the desirable robustness of RMEE

Artificial intelligence-informed planning for the rapid response of hazard-impacted road networks

Post-hazard rapid response has emerged as a promising pathway towards resilient critical infrastructure systems (CISs). Nevertheless, it is challenging to scheme the optimal plan for those rapid responses, given the enormous search space and the hardship of assessment on the spatiotemporal status of CISs. We now present a new approach to post-shock rapid responses of road networks (RNs), based upon lookahead searches supported by machine learning. Following this approach, we examined the resilience-oriented rapid response of a real-world RN across Luchon, France, under destructive earthquake scenarios. Our results show that the introduction of one-step lookahead searches can effectively offset the lack of adaptivity due to the deficient heuristic of rapid responses. Furthermore, the performance of rapid responses following such a strategy is far surpassed, when a series of deep neural networks trained based solely on machine learning, without human interventions, are employed to replace the heuristic and guide the searches

MACHINE LEARNING-BASED PATH LOSS MODELS FOR HETEROGENEOUS RADIO NETWORK PLANNING IN A SMART CAMPUS

An easy-to-use and accurate multi-frequency path loss model is a necessary tool for heterogeneous radio network planning and optimization towards achieving a smart campus. The learning ability in artificial intelligence may be exploited to reduce computational complexity and to improve prediction accuracy. In this research project, an optimal heterogeneous model was developed for path loss predictions in a typical university campus propagation environment using machine learning approach. Radio signal measurements were conducted within the campus of Covenant University, Ota, Nigeria to obtain the logs of signal path loss at 900, 1800, and 2100 MHz. Different path loss prediction models were developed based on Artificial Neural Network (ANN) and Support Vector Machine (SVM) learning algorithms. The prediction accuracy and generalization ability of the ANN-based model, which has seven input nodes (distance, frequency, clutter height, elevation, altitude, latitude, and longitude), single hidden layer with 43 neurons and logarithmic sigmoid (logsig) activation function, and a single output neuron (for path loss variable) with tangent hyperbolic sigmoid (tansig) activation function, was found to be the best when compared to the prediction outputs of SVM-based model, and popular empirical models (i.e. Okumura-Hata, COST 231, ECC-33, and Egli). The ANN-based path loss model was trained based on Levenberg-Marquardt learning (LM) learning algorithm. The prediction outputs of the ANN-based path loss model has the lowest Root Mean Square Error (RMSE) of 4.480 dB, Standard Error Deviation (SED) of 4.479 dB, and the highest value of correlation coefficient (R) of 0.917, relative to the measured path loss values. This finding was further validated by the results of Analysis of Variance (ANOVA) and multiple comparison post-hoc tests. In essence, ANN-based path loss model was found to be the optimal model for heterogeneous radio network planning, deployment, and optimization in a smart campus propagation environmen