Conformal Prediction: a Unified Review of Theory and New Challenges

In this work we provide a review of basic ideas and novel developments about Conformal Prediction -- an innovative distribution-free, non-parametric forecasting method, based on minimal assumptions -- that is able to yield in a very straightforward way predictions sets that are valid in a statistical sense also in in the finite sample case. The in-depth discussion provided in the paper covers the theoretical underpinnings of Conformal Prediction, and then proceeds to list the more advanced developments and adaptations of the original idea.Comment: arXiv admin note: text overlap with arXiv:0706.3188, arXiv:1604.04173, arXiv:1709.06233, arXiv:1203.5422 by other author

3d Face Reconstruction And Emotion Analytics With Part-Based Morphable Models

3D face reconstruction and facial expression analytics using 3D facial data are new and hot research topics in computer graphics and computer vision. In this proposal, we first review the background knowledge for emotion analytics using 3D morphable face model, including geometry feature-based methods, statistic model-based methods and more advanced deep learning-bade methods. Then, we introduce a novel 3D face modeling and reconstruction solution that robustly and accurately acquires 3D face models from a couple of images captured by a single smartphone camera. Two selfie photos of a subject taken from the front and side are used to guide our Non-Negative Matrix Factorization (NMF) induced part-based face model to iteratively reconstruct an initial 3D face of the subject. Then, an iterative detail updating method is applied to the initial generated 3D face to reconstruct facial details through optimizing lighting parameters and local depths. Our iterative 3D face reconstruction method permits fully automatic registration of a part-based face representation to the acquired face data and the detailed 2D/3D features to build a high-quality 3D face model. The NMF part-based face representation learned from a 3D face database facilitates effective global and adaptive local detail data fitting alternatively. Our system is flexible and it allows users to conduct the capture in any uncontrolled environment. We demonstrate the capability of our method by allowing users to capture and reconstruct their 3D faces by themselves. Based on the 3D face model reconstruction, we can analyze the facial expression and the related emotion in 3D space. We present a novel approach to analyze the facial expressions from images and a quantitative information visualization scheme for exploring this type of visual data. From the reconstructed result using NMF part-based morphable 3D face model, basis parameters and a displacement map are extracted as features for facial emotion analysis and visualization. Based upon the features, two Support Vector Regressions (SVRs) are trained to determine the fuzzy Valence-Arousal (VA) values to quantify the emotions. The continuously changing emotion status can be intuitively analyzed by visualizing the VA values in VA-space. Our emotion analysis and visualization system, based on 3D NMF morphable face model, detects expressions robustly from various head poses, face sizes and lighting conditions, and is fully automatic to compute the VA values from images or a sequence of video with various facial expressions. To evaluate our novel method, we test our system on publicly available databases and evaluate the emotion analysis and visualization results. We also apply our method to quantifying emotion changes during motivational interviews. These experiments and applications demonstrate effectiveness and accuracy of our method. In order to improve the expression recognition accuracy, we present a facial expression recognition approach with 3D Mesh Convolutional Neural Network (3DMCNN) and a visual analytics guided 3DMCNN design and optimization scheme. The geometric properties of the surface is computed using the 3D face model of a subject with facial expressions. Instead of using regular Convolutional Neural Network (CNN) to learn intensities of the facial images, we convolve the geometric properties on the surface of the 3D model using 3DMCNN. We design a geodesic distance-based convolution method to overcome the difficulties raised from the irregular sampling of the face surface mesh. We further present an interactive visual analytics for the purpose of designing and modifying the networks to analyze the learned features and cluster similar nodes in 3DMCNN. By removing low activity nodes in the network, the performance of the network is greatly improved. We compare our method with the regular CNN-based method by interactively visualizing each layer of the networks and analyze the effectiveness of our method by studying representative cases. Testing on public datasets, our method achieves a higher recognition accuracy than traditional image-based CNN and other 3D CNNs. The presented framework, including 3DMCNN and interactive visual analytics of the CNN, can be extended to other applications

Hyperbolic Interaction Model For Hierarchical Multi-Label Classification

Different from the traditional classification tasks which assume mutual exclusion of labels, hierarchical multi-label classification (HMLC) aims to assign multiple labels to every instance with the labels organized under hierarchical relations. Besides the labels, since linguistic ontologies are intrinsic hierarchies, the conceptual relations between words can also form hierarchical structures. Thus it can be a challenge to learn mappings from word hierarchies to label hierarchies. We propose to model the word and label hierarchies by embedding them jointly in the hyperbolic space. The main reason is that the tree-likeness of the hyperbolic space matches the complexity of symbolic data with hierarchical structures. A new Hyperbolic Interaction Model (HyperIM) is designed to learn the label-aware document representations and make predictions for HMLC. Extensive experiments are conducted on three benchmark datasets. The results have demonstrated that the new model can realistically capture the complex data structures and further improve the performance for HMLC comparing with the state-of-the-art methods. To facilitate future research, our code is publicly available