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

Novel support vector machines for diverse learning paradigms

This dissertation introduces novel support vector machines (SVM) for the following traditional and non-traditional learning paradigms: Online classification, Multi-Target Regression, Multiple-Instance classification, and Data Stream classification. Three multi-target support vector regression (SVR) models are first presented. The first involves building independent, single-target SVR models for each target. The second builds an ensemble of randomly chained models using the first single-target method as a base model. The third calculates the targets\u27 correlations and forms a maximum correlation chain, which is used to build a single chained SVR model, improving the model\u27s prediction performance, while reducing computational complexity. Under the multi-instance paradigm, a novel SVM multiple-instance formulation and an algorithm with a bag-representative selector, named Multi-Instance Representative SVM (MIRSVM), are presented. The contribution trains the SVM based on bag-level information and is able to identify instances that highly impact classification, i.e. bag-representatives, for both positive and negative bags, while finding the optimal class separation hyperplane. Unlike other multi-instance SVM methods, this approach eliminates possible class imbalance issues by allowing both positive and negative bags to have at most one representative, which constitute as the most contributing instances to the model. Due to the shortcomings of current popular SVM solvers, especially in the context of large-scale learning, the third contribution presents a novel stochastic, i.e. online, learning algorithm for solving the L1-SVM problem in the primal domain, dubbed OnLine Learning Algorithm using Worst-Violators (OLLAWV). This algorithm, unlike other stochastic methods, provides a novel stopping criteria and eliminates the need for using a regularization term. It instead uses early stopping. Because of these characteristics, OLLAWV was proven to efficiently produce sparse models, while maintaining a competitive accuracy. OLLAWV\u27s online nature and success for traditional classification inspired its implementation, as well as its predecessor named OnLine Learning Algorithm - List 2 (OLLA-L2), under the batch data stream classification setting. Unlike other existing methods, these two algorithms were chosen because their properties are a natural remedy for the time and memory constraints that arise from the data stream problem. OLLA-L2\u27s low spacial complexity deals with memory constraints imposed by the data stream setting, and OLLAWV\u27s fast run time, early self-stopping capability, as well as the ability to produce sparse models, agrees with both memory and time constraints. The preliminary results for OLLAWV showed a superior performance to its predecessor and was chosen to be used in the final set of experiments against current popular data stream methods. Rigorous experimental studies and statistical analyses over various metrics and datasets were conducted in order to comprehensively compare the proposed solutions against modern, widely-used methods from all paradigms. The experimental studies and analyses confirm that the proposals achieve better performances and more scalable solutions than the methods compared, making them competitive in their respected fields

{3D} Morphable Face Models -- Past, Present and Future

In this paper, we provide a detailed survey of 3D Morphable Face Models over the 20 years since they were first proposed. The challenges in building and applying these models, namely capture, modeling, image formation, and image analysis, are still active research topics, and we review the state-of-the-art in each of these areas. We also look ahead, identifying unsolved challenges, proposing directions for future research and highlighting the broad range of current and future applications

Learning with Single View Co-training and Marginalized Dropout

The generalization properties of most existing machine learning techniques are predicated on the assumptions that 1) a sufficiently large quantity of training data is available; 2) the training and testing data come from some common distribution. Although these assumptions are often met in practice, there are also many scenarios in which training data from the relevant distribution is insufficient. We focus on making use of additional data, which is readily available or can be obtained easily but comes from a different distribution than the testing data, to aid learning. We present five learning scenarios, depending on how the distribution we used to sample the additional training data differs from the testing distribution: 1) learning with weak supervision; 2) domain adaptation; 3) learning from multiple domains; 4) learning from corrupted data; 5) learning with partial supervision. We introduce two strategies and manifest them in five ways to cope with the difference between the training and testing distribution. The first strategy, which gives rise to Pseudo Multi-view Co-training: PMC) and Co-training for Domain Adaptation: CODA), is inspired by the co-training algorithm for multi-view data. PMC generalizes co-training to the more common single view data and allows us to learn from weakly labeled data retrieved free from the web. CODA integrates PMC with an another feature selection component to address the feature incompatibility between domains for domain adaptation. PMC and CODA are evaluated on a variety of real datasets, and both yield record performance. The second strategy marginalized dropout leads to marginalized Stacked Denoising Autoencoders: mSDA), Marginalized Corrupted Features: MCF) and FastTag: FastTag). mSDA diminishes the difference between distributions associated with different domains by learning a new representation through marginalized corruption and reconstruciton. MCF learns from a known distribution which is created by corrupting a small set of training data, and improves robustness of learned classifiers by training on ``infinitely\u27\u27 many data sampled from the distribution. FastTag applies marginalized dropout to the output of partially labeled data to recover missing labels for multi-label tasks. These three algorithms not only achieve the state-of-art performance in various tasks, but also deliver orders of magnitude speed up at training and testing comparing to competing algorithms

An Exploration of Controlling the Content Learned by Deep Neural Networks

With the great success of the Deep Neural Network (DNN), how to get a trustworthy model attracts more and more attention. Generally, people intend to provide the raw data to the DNN directly in training. However, the entire training process is in a black box, in which the knowledge learned by the DNN is out of control. There are many risks inside. The most common one is overfitting. With the deepening of research on neural networks, additional and probably greater risks were discovered recently. The related research shows that unknown clues can hide in the training data because of the randomization of the data and the finite scale of the training data. Some of the clues build meaningless but explicit links between input data the output data called ``shortcuts\u27\u27. The DNN makes the decision based on these ``shortcuts\u27\u27. This phenomenon is also called ``network cheating\u27\u27. The knowledge of such shortcuts learned by DNN ruins all the training and makes the performance of the DNN unreliable. Therefore, we need to control the raw data using in training. Here, we name the explicit raw data as ``content\u27\u27 and the implicit logic learned by the DNN as ``knowledge\u27\u27 in this dissertation. By quantifying the information in DNN\u27s training, we find that the information learned by the network is much less than the information contained in the dataset. It indicates that it is unnecessary to train the neural network with all of the information, which means using partial information for training can also achieve a similar effect of using full information. In other words, it is possible to control the content fed into the DNN, and this strategy shown in this study can reduce the risks (e.g., overfitting and shortcuts) mentioned above. Moreover, use reconstructed data (with partial information) to train the network can reduce the complexity of the network and accelerate the training. In this dissertation, we provide a pipeline to implement content control in DNN\u27s training. We use a series of experiments to prove its feasibility in two applications. One is human brain anatomy structure analysis, and the other is human pose detection and classification

Regularized System Identification

This open access book provides a comprehensive treatment of recent developments in kernel-based identification that are of interest to anyone engaged in learning dynamic systems from data. The reader is led step by step into understanding of a novel paradigm that leverages the power of machine learning without losing sight of the system-theoretical principles of black-box identification. The authors’ reformulation of the identification problem in the light of regularization theory not only offers new insight on classical questions, but paves the way to new and powerful algorithms for a variety of linear and nonlinear problems. Regression methods such as regularization networks and support vector machines are the basis of techniques that extend the function-estimation problem to the estimation of dynamic models. Many examples, also from real-world applications, illustrate the comparative advantages of the new nonparametric approach with respect to classic parametric prediction error methods. The challenges it addresses lie at the intersection of several disciplines so Regularized System Identification will be of interest to a variety of researchers and practitioners in the areas of control systems, machine learning, statistics, and data science. This is an open access book

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Exploring QCD matter in extreme conditions with Machine Learning

In recent years, machine learning has emerged as a powerful computational tool and novel problem-solving perspective for physics, offering new avenues for studying strongly interacting QCD matter properties under extreme conditions. This review article aims to provide an overview of the current state of this intersection of fields, focusing on the application of machine learning to theoretical studies in high energy nuclear physics. It covers diverse aspects, including heavy ion collisions, lattice field theory, and neutron stars, and discuss how machine learning can be used to explore and facilitate the physics goals of understanding QCD matter. The review also provides a commonality overview from a methodology perspective, from data-driven perspective to physics-driven perspective. We conclude by discussing the challenges and future prospects of machine learning applications in high energy nuclear physics, also underscoring the importance of incorporating physics priors into the purely data-driven learning toolbox. This review highlights the critical role of machine learning as a valuable computational paradigm for advancing physics exploration in high energy nuclear physics.Comment: 146 pages,53 figure