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Multi-source data refers to data that are collected from multiple sources or modalities. With the increasing availability of digital data, multi-source data has been applied to a wide range of applications, including sentiment analysis, object recognition, and recommendation systems. For example, in sentiment analysis, multi-source data has been used to combine text, images, and audio to improve the accuracy of sentiment classification. In recommendation systems, multi-source data has been used to combine data from different sources, such as text, images, and audio, to improve the quality of recommendations. The integration of these diverse and heterogeneous sources of data can provide a more comprehensive understanding of a particular phenomenon or problem. However, there are many challenges for learning multi-source data, such as dealing with heterogeneous data and developing interpretable models. To address these challenges, a number of statistical and machine learning methods have been developed, including multi-view learning and transfer learning. Multi-view learning is a technique that involves the analysis of data from multiple sources or views to learn a common representation of the data. Transfer learning is a machine learning technique that enables the transfer of knowledge from one domain or task to another. This dissertation develops new methods on multi-view learning and transfer learning. Chapter 3 presents a weighted multi-view NMF algorithm, termed as WM- NMF, to conduct integrative clustering of multi-view heterogeneous or corrupted data. We improve the existing multi-view NMF algorithms and propose to perform multi-view clustering by quantifying each view's content through learning both the view-specific and reconstruction weights. Our proposed algorithm can enlarge the positive effects and alleviate the adverse effects of the important and unnecessary views, respectively. We further demonstrate the competing performance of WM- NMF with regard to clustering performance. Using several datasets, we show that our algorithm significantly outperforms the existing multi-view algorithms in terms of six evaluation metrics. In Chapters 4 and 5, we propose a novel, interpretable, one-step, and unified framework for transfer learning. We first apply it to the high-dimensional linear regression in Chapter 4 and extend it to the generalized linear models in Chapter 5. More specifically, we propose a novel unified transfer learning model by re-defining the design matrix and the response vector in the context of the high-dimensional statistical models. To the best of our knowledge, this is the first work on unified transfer learning. The theoretical results show that it attains tighter upper bounds of the estimation errors than Lasso using the target data only, assuming the target data and source data are sufficiently close to some extent. We also prove that our bound is better than the existing methods, including a tighter minimax rate and a wider range of values for the transferring level. Detecting the transferable data, including the transferable source data and the transferable variables, is a major task in transfer learning. Our unified model is able to automatically identify the transferable variables due to its nature. We develop a hypothesis testing method and a data-driven method for source detection in Chapter 4 and Chapter 5, respectively. To the best of our knowledge, this is the first work for identifying the transferable variables by the model's nature and the first work to incorporate statistical inference in transfer learning.
This book features research contributions from The Abel Symposium on Statistical Analysis for High Dimensional Data, held in Nyvågar, Lofoten, Norway, in May 2014. The focus of the symposium was on statistical and machine learning methodologies specifically developed for inference in “big data” situations, with particular reference to genomic applications. The contributors, who are among the most prominent researchers on the theory of statistics for high dimensional inference, present new theories and methods, as well as challenging applications and computational solutions. Specific themes include, among others, variable selection and screening, penalised regression, sparsity, thresholding, low dimensional structures, computational challenges, non-convex situations, learning graphical models, sparse covariance and precision matrices, semi- and non-parametric formulations, multiple testing, classification, factor models, clustering, and preselection. Highlighting cutting-edge research and casting light on future research directions, the contributions will benefit graduate students and researchers in computational biology, statistics and the machine learning community.
• Real-world problems can be high-dimensional, complex, and noisy • More data does not imply more information • Different approaches deal with the so-called curse of dimensionality to reduce irrelevant information • A process with multidimensional information is not necessarily easy to interpret nor process • In some real-world applications, the number of elements of a class is clearly lower than the other. The models tend to assume that the importance of the analysis belongs to the majority class and this is not usually the truth • The analysis of complex diseases such as cancer are focused on more-than-one dimensional omic data • The increasing amount of data thanks to the reduction of cost of the high-throughput experiments opens up a new era for integrative data-driven approaches • Entropy-based approaches are of interest to reduce the dimensionality of high-dimensional data
Through extensive empirical studies on several large and high-dimensional image datasets, we show that our proposed approaches are able to perform data retrievals more effectively, and efficiently than traditional methods.
This modern approach integrates classical and contemporary methods, fusing theory and practice and bridging the gap to statistical learning.
This book presents the peer-reviewed proceedings of the 4th International Conference on Advanced Machine Learning Technologies and Applications (AMLTA 2019), held in Cairo, Egypt, on March 28–30, 2019, and organized by the Scientific Research Group in Egypt (SRGE). The papers cover the latest research on machine learning, deep learning, biomedical engineering, control and chaotic systems, text mining, summarization and language identification, machine learning in image processing, renewable energy, cyber security, and intelligence swarms and optimization.
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.