Coal Price Index Forecast by a New Partial Least-Squares Regression

AbstractDeviation of coal price has great influence on growth of China's economic. Daily coal price indexes in Qinhuangdao were collected. Past twenty days were used to predict next day index. The principal components of twenty days were extracted. The function between output variable and components was fitted by linear, quadratic and exponential model. This improved traditional partial least-squares regression. Traditional method such as multivariate linear regression and polynomial regression were coming into comparing with our method. Improved quadratic partial least-squares obtained the smallest relative errors in mean and variance for ten reserved indexes. Those ten errors had minimum 0.3%, median 3.3% and maximum 9.7%. The ideal forecast precision certified that quadratic partial least-squares was suitable for coal price indexes

Tensor-based regression models and applications

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2017-2018Avec l’avancement des technologies modernes, les tenseurs d’ordre élevé sont assez répandus et abondent dans un large éventail d’applications telles que la neuroscience informatique, la vision par ordinateur, le traitement du signal et ainsi de suite. La principale raison pour laquelle les méthodes de régression classiques ne parviennent pas à traiter de façon appropriée des tenseurs d’ordre élevé est due au fait que ces données contiennent des informations structurelles multi-voies qui ne peuvent pas être capturées directement par les modèles conventionnels de régression vectorielle ou matricielle. En outre, la très grande dimensionnalité de l’entrée tensorielle produit une énorme quantité de paramètres, ce qui rompt les garanties théoriques des approches de régression classique. De plus, les modèles classiques de régression se sont avérés limités en termes de difficulté d’interprétation, de sensibilité au bruit et d’absence d’unicité. Pour faire face à ces défis, nous étudions une nouvelle classe de modèles de régression, appelés modèles de régression tensor-variable, où les prédicteurs indépendants et (ou) les réponses dépendantes prennent la forme de représentations tensorielles d’ordre élevé. Nous les appliquons également dans de nombreuses applications du monde réel pour vérifier leur efficacité et leur efficacité.With the advancement of modern technologies, high-order tensors are quite widespread and abound in a broad range of applications such as computational neuroscience, computer vision, signal processing and so on. The primary reason that classical regression methods fail to appropriately handle high-order tensors is due to the fact that those data contain multiway structural information which cannot be directly captured by the conventional vector-based or matrix-based regression models, causing substantial information loss during the regression. Furthermore, the ultrahigh dimensionality of tensorial input produces huge amount of parameters, which breaks the theoretical guarantees of classical regression approaches. Additionally, the classical regression models have also been shown to be limited in terms of difficulty of interpretation, sensitivity to noise and absence of uniqueness. To deal with these challenges, we investigate a novel class of regression models, called tensorvariate regression models, where the independent predictors and (or) dependent responses take the form of high-order tensorial representations. We also apply them in numerous real-world applications to verify their efficiency and effectiveness. Concretely, we first introduce hierarchical Tucker tensor regression, a generalized linear tensor regression model that is able to handle potentially much higher order tensor input. Then, we work on online local Gaussian process for tensor-variate regression, an efficient nonlinear GPbased approach that can process large data sets at constant time in a sequential way. Next, we present a computationally efficient online tensor regression algorithm with general tensorial input and output, called incremental higher-order partial least squares, for the setting of infinite time-dependent tensor streams. Thereafter, we propose a super-fast sequential tensor regression framework for general tensor sequences, namely recursive higher-order partial least squares, which addresses issues of limited storage space and fast processing time allowed by dynamic environments. Finally, we introduce kernel-based multiblock tensor partial least squares, a new generalized nonlinear framework that is capable of predicting a set of tensor blocks by merging a set of tensor blocks from different sources with a boosted predictive power

Approximation and Relaxation Approaches for Parallel and Distributed Machine Learning

Large scale machine learning requires tradeoffs. Commonly this tradeoff has led practitioners to choose simpler, less powerful models, e.g. linear models, in order to process more training examples in a limited time. In this work, we introduce parallelism to the training of non-linear models by leveraging a different tradeoff--approximation. We demonstrate various techniques by which non-linear models can be made amenable to larger data sets and significantly more training parallelism by strategically introducing approximation in certain optimization steps. For gradient boosted regression tree ensembles, we replace precise selection of tree splits with a coarse-grained, approximate split selection, yielding both faster sequential training and a significant increase in parallelism, in the distributed setting in particular. For metric learning with nearest neighbor classification, rather than explicitly train a neighborhood structure we leverage the implicit neighborhood structure induced by task-specific random forest classifiers, yielding a highly parallel method for metric learning. For support vector machines, we follow existing work to learn a reduced basis set with extremely high parallelism, particularly on GPUs, via existing linear algebra libraries. We believe these optimization tradeoffs are widely applicable wherever machine learning is put in practice in large scale settings. By carefully introducing approximation, we also introduce significantly higher parallelism and consequently can process more training examples for more iterations than competing exact methods. While seemingly learning the model with less precision, this tradeoff often yields noticeably higher accuracy under a restricted training time budget

Tensor Regression

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies such as neuroimaging, computer vision, climatology and social networks, has brought challenges to traditional data representation methods. Tensors, as high dimensional extensions of vectors, are considered as natural representations of high dimensional data. In this book, the authors provide a systematic study and analysis of tensor-based regression models and their applications in recent years. It groups and illustrates the existing tensor-based regression methods and covers the basics, core ideas, and theoretical characteristics of most tensor-based regression methods. In addition, readers can learn how to use existing tensor-based regression methods to solve specific regression tasks with multiway data, what datasets can be selected, and what software packages are available to start related work as soon as possible. Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis. It is essential reading for all students, researchers and practitioners of working on high dimensional data.Comment: 187 pages, 32 figures, 10 table

Probabilistic Numerical Linear Algebra for Machine Learning

Machine learning models are becoming increasingly essential in domains where critical decisions must be made under uncertainty, such as in public policy, medicine or robotics. For a model to be useful for decision-making, it must convey a degree of certainty in its predictions. Bayesian models are well-suited to such settings due to their principled uncertainty quantification, given a set of assumptions about the problem and data-generating process. While in theory, inference in a Bayesian model is fully specified, in practice, numerical approximations have a significant impact on the resulting posterior. Therefore, model-based decisions are not just determined by the data but also by the numerical method. This begs the question of how we can account for the adverse impact of numerical approximations on inference. Arguably, the most common numerical task in scientific computing is the solution of linear systems, which arise in probabilistic inference, graph theory, differential equations and optimization. In machine learning, these systems are typically large-scale, subject to noise and arise from generative processes. These unique characteristics call for specialized solvers. In this thesis, we propose a class of probabilistic linear solvers, which infer the solution to a linear system and can be interpreted as learning algorithms themselves. Importantly, they can leverage problem structure and propagate their error to the prediction of the underlying probabilistic model. Next, we apply such solvers to accelerate Gaussian process inference. While Gaussian processes are a principled and flexible model class, for large datasets inference is computationally prohibitive both in time and memory due to the required computations with the kernel matrix. We show that by approximating the posterior with a probabilistic linear solver, we can invest an arbitrarily small amount of computation and still obtain a provably coherent prediction that quantifies uncertainty exactly. Finally, we demonstrate that Gaussian process hyperparameter optimization can similarly be accelerated by leveraging structural prior knowledge in the model via preconditioning of iterative methods. Combined with modern parallel hardware, this enables training Gaussian process models on datasets with hundreds of thousands of data points. In summary, we demonstrate that interpreting numerical methods in linear algebra as probabilistic learning algorithms unlocks significant performance improvements for Gaussian process models. Crucially, we show how to account for the impact of numerical approximations on model predictions via uncertainty quantification. This enables an explicit trade-off between computational resources and confidence in a prediction. The techniques developed in this thesis have advanced the understanding of probabilistic linear solvers, they have shifted the goalposts of what can be expected from Gaussian process approximations and they have defined the way large-scale Gaussian process hyperparameter optimization is performed in GPyTorch, arguably the most popular library for Gaussian processes in Python

Face Recognition and Facial Attribute Analysis from Unconstrained Visual Data

Analyzing human faces from visual data has been one of the most active research areas in the computer vision community. However, it is a very challenging problem in unconstrained environments due to variations in pose, illumination, expression, occlusion and blur between training and testing images. The task becomes even more difficult when only a limited number of images per subject is available for modeling these variations. In this dissertation, different techniques for performing classification of human faces as well as other facial attributes such as expression, age, gender, and head pose in uncontrolled settings are investigated. In the first part of the dissertation, a method for reconstructing the virtual frontal view from a given non-frontal face image using Markov Random Fields (MRFs) and an efficient variant of the Belief Propagation (BP) algorithm is introduced. In the proposed approach, the input face image is divided into a grid of overlapping patches and a globally optimal set of local warps is estimated to synthesize the patches at the frontal view. A set of possible warps for each patch is obtained by aligning it with images from a training database of frontal faces. The alignments are performed efficiently in the Fourier domain using an extension of the Lucas-Kanade (LK) algorithm that can handle illumination variations. The problem of finding the optimal warps is then formulated as a discrete labeling problem using an MRF. The reconstructed frontal face image can then be used with any face recognition technique. The two main advantages of our method are that it does not require manually selected facial landmarks as well as no head pose estimation is needed. In the second part, the task of face recognition in unconstrained settings is formulated as a domain adaptation problem. The domain shift is accounted for by deriving a latent subspace or domain, which jointly characterizes the multifactor variations using appropriate image formation models for each factor. The latent domain is defined as a product of Grassmann manifolds based on the underlying geometry of the tensor space, and recognition is performed across domain shift using statistics consistent with the tensor geometry. More specifically, given a face image from the source or target domain, multiple images of that subject are first synthesized under different illuminations, blur conditions, and 2D perturbations to form a tensor representation of the face. The orthogonal matrices obtained from the decomposition of this tensor, where each matrix corresponds to a factor variation, are used to characterize the subject as a point on a product of Grassmann manifolds. For cases with only one image per subject in the source domain, the identity of target domain faces is estimated using the geodesic distance on product manifolds. When multiple images per subject are available, an extension of kernel discriminant analysis is developed using a novel kernel based on the projection metric on product spaces. Furthermore, a probabilistic approach to the problem of classifying image sets on product manifolds is introduced. Understanding attributes such as expression, age class, and gender from face images has many applications in multimedia processing including content personalization, human-computer interaction, and facial identification. To achieve good performance in these tasks, it is important to be able to extract pertinent visual structures from the input data. In the third part of the dissertation, a fully automatic approach for performing classification of facial attributes based on hierarchical feature learning using sparse coding is presented. The proposed approach is generative in the sense that it does not use label information in the process of feature learning. As a result, the same feature representation can be applied for different tasks such as expression, age, and gender classification. Final classification is performed by linear SVM trained with the corresponding labels for each task. The last part of the dissertation presents an automatic algorithm for determining the head pose from a given face image. The face image is divided into a regular grid and represented by dense SIFT descriptors extracted from the grid points. Random Projection (RP) is then applied to reduce the dimension of the concatenated SIFT descriptor vector. Classification and regression using Support Vector Machine (SVM) are combined in order to obtain an accurate estimate of the head pose. The advantage of the proposed approach is that it does not require facial landmarks such as the eye and mouth corners, the nose tip to be extracted from the input face image as in many other methods

Object Detection in 20 Years: A Survey

Object detection, as of one the most fundamental and challenging problems in computer vision, has received great attention in recent years. Its development in the past two decades can be regarded as an epitome of computer vision history. If we think of today's object detection as a technical aesthetics under the power of deep learning, then turning back the clock 20 years we would witness the wisdom of cold weapon era. This paper extensively reviews 400+ papers of object detection in the light of its technical evolution, spanning over a quarter-century's time (from the 1990s to 2019). A number of topics have been covered in this paper, including the milestone detectors in history, detection datasets, metrics, fundamental building blocks of the detection system, speed up techniques, and the recent state of the art detection methods. This paper also reviews some important detection applications, such as pedestrian detection, face detection, text detection, etc, and makes an in-deep analysis of their challenges as well as technical improvements in recent years.Comment: This work has been submitted to the IEEE TPAMI for possible publicatio

Learning Binary Code Representations for Effective and Efficient Image Retrieval

The size of online image datasets is constantly increasing. Considering an image dataset with millions of images, image retrieval becomes a seemingly intractable problem for exhaustive similarity search algorithms. Hashing methods, which encodes high-dimensional descriptors into compact binary strings, have become very popular because of their high efficiency in search and storage capacity. In the first part, we propose a multimodal retrieval method based on latent feature models. The procedure consists of a nonparametric Bayesian framework for learning underlying semantically meaningful abstract features in a multimodal dataset, a probabilistic retrieval model that allows cross-modal queries and an extension model for relevance feedback. In the second part, we focus on supervised hashing with kernels. We describe a flexible hashing procedure that treats binary codes and pairwise semantic similarity as latent and observed variables, respectively, in a probabilistic model based on Gaussian processes for binary classification. We present a scalable inference algorithm with the sparse pseudo-input Gaussian process (SPGP) model and distributed computing. In the last part, we define an incremental hashing strategy for dynamic databases where new images are added to the databases frequently. The method is based on a two-stage classification framework using binary and multi-class SVMs. The proposed method also enforces balance in binary codes by an imbalance penalty to obtain higher quality binary codes. We learn hash functions by an efficient algorithm where the NP-hard problem of finding optimal binary codes is solved via cyclic coordinate descent and SVMs are trained in a parallelized incremental manner. For modifications like adding images from an unseen class, we propose an incremental procedure for effective and efficient updates to the previous hash functions. Experiments on three large-scale image datasets demonstrate that the incremental strategy is capable of efficiently updating hash functions to the same retrieval performance as hashing from scratch

On the predictability of U.S. stock market using machine learning and deep learning techniques

Conventional market theories are considered to be inconsistent approach in modern financial analysis. This thesis focuses mainly on the application of sophisticated machine learning and deep learning techniques in stock market statistical predictability and economic significance over the benchmark conventional efficient market hypothesis and econometric models. Five chapters and three publishable papers were proposed altogether, and each chapter is developed to solve specific identifiable problem(s). Chapter one gives the general introduction of the thesis. It presents the statement of the research problems identified in the relevant literature, the objective of the study and the significance of the study. Chapter two applies a plethora of machine learning techniques to forecast the direction of the U.S. stock market. The notable sophisticated techniques such as regularization, discriminant analysis, classification trees, Bayesian and neural networks were employed. The empirical findings revealed that the discriminant analysis classifiers, classification trees, Bayesian classifiers and penalized binary probit models demonstrate significant outperformance over the binary probit models both statistically and economically, proving significant alternatives to portfolio managers. Chapter three focuses mainly on the application of regression training (RT) techniques to forecast the U.S. equity premium. The RT models demonstrate significant evidence of equity premium predictability both statistically and economically relative to the benchmark historical average, delivering significant utility gains. Chapter four investigates the statistical predictive power and economic significance of financial stock market data by deep learning techniques. Chapter five give the summary, conclusion and present area(s) of further research. The techniques are proven to be robust both statistically and economically when forecasting the equity premium out-of-sample using recursive window method. Overall, the deep learning techniques produced the best result in this thesis. They seek to provide meaningful economic information on mean-variance portfolio investment for investors who are timing the market to earn future gains at minimal risk