Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Neural Networks

We present an overview of current research on artificial neural networks, emphasizing a statistical perspective. We view neural networks as parameterized graphs that make probabilistic assumptions about data, and view learning algorithms as methods for finding parameter values that look probable in the light of the data. We discuss basic issues in representation and learning, and treat some of the practical issues that arise in fitting networks to data. We also discuss links between neural networks and the general formalism of graphical models

Building Predictive Models in R Using the caret Package

The caret package, short for classification and regression training, contains numerous tools for developing predictive models using the rich set of models available in R. The package focuses on simplifying model training and tuning across a wide variety of modeling techniques. It also includes methods for pre-processing training data, calculating variable importance, and model visualizations. An example from computational chemistry is used to illustrate the functionality on a real data set and to benchmark the benefits of parallel processing with several types of models.

Restricting Supervised Learning: Feature Selection and Feature Space Partition

Many supervised learning problems are considered difficult to solve either because of the redundant features or because of the structural complexity of the generative function. Redundant features increase the learning noise and therefore decrease the prediction performance. Additionally, a number of problems in various applications such as bioinformatics or image processing, whose data are sampled in a high dimensional space, suffer the curse of dimensionality, and there are not enough observations to obtain good estimates. Therefore, it is necessary to reduce such features under consideration. Another issue of supervised learning is caused by the complexity of an unknown generative model. To obtain a low variance predictor, linear or other simple functions are normally suggested, but they usually result in high bias. Hence, a possible solution is to partition the feature space into multiple non-overlapping regions such that each region is simple enough to be classified easily. In this dissertation, we proposed several novel techniques for restricting supervised learning problems with respect to either feature selection or feature space partition. Among different feature selection methods, 1-norm regularization is advocated by many researchers because it incorporates feature selection as part of the learning process. We give special focus here on ranking problems because very little work has been done for ranking using L1 penalty. We present here a 1-norm support vector machine method to simultaneously find a linear ranking function and to perform feature subset selection in ranking problems. Additionally, because ranking is formulated as a classification task when pair-wise data are considered, it increases the computational complexity from linear to quadratic in terms of sample size. We also propose a convex hull reduction method to reduce this impact. The method was tested on one artificial data set and two benchmark real data sets, concrete compressive strength set and Abalone data set. Theoretically, by tuning the trade-off parameter between the 1-norm penalty and the empirical error, any desired size of feature subset could be achieved, but computing the whole solution path in terms of the trade-off parameter is extremely difficult. Therefore, using 1-norm regularization alone may not end up with a feature subset of small size. We propose a recursive feature selection method based on 1-norm regularization which can handle the multi-class setting effectively and efficiently. The selection is performed iteratively. In each iteration, a linear multi-class classifier is trained using 1-norm regularization, which leads to sparse weight vectors, i.e., many feature weights are exactly zero. Those zero-weight features are eliminated in the next iteration. The selection process has a fast rate of convergence. We tested our method on an earthworm microarray data set and the empirical results demonstrate that the selected features (genes) have very competitive discriminative power. Feature space partition separates a complex learning problem into multiple non-overlapping simple sub-problems. It is normally implemented in a hierarchical fashion. Different from decision tree, a leaf node of this hierarchical structure does not represent a single decision, but represents a region (sub-problem) that is solvable with respect to linear functions or other simple functions. In our work, we incorporate domain knowledge in the feature space partition process. We consider domain information encoded by discrete or categorical attributes. A discrete or categorical attribute provides a natural partition of the problem domain, and hence divides the original problem into several non-overlapping sub-problems. In this sense, the domain information is useful if the partition simplifies the learning task. However it is not trivial to select the discrete or categorical attribute that maximally simplify the learning task. A naive approach exhaustively searches all the possible restructured problems. It is computationally prohibitive when the number of discrete or categorical attributes is large. We describe a metric to rank attributes according to their potential to reduce the uncertainty of a classification task. It is quantified as a conditional entropy achieved using a set of optimal classifiers, each of which is built for a sub-problem defined by the attribute under consideration. To avoid high computational cost, we approximate the solution by the expected minimum conditional entropy with respect to random projections. This approach was tested on three artificial data sets, three cheminformatics data sets, and two leukemia gene expression data sets. Empirical results demonstrate that our method is capable of selecting a proper discrete or categorical attribute to simplify the problem, i.e., the performance of the classifier built for the restructured problem always beats that of the original problem. Restricting supervised learning is always about building simple learning functions using a limited number of features. Top Selected Pair (TSP) method builds simple classifiers based on very few (for example, two) features with simple arithmetic calculation. However, traditional TSP method only deals with static data. In this dissertation, we propose classification methods for time series data that only depend on a few pairs of features. Based on the different comparison strategies, we developed the following approaches: TSP based on average, TSP based on trend, and TSP based on trend and absolute difference amount. In addition, inspired by the idea of using two features, we propose a time series classification method based on few feature pairs using dynamic time warping and nearest neighbor

Advances in Hyperspectral Image Classification Methods for Vegetation and Agricultural Cropland Studies

Hyperspectral data are becoming more widely available via sensors on airborne and unmanned aerial vehicle (UAV) platforms, as well as proximal platforms. While space-based hyperspectral data continue to be limited in availability, multiple spaceborne Earth-observing missions on traditional platforms are scheduled for launch, and companies are experimenting with small satellites for constellations to observe the Earth, as well as for planetary missions. Land cover mapping via classification is one of the most important applications of hyperspectral remote sensing and will increase in significance as time series of imagery are more readily available. However, while the narrow bands of hyperspectral data provide new opportunities for chemistry-based modeling and mapping, challenges remain. Hyperspectral data are high dimensional, and many bands are highly correlated or irrelevant for a given classification problem. For supervised classification methods, the quantity of training data is typically limited relative to the dimension of the input space. The resulting Hughes phenomenon, often referred to as the curse of dimensionality, increases potential for unstable parameter estimates, overfitting, and poor generalization of classifiers. This is particularly problematic for parametric approaches such as Gaussian maximum likelihoodbased classifiers that have been the backbone of pixel-based multispectral classification methods. This issue has motivated investigation of alternatives, including regularization of the class covariance matrices, ensembles of weak classifiers, development of feature selection and extraction methods, adoption of nonparametric classifiers, and exploration of methods to exploit unlabeled samples via semi-supervised and active learning. Data sets are also quite large, motivating computationally efficient algorithms and implementations. This chapter provides an overview of the recent advances in classification methods for mapping vegetation using hyperspectral data. Three data sets that are used in the hyperspectral classification literature (e.g., Botswana Hyperion satellite data and AVIRIS airborne data over both Kennedy Space Center and Indian Pines) are described in Section 3.2 and used to illustrate methods described in the chapter. An additional high-resolution hyperspectral data set acquired by a SpecTIR sensor on an airborne platform over the Indian Pines area is included to exemplify the use of new deep learning approaches, and a multiplatform example of airborne hyperspectral data is provided to demonstrate transfer learning in hyperspectral image classification. Classical approaches for supervised and unsupervised feature selection and extraction are reviewed in Section 3.3. In particular, nonlinearities exhibited in hyperspectral imagery have motivated development of nonlinear feature extraction methods in manifold learning, which are outlined in Section 3.3.1.4. Spatial context is also important in classification of both natural vegetation with complex textural patterns and large agricultural fields with significant local variability within fields. Approaches to exploit spatial features at both the pixel level (e.g., co-occurrencebased texture and extended morphological attribute profiles [EMAPs]) and integration of segmentation approaches (e.g., HSeg) are discussed in this context in Section 3.3.2. Recently, classification methods that leverage nonparametric methods originating in the machine learning community have grown in popularity. An overview of both widely used and newly emerging approaches, including support vector machines (SVMs), Gaussian mixture models, and deep learning based on convolutional neural networks is provided in Section 3.4. Strategies to exploit unlabeled samples, including active learning and metric learning, which combine feature extraction and augmentation of the pool of training samples in an active learning framework, are outlined in Section 3.5. Integration of image segmentation with classification to accommodate spatial coherence typically observed in vegetation is also explored, including as an integrated active learning system. Exploitation of multisensor strategies for augmenting the pool of training samples is investigated via a transfer learning framework in Section 3.5.1.2. Finally, we look to the future, considering opportunities soon to be provided by new paradigms, as hyperspectral sensing is becoming common at multiple scales from ground-based and airborne autonomous vehicles to manned aircraft and space-based platforms