Semantic Document Distance Measures and Unsupervised Document Revision Detection

In this paper, we model the document revision detection problem as a minimum cost branching problem that relies on computing document distances. Furthermore, we propose two new document distance measures, word vector-based Dynamic Time Warping (wDTW) and word vector-based Tree Edit Distance (wTED). Our revision detection system is designed for a large scale corpus and implemented in Apache Spark. We demonstrate that our system can more precisely detect revisions than state-of-the-art methods by utilizing the Wikipedia revision dumps https://snap.stanford.edu/data/wiki-meta.html and simulated data sets.

L1-norm Kernel PCA

We present the first model and algorithm for L1-norm kernel PCA. While L2-norm kernel PCA has been widely studied, there has been no work on L1-norm kernel PCA. For this non-convex and non-smooth problem, we offer geometric understandings through reformulations and present an efficient algorithm where the kernel trick is applicable. To attest the efficiency of the algorithm, we provide a convergence analysis including linear rate of convergence. Moreover, we prove that the output of our algorithm is a local optimal solution to the L1-norm kernel PCA problem. We also numerically show its robustness when extracting principal components in the presence of influential outliers, as well as its runtime comparability to L2-norm kernel PCA. Lastly, we introduce its application to outlier detection and show that the L1-norm kernel PCA based model outperforms especially for high dimensional data.

Unsupervised Terminological Ontology Learning based on Hierarchical Topic Modeling

In this paper, we present hierarchical relationbased latent Dirichlet allocation (hrLDA), a data-driven hierarchical topic model for extracting terminological ontologies from a large number of heterogeneous documents. In contrast to traditional topic models, hrLDA relies on noun phrases instead of unigrams, considers syntax and document structures, and enriches topic hierarchies with topic relations. Through a series of experiments, we demonstrate the superiority of hrLDA over existing topic models, especially for building hierarchies. Furthermore, we illustrate the robustness of hrLDA in the settings of noisy data sets, which are likely to occur in many practical scenarios. Our ontology evaluation results show that ontologies extracted from hrLDA are very competitive with the ontologies created by domain experts.

Bayesian Network Learning via Topological Order

We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of constraints compared to popular MIP models based on cycle elimination constraints and triangular inequalities. The proposed iterative algorithms use gradient descent and iterative reordering approaches, respectively, for searching topological orders. A computational experiment is presented for the Gaussian Bayesian network learning problem, an optimization problem minimizing the sum of squared errors of regression models with L1 penalty over a feature network with application of gene network inference in bioinformatics.

Classification-based Financial Markets Prediction using Deep Neural Networks

Deep neural networks (DNNs) are powerful types of artificial neural networks (ANNs) that use several hidden layers. They have recently gained considerable attention in the speech transcription and image recognition community (Krizhevsky et al., 2012) for their superior predictive properties including robustness to overfitting. However their application to algorithmic trading has not been previously researched, partly because of their computational complexity. This paper describes the application of DNNs to predicting financial market movement directions. In particular we describe the configuration and training approach and then demonstrate their application to backtesting a simple trading strategy over 43 different Commodity and FX future mid-prices at 5-minute intervals. All results in this paper are generated using a C++ implementation on the Intel Xeon Phi co-processor which is 11.4x faster than the serial version and a Python strategy backtesting environment both of which are available as open source code written by the authors.

Improving the Expected Improvement Algorithm

The expected improvement (EI) algorithm is a popular strategy for information collection in optimization under uncertainty. The algorithm is widely known to be too greedy, but nevertheless enjoys wide use due to its simplicity and ability to handle uncertainty and noise in a coherent decision theoretic framework. To provide rigorous insight into EI, we study its properties in a simple setting of Bayesian optimization where the domain consists of a finite grid of points. This is the so-called best-arm identification problem, where the goal is to allocate measurement effort wisely to confidently identify the best arm using a small number of measurements. In this framework, one can show formally that EI is far from optimal. To overcome this shortcoming, we introduce a simple modification of the expected improvement algorithm. Surprisingly, this simple change results in an algorithm that is asymptotically optimal for Gaussian best-arm identification problems, and provably outperforms standard EI by an order of magnitude.

Convergence Analysis of Batch Normalization for Deep Neural Nets

Batch normalization (BN) is very effective in accelerating the convergence of a neural network training phase that it has become a common practice. We propose a generalization of BN, the diminishing batch normalization (DBN) algorithm. We provide an analysis of the convergence of the DBN algorithm that converges to a stationary point with respect to trainable parameters. We analyze a two layer model with linear activation. The main challenge of the analysis is the fact that some parameters are updated by gradient while others are not. In the numerical experiments, we use models with more layers and ReLU activation. We observe that DBN outperforms the original BN algorithm on MNIST, NI and CIFAR-10 datasets with reasonable complex FNN and CNN models.

Optimization for Large-Scale Machine Learning with Distributed Features and Observations

As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine learning and predictive modeling, distributed optimization methods have recently garnered ample attention in the literature. Although previous research has mostly focused on settings where either the observations, or features of the problem at hand are stored in distributed fashion, the situation where both are partitioned across the nodes of a computer cluster (doubly distributed) has barely been studied. In this work we propose two doubly distributed optimization algorithms. The first one falls under the umbrella of distributed dual coordinate ascent methods, while the second one belongs to the class of stochastic gradient/coordinate descent hybrid methods. We conduct numerical experiments in Spark using real-world and simulated data sets and study the scaling properties of our methods. Our empirical evaluation of the proposed algorithms demonstrates the out-performance of a block distributed ADMM method, which, to the best of our knowledge is the only other existing doubly distributed optimization algorithm.

Activation Ensembles for Deep Neural Networks

Many activation functions have been proposed in the past, but selecting an adequate one requires trial and error. We propose a new methodology of designing activation functions within a neural network at each layer. We call this technique an "activation ensemble" because it allows the use of multiple activation functions at each layer. This is done by introducing additional variables, $\alpha$, at each activation layer of a network to allow for multiple activation functions to be active at each neuron. By design, activations with larger $\alpha$ values at a neuron is equivalent to having the largest magnitude. Hence, those higher magnitude activations are "chosen" by the network. We implement the activation ensembles on a variety of datasets using an array of Feed Forward and Convolutional Neural Networks. By using the activation ensemble, we achieve superior results compared to traditional techniques. In addition, because of the flexibility of this methodology, we more deeply explore activation functions and the features that they capture.

Regularization for Unsupervised Deep Neural Nets

Unsupervised neural networks, such as restricted Boltzmann machines (RBMs) and deep belief networks (DBNs), are powerful tools for feature selection and pattern recognition tasks. We demonstrate that overfitting occurs in such models just as in deep feedforward neural networks, and discuss possible regularization methods to reduce overfitting. We also propose a "partial" approach to improve the efficiency of Dropout/DropConnect in this scenario, and discuss the theoretical justification of these methods from model convergence and likelihood bounds. Finally, we compare the performance of these methods based on their likelihood and classification error rates for various pattern recognition data sets.