This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. We also give conditions under which no relevant variables are excluded. Next, non-asymptotic probabilities are given for the Adaptive LASSO to select the correct sparsity pattern. We then give conditions under which the Adaptive LASSO reveals the correct sparsity pattern asymptotically. We establish that the estimates of the non-zero coefficients are asymptotically equivalent to the oracle assisted least squares estimator. This is used to show that the rate of convergence of the estimates of the non-zero coefficients is identical to the one of least squares only including the relevant covariates.

We propose a new two stage algorithm LING for large scale regression problems. LING has the same risk as the well known Ridge Regression under the fixed design setting and can be computed much faster. Our experiments have shown that LING performs well in terms of both prediction accuracy and computational efficiency compared with other large scale regression algorithms like Gradient Descent, Stochastic Gradient Descent and Principal Component Regression on both simulated and real datasets.

Time series of counts arise in a variety of forecasting applications, for which traditional models are generally inappropriate. This paper introduces a hierarchical Bayesian formulation applicable to count time series that can easily account for explanatory variables and share statistical strength across groups of related time series. We derive an efficient approximate inference technique, and illustrate its performance on a number of datasets from supply chain planning.

Social network analysis (SNA), which is a research field describing and modeling the social connection of a certain group of people, is popular among network services. Our topic words analysis project is a SNA method to visualize the topic words among emails from Obama.com to accounts registered in Columbus, Ohio. Based on Latent Dirichlet Allocation (LDA) model, a popular topic model of SNA, our project characterizes the preference of senders for target group of receptors. Gibbs sampling is used to estimate topic and word distribution. Our training and testing data are emails from the carbon-free server Datagreening.com. We use parallel computing tool BashReduce for word processing and generate related words under each latent topic to discovers typical information of political news sending specially to local Columbus receptors. Running on two instances using paralleling tool BashReduce, our project contributes almost 30% speedup processing the raw contents, comparing with processing contents on one instance locally. Also, the experimental result shows that the LDA model applied in our project provides precision rate 53.96% higher than TF-IDF model finding target words, on the condition that appropriate size of topic words list is selected.

Bayesian model averaging (BMA) is the state of the art approach for overcoming model uncertainty. Yet, especially on small data sets, the results yielded by BMA might be sensitive to the prior over the models. Credal Model Averaging (CMA) addresses this problem by substituting the single prior over the models by a set of priors (credal set). Such approach solves the problem of how to choose the prior over the models and automates sensitivity analysis. We discuss various CMA algorithms for building an ensemble of logistic regressors characterized by different sets of covariates. We show how CMA can be appropriately tuned to the case in which one is prior-ignorant and to the case in which instead domain knowledge is available. CMA detects prior-dependent instances, namely instances in which a different class is more probable depending on the prior over the models. On such instances CMA suspends the judgment, returning multiple classes. We thoroughly compare different BMA and CMA variants on a real case study, predicting presence of Alpine marmot burrows in an Alpine valley. We find that BMA is almost a random guesser on the instances recognized as prior-dependent by CMA.

Additive models play an important role in semiparametric statistics. This paper gives learning rates for regularized kernel based methods for additive models. These learning rates compare favourably in particular in high dimensions to recent results on optimal learning rates for purely nonparametric regularized kernel based quantile regression using the Gaussian radial basis function kernel, provided the assumption of an additive model is valid. Additionally, a concrete example is presented to show that a Gaussian function depending only on one variable lies in a reproducing kernel Hilbert space generated by an additive Gaussian kernel, but does not belong to the reproducing kernel Hilbert space generated by the multivariate Gaussian kernel of the same variance.

Several methods have been recently proposed for estimating sparse Gaussian graphical models using $\ell_{1}$ regularization on the inverse covariance matrix. Despite recent advances, contemporary applications require methods that are even faster in order to handle ill-conditioned high dimensional modern day datasets. In this paper, we propose a new method, G-AMA, to solve the sparse inverse covariance estimation problem using Alternating Minimization Algorithm (AMA), that effectively works as a proximal gradient algorithm on the dual problem. Our approach has several novel advantages over existing methods. First, we demonstrate that G-AMA is faster than the previous best algorithms by many orders of magnitude and is thus an ideal approach for modern high throughput applications. Second, global linear convergence of G-AMA is demonstrated rigorously, underscoring its good theoretical properties. Third, the dual algorithm operates on the covariance matrix, and thus easily facilitates incorporating additional constraints on pairwise/marginal relationships between feature pairs based on domain specific knowledge. Over and above estimating a sparse inverse covariance matrix, we also illustrate how to (1) incorporate constraints on the (bivariate) correlations and, (2) incorporate equality (equisparsity) or linear constraints between individual inverse covariance elements. Fourth, we also show that G-AMA is better adept at handling extremely ill-conditioned problems, as is often the case with real data. The methodology is demonstrated on both simulated and real datasets to illustrate its superior performance over recently proposed methods.

Stochastic Gradient Descent (SGD) is a popular optimization method which has been applied to many important machine learning tasks such as Support Vector Machines and Deep Neural Networks. In order to parallelize SGD, minibatch training is often employed. The standard approach is to uniformly sample a minibatch at each step, which often leads to high variance. In this paper we propose a stratified sampling strategy, which divides the whole dataset into clusters with low within-cluster variance; we then take examples from these clusters using a stratified sampling technique. It is shown that the convergence rate can be significantly improved by the algorithm. Encouraging experimental results confirm the effectiveness of the proposed method.

This paper provides new insight into maximizing F1 scores in the context of binary classification and also in the context of multilabel classification. The harmonic mean of precision and recall, F1 score is widely used to measure the success of a binary classifier when one class is rare. Micro average, macro average, and per instance average F1 scores are used in multilabel classification. For any classifier that produces a real-valued output, we derive the relationship between the best achievable F1 score and the decision-making threshold that achieves this optimum. As a special case, if the classifier outputs are well-calibrated conditional probabilities, then the optimal threshold is half the optimal F1 score. As another special case, if the classifier is completely uninformative, then the optimal behavior is to classify all examples as positive. Since the actual prevalence of positive examples typically is low, this behavior can be considered undesirable. As a case study, we discuss the results, which can be surprising, of applying this procedure when predicting 26,853 labels for Medline documents.

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale. In a separate strand of recent research, randomized methods have been proposed to construct features that help reveal nonlinear patterns in data. For basic tasks such as regression or classification, random features exhibit little or no loss in performance, while achieving drastic savings in computational requirements. In this paper we leverage randomness to design scalable new variants of nonlinear PCA and CCA; our ideas extend to key multivariate analysis tools such as spectral clustering or LDA. We demonstrate our algorithms through experiments on real-world data, on which we compare against the state-of-the-art. A simple R implementation of the presented algorithms is provided.