This work gives a simultaneous analysis of both the ordinary least squares estimator and the ridge regression estimator in the random design setting under mild assumptions on the covariate/response distributions. In particular, the analysis provides sharp results on the ``out-of-sample'' prediction error, as opposed to the ``in-sample'' (fixed design) error. The analysis also reveals the effect of errors in the estimated covariance structure, as well as the effect of modeling errors, neither of which effects are present in the fixed design setting. The proofs of the main results are based on a simple decomposition lemma combined with concentration inequalities for random vectors and matrices.

The inherent nature of social media content poses serious challenges to practical applications of sentiment analysis. We present VADER, a simple rule-based model for general sentiment analysis, and compare its effectiveness to eleven typical state-of-practice benchmarks including LIWC, ANEW, the General Inquirer, SentiWordNet, and machine learning oriented techniques relying on Naive Bayes, Maximum Entropy, and Support Vector Machine (SVM) algorithms. Using a combination of qualitative and quantitative methods, we first construct and empirically validate a gold-standard list of lexical features (along with their associated sentiment intensity measures) which are specifically attuned to sentiment in microblog-like contexts. We then combine these lexical features with consideration for five general rules that embody grammatical and syntactical conventions for expressing and emphasizing sentiment intensity. Interestingly, using our parsimonious rule-based model to assess the sentiment of tweets, we find that VADER outperforms individual human raters (F1 Classification Accuracy = 0.96 and 0.84, respectively), and generalizes more favorably across contexts than any of our benchmarks.

Geographical location is vital to geospatial applications like local search and event detection. In this paper, we investigate and improve on the task of text-based geolocation prediction of Twitter users. Previous studies on this topic have typically assumed that geographical references (e.g., gazetteer terms, dialectal words) in a text are indicative of its authors location. However, these references are often buried in informal, ungrammatical, and multilingual data, and are therefore non-trivial to identify and exploit. We present an integrated geolocation prediction framework and investigate what factors impact on prediction accuracy. First, we evaluate a range of feature selection methods to obtain location indicative words. We then evaluate the impact of non-geotagged tweets, language, and user-declared metadata on geolocation prediction. In addition, we evaluate the impact of temporal variance on model generalisation, and discuss how users differ in terms of their geolocatability. We achieve state-of-the-art results for the text-based Twitter user geolocation task, and also provide the most extensive exploration of the task to date. Our findings provide valuable insights into the design of robust, practical text-based geolocation prediction systems.

There has been growing recent interest in probabilistic interpretations of kernel-based methods as well as learning in Banach spaces. The absence of a useful Lebesgue measure on an infinite-dimensional reproducing kernel Hilbert space is a serious obstacle for such stochastic models. We propose an estimation model for the ridge regression problem within the framework of abstract Wiener spaces and show how the support vector machine solution to such problems can be interpreted in terms of the Gaussian Radon transform.

Multi-label classification has attracted an increasing amount of attention in recent years. To this end, many algorithms have been developed to classify multi-label data in an effective manner. However, they usually do not consider the pairwise relations indicated by sample labels, which actually play important roles in multi-label classification. Inspired by this, we naturally extend the traditional pairwise constraints to the multi-label scenario via a flexible thresholding scheme. Moreover, to improve the generalization ability of the classifier, we adopt a boosting-like strategy to construct a multi-label ensemble from a group of base classifiers. To achieve these goals, this paper presents a novel multi-label classification framework named Variable Pairwise Constraint projection for Multi-label Ensemble (VPCME). Specifically, we take advantage of the variable pairwise constraint projection to learn a lower-dimensional data representation, which preserves the correlations between samples and labels. Thereafter, the base classifiers are trained in the new data space. For the boosting-like strategy, we employ both the variable pairwise constraints and the bootstrap steps to diversify the base classifiers. Empirical studies have shown the superiority of the proposed method in comparison with other approaches.

It is widely known in the machine learning community that class noise can be (and often is) detrimental to inducing a model of the data. Many current approaches use a single, often biased, measurement to determine if an instance is noisy. A biased measure may work well on certain data sets, but it can also be less effective on a broader set of data sets. In this paper, we present noise identification using classifier diversity (NICD) -- a method for deriving a less biased noise measurement and integrating it into the learning process. To lessen the bias of the noise measure, NICD selects a diverse set of classifiers (based on their predictions of novel instances) to determine which instances are noisy. We examine NICD as a technique for filtering, instance weighting, and selecting the base classifiers of a voting ensemble. We compare NICD with several other noise handling techniques that do not consider classifier diversity on a set of 54 data sets and 5 learning algorithms. NICD significantly increases the classification accuracy over the other considered approaches and is effective across a broad set of data sets and learning algorithms.

We consider new formulations and methods for sparse quantile regression in the high-dimensional setting. Quantile regression plays an important role in many applications, including outlier-robust exploratory analysis in gene selection. In addition, the sparsity consideration in quantile regression enables the exploration of the entire conditional distribution of the response variable given the predictors and therefore yields a more comprehensive view of the important predictors. We propose a generalized OMP algorithm for variable selection, taking the misfit loss to be either the traditional quantile loss or a smooth version we call quantile Huber, and compare the resulting greedy approaches with convex sparsity-regularized formulations. We apply a recently proposed interior point methodology to efficiently solve all convex formulations as well as convex subproblems in the generalized OMP setting, pro- vide theoretical guarantees of consistent estimation, and demonstrate the performance of our approach using empirical studies of simulated and genomic datasets.

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. COCA improves upon PCA and sparse PCA in three aspects: (i) It is robust to modeling assumptions; (ii) It is robust to outliers and data contamination; (iii) It is scale-invariant and yields more interpretable results. We prove that the COCA estimators obtain fast estimation rates and are feature selection consistent when the dimension is nearly exponentially large relative to the sample size. Careful experiments confirm that COCA outperforms sparse PCA on both synthetic and real-world datasets.

Ranking measures play an important role in model evaluation and selection. Using both synthetic and real-world data sets, we investigate how different types and levels of noise affect the area under the ROC curve (AUC), the area under the ROC convex hull, the scored AUC, the Kolmogorov-Smirnov statistic, and the H-measure. In our experiments, the AUC was, overall, the most robust among these measures, thereby reinvigorating it as a reliable metric despite its well-known deficiencies. This paper also introduces a novel ranking measure, which is remarkably robust to noise yet conceptually simple.

From a fresh data science perspective, this thesis discusses the prediction of coronary artery disease based on genetic variations at the DNA base pair level, called Single-Nucleotide Polymorphisms (SNPs), collected from the Ontario Heart Genomics Study (OHGS). First, the thesis explains two commonly used supervised learning algorithms, the k-Nearest Neighbour (k-NN) and Random Forest classifiers, and includes a complete proof that the k-NN classifier is universally consistent in any finite dimensional normed vector space. Second, the thesis introduces two dimensionality reduction steps, Random Projections, a known feature extraction technique based on the Johnson-Lindenstrauss lemma, and a new method termed Mass Transportation Distance (MTD) Feature Selection for discrete domains. Then, this thesis compares the performance of Random Projections with the k-NN classifier against MTD Feature Selection and Random Forest, for predicting artery disease based on accuracy, the F-Measure, and area under the Receiver Operating Characteristic (ROC) curve. The comparative results demonstrate that MTD Feature Selection with Random Forest is vastly superior to Random Projections and k-NN. The Random Forest classifier is able to obtain an accuracy of 0.6660 and an area under the ROC curve of 0.8562 on the OHGS genetic dataset, when 3335 SNPs are selected by MTD Feature Selection for classification. This area is considerably better than the previous high score of 0.608 obtained by Davies et al. in 2010 on the same dataset.