A Survey on Metric Learning for Feature Vectors and Structured Data

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning and related fields for the past ten years. This survey paper proposes a systematic review of the metric learning literature, highlighting the pros and cons of each approach. We pay particular attention to Mahalanobis distance metric learning, a well-studied and successful framework, but additionally present a wide range of methods that have recently emerged as powerful alternatives, including nonlinear metric learning, similarity learning and local metric learning. Recent trends and extensions, such as semi-supervised metric learning, metric learning for histogram data and the derivation of generalization guarantees, are also covered. Finally, this survey addresses metric learning for structured data, in particular edit distance learning, and attempts to give an overview of the remaining challenges in metric learning for the years to come.Comment: Technical report, 59 pages. Changes in v2: fixed typos and improved presentation. Changes in v3: fixed typos. Changes in v4: fixed typos and new method

An Empirical Analysis of Predictive Machine Learning Algorithms on High-Dimensional Microarray Cancer Data

This research evaluates pattern recognition techniques on a subclass of big data where the dimensionality of the input space p is much larger than the number of observations n. Seven gene-expression microarray cancer datasets, where the ratio κ = n/p is less than one, were chosen for evaluation. The statistical and computational challenges inherent with this type of high-dimensional low sample size (HDLSS) data were explored. The capability and performance of a diverse set of machine learning algorithms is presented and compared. The sparsity and collinearity of the data being employed, in conjunction with the complexity of the algorithms studied, demanded rigorous and careful tuning of the hyperparameters and regularization parameters. This necessitated several extensions of cross-validation to be investigated, with the purpose of culminating in the best predictive performance. For the techniques evaluated in this thesis, regularization or kernelization, and often both, produced lower classification error rates than randomized ensemble for all datasets used in this research. However, no one technique evaluated for classifying HDLSS microarray cancer data emerged as the universally best technique for predicting the generalization error.1 From the empirical analysis performed in this thesis, the following fundamentals emerged as being instrumental in consistently resulting in lower error rates when estimating the generalization error in this HDLSS microarray cancer data: • Thoroughly investigate and understand the data • Stratify during all sampling due to the uneven classes and extreme sparsity of this data. • Perform 3 to 5 replicates of stratified cross-validation, implementing an adaptive K-fold, to determine the optimal tuning parameters. • To estimate the generalization error in HDLSS data, replication is paramount. Replicate R=500 or R=1000 times with training and test sets of 2/3 and 1/3, respectively, to get the best generalization error estimate. • Whenever possible, obtain an independent validation dataset. • Seed the data for a fair and unbiased comparison among techniques. • Define a methodology or standard set of process protocols to apply to machine learning research. This would prove very beneficial in ensuring reproducibility and would enable better comparisons among techniques. _____ 1A predominant portion of this research was published in the Serdica Journal of Computing (Volume 8, Number 2, 2014) as proceedings from the 2014 Flint International Statistical Conference at Kettering University, Michigan, USA

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