Altitude Training: Strong Bounds for Single-Layer Dropout

Dropout training, originally designed for deep neural networks, has been successful on high-dimensional single-layer natural language tasks. This paper proposes a theoretical explanation for this phenomenon: we show that, under a generative Poisson topic model with long documents, dropout training improves the exponent in the generalization bound for empirical risk minimization. Dropout achieves this gain much like a marathon runner who practices at altitude: once a classifier learns to perform reasonably well on training examples that have been artificially corrupted by dropout, it will do very well on the uncorrupted test set. We also show that, under similar conditions, dropout preserves the Bayes decision boundary and should therefore induce minimal bias in high dimensions.Comment: Advances in Neural Information Processing Systems (NIPS), 201

Consistency in Models for Distributed Learning under Communication Constraints

Motivated by sensor networks and other distributed settings, several models for distributed learning are presented. The models differ from classical works in statistical pattern recognition by allocating observations of an independent and identically distributed (i.i.d.) sampling process amongst members of a network of simple learning agents. The agents are limited in their ability to communicate to a central fusion center and thus, the amount of information available for use in classification or regression is constrained. For several basic communication models in both the binary classification and regression frameworks, we question the existence of agent decision rules and fusion rules that result in a universally consistent ensemble. The answers to this question present new issues to consider with regard to universal consistency. Insofar as these models present a useful picture of distributed scenarios, this paper addresses the issue of whether or not the guarantees provided by Stone's Theorem in centralized environments hold in distributed settings.Comment: To appear in the IEEE Transactions on Information Theor

Feature Augmentation via Nonparametrics and Selection (FANS) in High Dimensional Classification

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.Comment: 30 pages, 2 figure

Naive Feature Selection: Sparsity in Naive Bayes

Due to its linear complexity, naive Bayes classification remains an attractive supervised learning method, especially in very large-scale settings. We propose a sparse version of naive Bayes, which can be used for feature selection. This leads to a combinatorial maximum-likelihood problem, for which we provide an exact solution in the case of binary data, or a bound in the multinomial case. We prove that our bound becomes tight as the marginal contribution of additional features decreases. Both binary and multinomial sparse models are solvable in time almost linear in problem size, representing a very small extra relative cost compared to the classical naive Bayes. Numerical experiments on text data show that the naive Bayes feature selection method is as statistically effective as state-of-the-art feature selection methods such as recursive feature elimination, $l_1$-penalized logistic regression and LASSO, while being orders of magnitude faster. For a large data set, having more than with $1.6$ million training points and about $12$ million features, and with a non-optimized CPU implementation, our sparse naive Bayes model can be trained in less than 15 seconds

Predicting regression test failures using genetic algorithm-selected dynamic performance analysis metrics

A novel framework for predicting regression test failures is proposed. The basic principle embodied in the framework is to use performance analysis tools to capture the runtime behaviour of a program as it executes each test in a regression suite. The performance information is then used to build a dynamically predictive model of test outcomes. Our framework is evaluated using a genetic algorithm for dynamic metric selection in combination with state-of-the-art machine learning classifiers. We show that if a program is modified and some tests subsequently fail, then it is possible to predict with considerable accuracy which of the remaining tests will also fail which can be used to help prioritise tests in time constrained testing environments