Measuring the relationship between any pair of variables is a rich and active area of research that is central to scientific practice. In contrast, characterizing the common information among any group of variables is typically a theoretical exercise with few practical methods for high-dimensional data. A promising solution would be a multivariate generalization of the famous Wyner common information, but this approach relies on solving an apparently intractable optimization problem. We leverage the recently introduced information sieve decomposition to formulate an incremental version of the common information problem that admits a simple fixed point solution, fast convergence, and complexity that is linear in the number of variables. This scalable approach allows us to demonstrate the usefulness of common information in high-dimensional learning problems. The sieve outperforms standard methods on dimensionality reduction tasks, solves a blind source separation problem that cannot be solved with ICA, and accurately recovers structure in brain imaging data.
Insofar as the sieve reduces the dependence in the data, it can be seen as an alternate approach to independent component analysis @cite_14 that is more directly comparable to least dependent component analysis'' @cite_3 . As an information theoretic learning framework, the sieve could be compared to the information bottleneck @cite_4 , which also has an interesting Gaussian counterpart @cite_37 . The bottleneck requires labeled data to define its objective. In contrast, the sieve relies on an unsupervised objective that fits more closely into a recent program for decomposing information in high-dimensional data @cite_6 @cite_19 @cite_33 , except that work focused on discrete latent factors.
@cite_37 @cite_14 @cite_4 @cite_33 @cite_6 @cite_3 @cite_19
2057546223 2605253252 2123469175 2793731154
Developers of rapidly growing applications must be able to anticipate potential scalability problems before they cause performance issues in production environments. A new type of data independence, called scale independence, seeks to address this challenge by guaranteeing a bounded amount of work is required to execute all queries in an application, independent of the size of the underlying data. While optimization strategies have been developed to provide these guarantees for the class of queries that are scale-independent when executed using simple indexes, there are important queries for which such techniques are insufficient. Executing these more complex queries scale-independently requires precomputation using incrementally-maintained materialized views. However, since this precomputation effectively shifts some of the query processing burden from execution time to insertion time, a scale-independent system must be careful to ensure that storage and maintenance costs do not threaten scalability. In this paper, we describe a scale-independent view selection and maintenance system, which uses novel static analysis techniques that ensure that created views do not themselves become scaling bottlenecks. Finally, we present an empirical analysis that includes all the queries from the TPC-W benchmark and validates our implementation's ability to maintain nearly constant high-quantile query and update latency even as an application scales to hundreds of machines. New classifier-independent, dynamic, unsupervised approach for detecting concept drift.Reduced number of false alarms and increased relevance of drift detection.Results comparable to supervised approaches, which require fully labeled streams.Our approach generalizes the notion of margin density, as a signal to detect drifts.Experiments on cybersecurity datasets, show efficacy for detecting adversarial drifts. Classifiers deployed in the real world operate in a dynamic environment, where the data distribution can change over time. These changes, referred to as concept drift, can cause the predictive performance of the classifier to drop over time, thereby making it obsolete. To be of any real use, these classifiers need to detect drifts and be able to adapt to them, over time. Detecting drifts has traditionally been approached as a supervised task, with labeled data constantly being used for validating the learned model. Although effective in detecting drifts, these techniques are impractical, as labeling is a difficult, costly and time consuming activity. On the other hand, unsupervised change detection techniques are unreliable, as they produce a large number of false alarms. The inefficacy of the unsupervised techniques stems from the exclusion of the characteristics of the learned classifier, from the detection process. In this paper, we propose the Margin Density Drift Detection (MD3) algorithm, which tracks the number of samples in the uncertainty region of a classifier, as a metric to detect drift. The MD3 algorithm is a distribution independent, application independent, model independent, unsupervised and incremental algorithm for reliably detecting drifts from data streams. Experimental evaluation on 6 drift induced datasets and 4 additional datasets from the cybersecurity domain demonstrates that the MD3 approach can reliably detect drifts, with significantly fewer false alarms compared to unsupervised feature based drift detectors. At the same time, it produces performance comparable to that of a fully labeled drift detector. The reduced false alarms enables the signaling of drifts only when they are most likely to affect classification performance. As such, the MD3 approach leads to a detection scheme which is credible, label efficient and general in its applicability. The Information Bottleneck is an information theoretic framework that finds concise representations for an 'input' random variable that are as relevant as possible for an 'output' random variable. This framework has been used successfully in various supervised and unsupervised applications. However, its learning theoretic properties and justification remained unclear as it differs from standard learning models in several crucial aspects, primarily its explicit reliance on the joint input-output distribution. In practice, an empirical plug-in estimate of the underlying distribution has been used, so far without any finite sample performance guarantees. In this paper we present several formal results that address these difficulties. We prove several finite sample bounds, which show that the information bottleneck can provide concise representations with good generalization, based on smaller sample sizes than needed to estimate the underlying distribution. The bounds are non-uniform and adaptive to the complexity of the specific model chosen. Based on these results, we also present a preliminary analysis on the possibility of analyzing the information bottleneck method as a learning algorithm in the familiar performance-complexity tradeoff framework. In addition, we formally describe the connection between the information bottleneck and minimal sufficient statistics. We present a formulation of deep learning that aims at producing a large margin classifier. The notion of margin, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any norm on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random adversarial input transform) and regularization techniques (such as weight decay, dropout, and batch norm).