Disordered quantum wires: microscopic origins of the DMPK theory and Ohm's law

We study the electronic transport properties of the Anderson model on a strip, modeling a quasi one-dimensional disordered quantum wire. In the literature, the standard description of such wires is via random matrix theory (RMT). Our objective is to firmly relate this theory to a microscopic model. We correct and extend previous work (arXiv:0912.1574) on the same topic. In particular, we obtain through a physically motivated scaling limit an ensemble of random matrices that is close to, but not identical to the standard transfer matrix ensembles (sometimes called TOE, TUE), corresponding to the Dyson symmetry classes \beta=1,2. In the \beta=2 class, the resulting conductance is the same as the one from the ideal ensemble, i.e.\ from TUE. In the \beta=1 class, we find a deviation from TOE. It remains to be seen whether or not this deviation vanishes in a thick-wire limit, which is the experimentally relevant regime. For the ideal ensembles, we also prove Ohm's law for all symmetry classes, making mathematically precise a moment expansion by Mello and Stone. This proof bypasses the explicit but intricate solution methods that underlie most previous results.Comment: Corrects and extends arXiv:0912.157

Survival ensembles by the sum of pairwise differences with application to lung cancer microarray studies

Lung cancer is among the most common cancers in the United States, in terms of incidence and mortality. In 2009, it is estimated that more than 150,000 deaths will result from lung cancer alone. Genetic information is an extremely valuable data source in characterizing the personal nature of cancer. Over the past several years, investigators have conducted numerous association studies where intensive genetic data is collected on relatively few patients compared to the numbers of gene predictors, with one scientific goal being to identify genetic features associated with cancer recurrence or survival. In this note, we propose high-dimensional survival analysis through a new application of boosting, a powerful tool in machine learning. Our approach is based on an accelerated lifetime model and minimizing the sum of pairwise differences in residuals. We apply our method to a recent microarray study of lung adenocarcinoma and find that our ensemble is composed of 19 genes, while a proportional hazards (PH) ensemble is composed of nine genes, a proper subset of the 19-gene panel. In one of our simulation scenarios, we demonstrate that PH boosting in a misspecified model tends to underfit and ignore moderately-sized covariate effects, on average. Diagnostic analyses suggest that the PH assumption is not satisfied in the microarray data and may explain, in part, the discrepancy in the sets of active coefficients. Our simulation studies and comparative data analyses demonstrate how statistical learning by PH models alone is insufficient.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS426 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Word statistics in Blogs and RSS feeds: Towards empirical universal evidence

We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words' frequencies, the empirical analysis is performed by studying classes of "frequently-equivalent" words, i.e. by grouping words depending on their frequencies. Two limiting cases are considered: the dilute limit, i.e. for those words that are used less than once a day, and the dense limit for frequent words. In both cases, extreme events occur more frequently than expected from the Poisson hypothesis. These deviations from Poisson statistics reveal non-trivial time correlations between events that are associated with bursts of activities. The distribution of waiting times is shown to behave like a stretched exponential and to have the same shape for different sets of words sharing a common frequency, thereby revealing universal features.Comment: 16 pages, 6 figure

Ensemble clustering for result diversification

This paper describes the participation of the University of Twente in the Web track of TREC 2012. Our baseline approach uses the Mirex toolkit, an open source tool that sequantially scans all the documents. For result diversification, we experimented with improving the quality of clusters through ensemble clustering. We combined clusters obtained by different clustering methods (such as LDA and K-means) and clusters obtained by using different types of data (such as document text and anchor text). Our two-layer ensemble run performed better than the LDA based diversification and also better than a non-diversification run

Ensemble of Example-Dependent Cost-Sensitive Decision Trees

Several real-world classification problems are example-dependent cost-sensitive in nature, where the costs due to misclassification vary between examples and not only within classes. However, standard classification methods do not take these costs into account, and assume a constant cost of misclassification errors. In previous works, some methods that take into account the financial costs into the training of different algorithms have been proposed, with the example-dependent cost-sensitive decision tree algorithm being the one that gives the highest savings. In this paper we propose a new framework of ensembles of example-dependent cost-sensitive decision-trees. The framework consists in creating different example-dependent cost-sensitive decision trees on random subsamples of the training set, and then combining them using three different combination approaches. Moreover, we propose two new cost-sensitive combination approaches; cost-sensitive weighted voting and cost-sensitive stacking, the latter being based on the cost-sensitive logistic regression method. Finally, using five different databases, from four real-world applications: credit card fraud detection, churn modeling, credit scoring and direct marketing, we evaluate the proposed method against state-of-the-art example-dependent cost-sensitive techniques, namely, cost-proportionate sampling, Bayes minimum risk and cost-sensitive decision trees. The results show that the proposed algorithms have better results for all databases, in the sense of higher savings.Comment: 13 pages, 6 figures, Submitted for possible publicatio

Learning Determinantal Point Processes

Determinantal point processes (DPPs), which arise in random matrix theory and quantum physics, are natural models for subset selection problems where diversity is preferred. Among many remarkable properties, DPPs offer tractable algorithms for exact inference, including computing marginal probabilities and sampling; however, an important open question has been how to learn a DPP from labeled training data. In this paper we propose a natural feature-based parameterization of conditional DPPs, and show how it leads to a convex and efficient learning formulation. We analyze the relationship between our model and binary Markov random fields with repulsive potentials, which are qualitatively similar but computationally intractable. Finally, we apply our approach to the task of extractive summarization, where the goal is to choose a small subset of sentences conveying the most important information from a set of documents. In this task there is a fundamental tradeoff between sentences that are highly relevant to the collection as a whole, and sentences that are diverse and not repetitive. Our parameterization allows us to naturally balance these two characteristics. We evaluate our system on data from the DUC 2003/04 multi-document summarization task, achieving state-of-the-art results

Evolutionary model type selection for global surrogate modeling

Due to the scale and computational complexity of currently used simulation codes, global surrogate (metamodels) models have become indispensable tools for exploring and understanding the design space. Due to their compact formulation they are cheap to evaluate and thus readily facilitate visualization, design space exploration, rapid prototyping, and sensitivity analysis. They can also be used as accurate building blocks in design packages or larger simulation environments. Consequently, there is great interest in techniques that facilitate the construction of such approximation models while minimizing the computational cost and maximizing model accuracy. Many surrogate model types exist ( Support Vector Machines, Kriging, Neural Networks, etc.) but no type is optimal in all circumstances. Nor is there any hard theory available that can help make this choice. In this paper we present an automatic approach to the model type selection problem. We describe an adaptive global surrogate modeling environment with adaptive sampling, driven by speciated evolution. Different model types are evolved cooperatively using a Genetic Algorithm ( heterogeneous evolution) and compete to approximate the iteratively selected data. In this way the optimal model type and complexity for a given data set or simulation code can be dynamically determined. Its utility and performance is demonstrated on a number of problems where it outperforms traditional sequential execution of each model type