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New Zealand fixed-line telecommunications provider Chorus has announced its full-year financial results for 2015-16, reporting earnings before interest, tax, depreciation, and amortisation (EBITDA) of NZ 594 million, down by NZ 8 million due to the regulator's copper pricing decision in December. In December, the New Zealand Commerce Commission released its final pricing determination for broadband services being delivered over Chorus' legacy copper network. A breakdown of revenue saw basic copper services contribute NZ 489 million, NZ 2 million less than last year; enhanced copper contribute NZ 242 million, down from NZ 268 million; and fibre contribute NZ 133 million, up by 35.7 percent year on year from NZ 98 million. Value Added Network Services, Field Services, and Infrastructure were all down by NZ 1 million to contribute NZ 35 million, NZ 83 million, and NZ 20 million, respectively.
Robust Discriminative Clustering with Sparse Regularizers
Flammarion, Nicolas, Palaniappan, Balamurugan, Bach, Francis
Clustering high-dimensional data often requires some form of dimensionality reduction, where clustered variables are separated from "noise-looking" variables. We cast this problem as finding a low-dimensional projection of the data which is well-clustered. This yields a one-dimensional projection in the simplest situation with two clusters, and extends naturally to a multi-label scenario for more than two clusters. In this paper, (a) we first show that this joint clustering and dimension reduction formulation is equivalent to previously proposed discriminative clustering frameworks, thus leading to convex relaxations of the problem, (b) we propose a novel sparse extension, which is still cast as a convex relaxation and allows estimation in higher dimensions, (c) we propose a natural extension for the multi-label scenario, (d) we provide a new theoretical analysis of the performance of these formulations with a simple probabilistic model, leading to scalings over the form $d=O(\sqrt{n})$ for the affine invariant case and $d=O(n)$ for the sparse case, where $n$ is the number of examples and $d$ the ambient dimension, and finally, (e) we propose an efficient iterative algorithm with running-time complexity proportional to $O(nd^2)$, improving on earlier algorithms which had quadratic complexity in the number of examples.
Visualizing and Understanding Sum-Product Networks
Vergari, Antonio, Di Mauro, Nicola, Esposito, Floriana
Sum-Product Networks (SPNs) are recently introduced deep tractable probabilistic models by which several kinds of inference queries can be answered exactly and in a tractable time. Up to now, they have been largely used as black box density estimators, assessed only by comparing their likelihood scores only. In this paper we explore and exploit the inner representations learned by SPNs. We do this with a threefold aim: first we want to get a better understanding of the inner workings of SPNs; secondly, we seek additional ways to evaluate one SPN model and compare it against other probabilistic models, providing diagnostic tools to practitioners; lastly, we want to empirically evaluate how good and meaningful the extracted representations are, as in a classic Representation Learning framework. In order to do so we revise their interpretation as deep neural networks and we propose to exploit several visualization techniques on their node activations and network outputs under different types of inference queries. To investigate these models as feature extractors, we plug some SPNs, learned in a greedy unsupervised fashion on image datasets, in supervised classification learning tasks. We extract several embedding types from node activations by filtering nodes by their type, by their associated feature abstraction level and by their scope. In a thorough empirical comparison we prove them to be competitive against those generated from popular feature extractors as Restricted Boltzmann Machines. Finally, we investigate embeddings generated from random probabilistic marginal queries as means to compare other tractable probabilistic models on a common ground, extending our experiments to Mixtures of Trees.
Wasserstein Discriminant Analysis
Flamary, Rรฉmi, Cuturi, Marco, Courty, Nicolas, Rakotomamonjy, Alain
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear Discriminant Analysis (LDA), WDA selects the projection matrix that maximizes the ratio of two quantities: the dispersion of projected points coming from different classes, divided by the dispersion of projected points coming from the same class. To quantify dispersion, WDA uses regularized Wasserstein distances, rather than cross-variance measures which have been usually considered, notably in LDA. Thanks to the the underlying principles of optimal transport, WDA is able to capture both global (at distribution scale) and local (at samples scale) interactions between classes. Regularized Wasserstein distances can be computed using the Sinkhorn matrix scaling algorithm; We show that the optimization of WDA can be tackled using automatic differentiation of Sinkhorn iterations. Numerical experiments show promising results both in terms of prediction and visualization on toy examples and real life datasets such as MNIST and on deep features obtained from a subset of the Caltech dataset.
Relevant based structure learning for feature selection
Feature selection is an important task in many problems occurring in pattern recognition, bioinformatics, machine learning and data mining applications. The feature selection approach enables us to reduce the computation burden and the falling accuracy effect of dealing with huge number of features in typical learning problems. There is a variety of techniques for feature selection in supervised learning problems based on different selection metrics. In this paper, we propose a novel unified framework for feature selection built on the graphical models and information theoretic tools. The proposed approach exploits the structure learning among features to select more relevant and less redundant features to the predictive modeling problem according to a primary novel likelihood based criterion. In line with the selection of the optimal subset of features through the proposed method, it provides us the Bayesian network classifier without the additional cost of model training on the selected subset of features. The optimal properties of our method are established through empirical studies and computational complexity analysis. Furthermore the proposed approach is evaluated on a bunch of benchmark datasets based on the well-known classification algorithms. Extensive experiments confirm the significant improvement of the proposed approach compared to the earlier works.
Discovering Patterns in Time-Varying Graphs: A Triclustering Approach
Guigourรจs, Romain, Boullรฉ, Marc, Rossi, Fabrice
This paper introduces a novel technique to track structures in time varying graphs. The method uses a maximum a posteriori approach for adjusting a three-dimensional co-clustering of the source vertices, the destination vertices and the time, to the data under study, in a way that does not require any hyper-parameter tuning. The three dimensions are simultaneously segmented in order to build clusters of source vertices, destination vertices and time segments where the edge distributions across clusters of vertices follow the same evolution over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make any a priori quantization. Experiments conducted on artificial data illustrate the good behavior of the technique, and a study of a real-life data set shows the potential of the proposed approach for exploratory data analysis.
Submodular Learning and Covering with Response-Dependent Costs
We consider interactive learning and covering problems, in a setting where actions may incur different costs, depending on the response to the action. We propose a natural greedy algorithm for response-dependent costs. We bound the approximation factor of this greedy algorithm in active learning settings as well as in the general setting. We show that a different property of the cost function controls the approximation factor in each of these scenarios. We further show that in both settings, the approximation factor of this greedy algorithm is near-optimal among all greedy algorithms. Experiments demonstrate the advantages of the proposed algorithm in the response-dependent cost setting.
Robust and Sparse Regression via $\gamma$-divergence
Kawashima, Takayuki, Fujisawa, Hironori
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding divergences have been discussed. One of such divergences is the $\gamma$-divergence and the robust estimator using the $\gamma$-divergence is known for having a strong robustness. In this paper, we consider the robust and sparse regression based on $\gamma$-divergence. We extend the $\gamma$-divergence to the regression problem and show that it has a strong robustness under heavy contamination even when outliers are heterogeneous. The loss function is constructed by an empirical estimate of the $\gamma$-divergence with sparse regularization and the parameter estimate is defined as the minimizer of the loss function. To obtain the robust and sparse estimate, we propose an efficient update algorithm which has a monotone decreasing property of the loss function. Particularly, we discuss a linear regression problem with $L_1$ regularization in detail. In numerical experiments and real data analyses, we see that the proposed method outperforms past robust and sparse methods.
The new way scientists are tracking global poverty
A group of Stanford researchers is using satellite imagery and artificial intelligence to track poverty reduction efforts around the world. By combining those satellite images with machine learning -- the ability for machines to learn things without being programmed to -- scientists hope to collect data that could help the U.N. achieve its 2030 goal to eradicate poverty in a cheap and efficient manner. Collecting that data in the past has been difficult for a number of reasons. "Most countries don't collect much data, and scaling up traditional household survey-based data collection efforts would be expensive," Stanford researchers explain in a short video explaining the project. But the researchers suggest that by using "less conventional data sources," such as algorithms and satellite imagery, they can put together an "accurate, inexpensive and scalable method for estimating consumption expenditure and asset wealth."