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Linear And Nonlinear Programming

How many countries are included in the 2013 HDI? The 2013 HDI covers 187 countries, the same number as in 2012 and 2011. Maintaining the same number of is the result of intensified efforts by the Human Development Report Office (HDRO) to work with international data providers and national statistical agencies to obtain required development indicators for the HDI which had been unavailable for some countries in previous years. For a full explanation of the results and methodology of the 2013HDI and other indexes in the 2014 Human Development Report, please see the Technical Notes 1-5. What does the HDI tell us? The HDI was created to emphasize that people and their capabilities should be the ultimate criteria for assessing the development of a country, not economic growth alone. The HDI can also be used to question national policy choices, asking how two countries with the same level of GNI per capita can end up with different human development outcomes. For example, Malaysia has GNI per capita higher than Chile but life expectancy at birth is about 5 years shorter, mean years of schooling is shorter and expected years of schooling is 2.5 years shorter resulting in Chile having a much higher HDI value than the Malaysia. These striking contrasts can stimulate debate about government policy priorities. Did the HDI rankings change for many countries in 2013? Based on the consistent data series that were available on 15 November 2013, there are few countries with changed ranks between 2012 and 2013. The HDI values for 2012 and 2013 are given in Table 1 of Statistical Annex. The HDI trends since 1980 are given in Table 2. In this table we also provide the change in ranks between 2008 and 2013. We advise users of the HDR not to compare the results from different Reports, but to use the consistent data given in Table 2 of the latest report. The consistent data are based on the latest data revisions and are obtained using the same methodology. The effect of change in achievements (improvement or declining) in human development indicators of

human Development Index

This paper provides a composite indicator of well-being for the 35 OECD countries, as well as South Africa, Russia and Brazil for the period 2013–2016, considering data on 10 different well-being domains from the OECD Better Life Index. In a first stage, countries are ranked according to their well-being indicator, constructed combining Data Envelopment Analysis with the Benefit-of-the-Doubt principle and Multi-Criteria-Decision-Making techniques. In a second stage, well-being clubs are identified using hierarchical cluster analysis, revealing that well-being is highly polarised. Moreover, as well-being affects people, population size is accounted for in the cluster analysis, showing that for the largest proportion of people in our sample, well-being is remarkably low.

OECD: One or Many? Ranking Countries with a Composite Well-Being Indicator

The Wasserstein metric or earth mover’s distance is a useful tool in statistics, computer science and engineering with many applications to biological or medical imaging, among others. Especially in the light of increasingly complex data, the computation of these distances via optimal transport is often the limiting factor. Inspired by this challenge, a variety of new approaches to optimal transport has been proposed in recent years and along with these new methods comes the need for a meaningful comparison. In this paper, we introduce a benchmark for discrete optimal transport, called DOTmark, which is designed to serve as a neutral collection of problems, where discrete optimal transport methods can be tested, compared with one another, and brought to their limits on large-scale instances. It consists of a variety of grayscale images, in various resolutions and classes, such as several types of randomly generated images, classical test images and real data from microscopy. Along with the DOTmark we present a survey and a performance test for a cross section of established methods ranging from more traditional algorithms, such as the transportation simplex, to recently developed approaches, such as the shielding neighborhood method, and including also a comparison with commercial solvers.

DOTmark – A Benchmark for Discrete Optimal Transport

Transport-based techniques for signal and data analysis have received increased attention recently. Given their abilities to provide accurate generative models for signal intensities and other data distributions, they have been used in a variety of applications including content-based retrieval, cancer detection, image super-resolution, and statistical machine learning, to name a few, and shown to produce state of the art in several applications. Moreover, the geometric characteristics of transport-related metrics have inspired new kinds of algorithms for interpreting the meaning of data distributions. Here we provide an overview of the mathematical underpinnings of mass transport-related methods, including numerical implementation, as well as a review, with demonstrations, of several applications.

Transport-based analysis, modeling, and learning from signal and data distributions.

We present a method of rank-optimal weighting which can be used to explore the best possible position of a subject in a ranking based on a composite indicator by means of a mathematical optimization problem. As an example, we explore the dataset of the OECD Better Life Index and compute for each country a weight vector which brings it as far up in the ranking as possible with the greatest advance of the immediate rivals. The method is able to answer the question “What is the best possible rank a country can achieve with a given set of weighted indicators?” Typically, weights in composite indicators are justified normatively and not empirically. Our approach helps to give bounds on what is achievable by such normative judgments from a purely output-oriented and strongly competitive perspective. The method can serve as a basis for exact bounds in sensitivity analysis focused on ranking positions. In the OECD Better Life Index data we find that 19 out the 36 countries in the OECD Better Life Index 2014 can be brought to the top of the ranking by specific weights. We give a table of weights for each country which brings it to its highest possible position. Many countries achieve their best rank by focusing on their strong dimensions and setting the weights of many others to zero. Although setting dimensions to zero is possible in the OECD’s online tool, this contradicts the idea of better life being multidimensional in essence. We discuss modifications of the optimization problem which could take this into account, e.g. by allowing only a minimal weight of one. Methods to find rank-optimal weights can be useful for various multidimensional datasets like the ones used to rank universities or employers.

Rank-Optimal Weighting or “How to be Best in the OECD Better Life Index?”

We propose sparse reconstruction techniques to improve the quality and/or reduce the bit-rate of standard speech coders. To that end, we assume signal sparsity in some transform domain and formulate the problem of reconstructing the original signal in terms of constrained l1-norm minimization. We use modern primal-dual methods in order to solve the resulting non-smooth convex optimization problem. Experiments show that with the proposed sparse reconstruction method the instrumentally predicted speech quality can be largely improved.

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Sparse reconstruction of quantized speech signals

We introduce a method to improve the quality of simple scalar quantization in the context of acoustic sensor networks by combining ideas from sparse reconstruction, artificial neural networks and weighting filters. We start from the observation that optimization methods based on sparse reconstruction resemble the structure of a neural network. Hence, building upon a successful enhancement method, we unroll the algorithms and use this to build a neural network which we train to obtain enhanced decoding. In addition, the weighting filter from code-excited linear predictive (CELP) speech coding is integrated into the loss function of the neural network, achieving perceptually improved reconstructed speech. Our experiments show that our proposed trained methods allow for better speech reconstruction than the reference optimization methods.

Learning to Dequantize Speech Signals by Primal-dual Networks: an Approach for Acoustic Sensor Networks

We consider the entropic regularization of discretized optimal transport and propose to solve its optimality conditions via a logarithmic Newton iteration. We show a quadratic convergence rate and validate numerically that the method compares favorably with the more commonly used Sinkhorn--Knopp algorithm for small regularization strength. We further investigate numerically the robustness of the proposed method with respect to parameters such as the mesh size of the discretization.

A Sinkhorn-Newton method for entropic optimal transport

We investigate the problem of decomposing an image into three parts, namely a cartoon part, a texture part and a noise part. We argue that norms originating in the theory of optimal transport should have the ability to distinguish certain noise types from textures. Hence, we present a brief introduction to optimal transport metrics and show their relation to previously proposed texture norms. We propose different variational models and investigate their performance.

Christoph Brauer

Papers

Rank-Optimal Weighting or “How to be Best in the OECD Better Life Index?”

Sparse reconstruction of quantized speech signals

Learning to Dequantize Speech Signals by Primal-dual Networks: an Approach for Acoustic Sensor Networks

A Sinkhorn-Newton method for entropic optimal transport

Cartoon-Texture-Noise Decomposition with Transport Norms