Convex Calibration Dimension for Multiclass Loss Matrices

We study consistency properties of surrogate loss functions for general multiclass learning problems, defined by a general multiclass loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be calibrated with respect to a loss matrix in this setting. We then introduce the notion of convex calibration dimension of a multiclass loss matrix, which measures the smallest `size' of a prediction space in which it is possible to design a convex surrogate that is calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, we apply our framework to study various subset ranking losses, and use the convex calibration dimension as a tool to show both the existence and non-existence of various types of convex calibrated surrogates for these losses. Our results strengthen recent results of Duchi et al. (2010) and Calauzenes et al. (2012) on the non-existence of certain types of convex calibrated surrogates in subset ranking. We anticipate the convex calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.Comment: Accepted to JMLR, pending editin

Transductive Ranking on Graphs

In ranking, one is given examples of order relationships among objects, and the goal is to learn from these examples a real-valued ranking function that induces a ranking or ordering over the object space. We consider the problem of learning such a ranking function in a transductive, graph-based setting, where the object space is finite and is represented as a graph in which vertices correspond to objects and edges encode similarities between objects. Building on recent developments in regularization theory for graphs and corresponding Laplacian-based learning methods, we develop an algorithmic framework for learning ranking functions on graphs. We derive generalization bounds for our algorithms in transductive models similar to those used to study other transductive learning problems, and give experimental evidence of the potential benefits of our framework

All slums are not equal: child health conditions among the urban poor

Increasing urbanization has resulted in a faster growth of slum population. Various agencies, especially those in developing countries are finding it difficult to respond to this situation effectively. Disparities among slums exist owing to various factors. This has led to varying degrees of health burden on the slum children. Child health conditions in slums with inadequate services are worse in comparison to relatively better served slums. Identification, mapping and assessment of all slums is important for locating the hitherto missed out slums and focusing on the neediest slums. In view of the differential vulnerabilities across slums, an urban child health program should build context appropriate and community-need-responsive approaches to improve children’s health in the slums

On Consistent Surrogate Risk Minimization and Property Elicitation

Abstract Surrogate risk minimization is a popular framework for supervised learning; property elicitation is a widely studied area in probability forecasting, machine learning, statistics and economics. In this paper, we connect these two themes by showing that calibrated surrogate losses in supervised learning can essentially be viewed as eliciting or estimating certain properties of the underlying conditional label distribution that are sufficient to construct an optimal classifier under the target loss of interest. Our study helps to shed light on the design of convex calibrated surrogates. We also give a new framework for designing convex calibrated surrogates under low-noise conditions by eliciting properties that allow one to construct 'coarse' estimates of the underlying distribution

Impact of institutions on land cover change and landscape fragmentation in an Indian dry tropical forest landscapes

Protected Areas (PAs) have been a cornerstone of conservation efforts. However, PAs have become increasingly isolated with protection. Human pressure has shifted towards the forests located outside PAs, which serve as important corridors for wildlife movement. In densely populated countries like India, connectivity across vast landscapes is not possible solely by the expansion of the PA network and requires support from local communities. The importance of local institutions has been considerably ignored due to the focus on PAs, which have limited capacity to meet local demands as well as conservation objectives for vast landscapes. This Ph.D. research integrates remote sensing, landscape ecology and institutional approaches to study social and ecological impacts of forest management institutions in a dry-deciduous forest landscape in the Vidarbha region of Maharashtra, India. The study area forms an important connection between Pench and Tadoba-Andhari Tiger Reserves. The study begins with a largescale landscape view to study the impact of different forest management regimes on forest change and fragmentation. It then zooms in to compare state and community institutions that differ in traditional norms as well as levels of local participation, assessing their effect on forests and local communities

On Consistent Surrogate Risk Minimization and Property Elicitation

Abstract Surrogate risk minimization is a popular framework for supervised learning; property elicitation is a widely studied area in probability forecasting, machine learning, statistics and economics. In this paper, we connect these two themes by showing that calibrated surrogate losses in supervised learning can essentially be viewed as eliciting or estimating certain properties of the underlying conditional label distribution that are sufficient to construct an optimal classifier under the target loss of interest. Our study helps to shed light on the design of convex calibrated surrogates. We also give a new framework for designing convex calibrated surrogates under low-noise conditions by eliciting properties that allow one to construct 'coarse' estimates of the underlying distribution