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

PUBLIC INVESTMENT IN AGRICULTURAL AND GDP GROWTH-- ANOTHER LOOK AT THE INTER SECTORAL LINKAGES AND POLICY IMPLICATIONS

Despite its reduced share in India’s GDP, agriculture continues to have a strategic importance in ensuring its overall growth and prosperity. As part of the new economic policy package introduced in the early nineties, there has been a reduction in the rate of public investment. While this may not be bad for the industrial sector, the impact of this policy on agriculture is a matter of concern, in sofar as it not only affects steady growth of agriculture but also influences the overall performance of the economy. This is more so because the agricultural sector public investment has also promoted private investment by way of what is termed as the crowding-in phenomenon. This phenomenon together with inter-sectoral linkages is used in this paper to examine the effect of higher public investment for agriculture on the stable growth of this sector as well as of the entire economy. Policy implications of this exercise are important for obvious reasons.Sectoral linkages, Public Investment, crowding-in

Sliding Wear Behaviour of Aluminum Alloy (Lm-13)Reinforced with Nano-ZrO2 Matrix Composites

In the present investigation, aluminum alloy (LM 13) is dispersed with Nano-ZrO2 particles by stir casting technique followed by the hot extrusion process. Particulate size dispersed varies from 50-80 nm and the amount of addiction varies from 2 to 10wt% in steps of 2%. The wear characteristics of the developed nano metal matrix composite are analyzed by pinon-disc dry sliding wear test against hardened steel under varying loads. Nano ZrO2 particulates have an excellent load bearing capacity under applied load in sliding process, thus enhancing the wear resistance of nano metal matrix composites. The wear resistance increases as the wt. % of reinforcement content increases in the matrix material and wear resistance decreases as the applied load increases. Wear resistance is more in nano composites as compared to the LM13 matrix material

A Study on the behaviour of Aluminium alloy (LM13) reinforced with Nano ZrO2 Particulate

The present work analyses the characteristic behaviour of the Aluminium alloy (LM13) reinforced with nano-zro2 particulates by Stir Casting technique . The experimentation is carried out by distribution nanozro2 particles of size varying from 50-80nm and quantity ranging from 2-10 wt. %. The composite synthesized is analysed and evaluated in various aspects of strength ,ductility, porosity and hardness by adapting microstructural, mechanical and fractographic techniques and it is arrived that the Nano composite developed has significantly improved strength, hardness, retains residual porosity while compromising slightly with of the resultant composite. The Al – NanoZr02 composite thus synthesised displays a significantly reduced Electrical Resistivity and Thermal conductivity

Influence of carbon & Glass Fiber Reinforcement on Flexural Strength of Epoxy Matrix Polymer Hybrid Composites

Hybrid composite materials are more attracted by the engineers because of their properties like stiffness and high specific strength which leads to the potential application in the area of aerospace, marine and automobile sectors. In the present investigation, the flexural strength and flexural modulus of carbon and glass fibers reinforced epoxy hybrid composite swere studied. The vacuum bagging technique was adopted for the fabrication of polymer hybrid composite materials. The hardness, flexural strength and flexural modulusof the hybrid composites were determined as per ASTM standards. The hardness, flexural strength and flexural modulus were improved as the fiber reinforcement contents increased in the epoxy matrix material