Search

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by early-stopped unconstrained mirror descent algorithms applied to the unregularized empirical risk. We consider the set-up of learning linear models and kernel methods for strongly convex and Lipschitz loss functions while imposing only boundedness conditions on the unknown data-generating mechanism. By completing an inequality that characterizes convexity for the squared loss, we identify an intrinsic link between offset Rademacher complexities and potential-based convergence analysis of mirror descent methods. Our observation immediately yields excess risk guarantees for the path traced by the iterates of mirror descent in terms of offset complexities of certain function classes depending only on the choice of the mirror map, initialization point, step size and the number of iterations. We apply our theory to recover, in a clean and elegant manner via rather short proofs, some of the recent results in the implicit regularization literature while also showing how to improve upon them in some settings. [ABSTRACT FROM AUTHOR]

In this paper, we perform deep neural networks for learning stationary ψ -weakly dependent processes. Such weak-dependence property includes a class of weak dependence conditions such as mixing, association ⋯ and the setting considered here covers many commonly used situations such as: regression estimation, time series prediction, time series classification ⋯ The consistency of the empirical risk minimization algorithm in the class of deep neural networks predictors is established. We achieve the generalization bound and obtain an asymptotic learning rate, which is less than O (n − 1 / α) , for all α > 2. A bound of the excess risk, for a wide class of target functions, is also derived. Applications to binary time series classification and prediction in affine causal models with exogenous covariates are carried out. Some simulation results are provided, as well as an application to the US recession data. [ABSTRACT FROM AUTHOR]

Purpose: This study on spatial analysis of child labour in India is a macro level analysis on child labour using the census data, 2011 of Government of India. The population census which is conducted once in 10 years only provides district level data on work-force distribution. The study has spatial analysis of child labour in the age group of 5–14 years in India. To assess the magnitude of the children in the labour force, district level data of Census 2011 has been used in the study. The study has made an attempt to identify the districts where there is high level of children in the labour force. This paper aims to estimate the magnitude and trends of children's workforce participation using the census data as it is the only data base, which is available at the district level since 1961 onwards. The study has made an attempt to identify the clustering of child labour across districts in India and how child labour is clustered by different background characteristics. Design/methodology/approach: The study has used ArcGIS software package, GeoDa software and local indicator of spatial association test. Findings: The findings of study reveal that the proportion of rural, total fertility rate (TFR) and poverty headcount ratio is positively associated, whereas female literacy and the pupil-teacher ratio are negatively associated with child labour. It suggests that in the hot-spot areas and areas where there is a high prevalence of child labour, there is need to increase the teacher's number at the school level to improve the teacher-pupil ratio and also suggested to promote the female education, promote family planning practices to reduce TFR in those areas for reducing the incidences of child labour. Research limitations/implications: The study also recommends that the incidences of child labour can be controlled by a comprehensive holistic action plan with the active participation of social workers. Practical implications: The promulgation of effective legislation, active involvement of judiciary and police, political will, effective poverty alleviation and income generation programmes, sensitisation of parents, corporates and media can play effective role in mitigating the incidences of child labour in India. To achieve the sustainable development goals (SDGs) adopted by world leaders in 2015 to eradicate child labour in all its forms by 2025. Social implications: The study aims to achieve the SDGs adopted by world leaders in 2015 to eradicate child labour in all its forms by 2025. Originality/value: The study is purely original and there are no such studies in Indian context by using the latest software. [ABSTRACT FROM AUTHOR]

The ranking problem has received increasing attention in both the statistical and machine learning literature. This paper considers support vector machines for ranking. Under some mild conditions, a learning rate is established. [ABSTRACT FROM AUTHOR]

The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. Ranking from binary comparisons is a ubiquitous problem in modern machine learning applications. In this paper, we consider ℓ1-norm SVM for ranking. As well known, learning with ℓ1-norm restrictions usually leads to sparsity. Moreover, instead of independently draw sample sequence, we are given sample of exponentially strongly mixing sequence. Under some mild conditions, a learning rate is established. [ABSTRACT FROM AUTHOR]

The problem of ranking is to predict or to guess the ordering between objects on the basis of their observed features. In this paper we consider ranking estimators that minimize the empirical convex risk. We prove generalization bounds for the excess risk of such estimators with rates that are faster than 1/√n. We apply our results to commonly used ranking algorithms, for instance boosting or support vector machines. Moreover, we study the performance of considered estimators on real data sets. [ABSTRACT FROM AUTHOR]