Sparse Conformal Predictors

Conformal predictors, introduced by Vovk et al. (2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. In the present paper, we propose a novel method for constructing prediction intervals for the response variable in multivariate linear models. The main emphasis is on sparse linear models, where only few of the covariates have significant influence on the response variable even if their number is very large. Our approach is based on combining the principle of conformal prediction with the $\ell_1$ penalized least squares estimator (LASSO). The resulting confidence set depends on a parameter $\epsilon>0$ and has a coverage probability larger than or equal to $1-\epsilon$. The numerical experiments reported in the paper show that the length of the confidence set is small. Furthermore, as a by-product of the proposed approach, we provide a data-driven procedure for choosing the LASSO penalty. The selection power of the method is illustrated on simulated data

Providing a Service for Interactive Online Decision Aids through Estimating Consumers\u27 Incremental Search Benefits

Consumer information search has been a focus of research nowadays, especially in the context of online business environments. One of the research questions is to determine how much information to search (i.e., when to stop searching), since extensive literature on behavior science has revealed that consumers often search either “too little” or “too much”, even with the help of existing interactive online decision aids (IODAs). In order to address this issue, this paper introduces a new approach to IODAs with effective estimation of the incremental search benefits. In doing so, the approach incorporates two important aspects into consideration, namely point estimation and distribution estimation, so as to make use of the relevant information by combining both current and historical facts in reflecting the behavioral patterns of the consumers in search. Moreover, experiments based on data provided by Netflix illustrate that the proposed approach is effective and advantageous over existing ones

Minimax semi-supervised confidence sets for multi-class classification

In this work we study the semi-supervised framework of confidence set classification with controlled expected size in minimax settings. We obtain semi-supervised minimax rates of convergence under the margin assumption and a Hölder condition on the regression function. Besides, we show that if no further assumptions are made, there is no supervised method that outperforms the semi-supervised estimator proposed in this work. We establish that the best achievable rate for any supervised method is n^{−1/2} , even if the margin assumption is extremely favorable. On the contrary, semi-supervised estimators can achieve faster rates of convergence provided that sufficiently many unlabeled samples are available. We additionally perform numerical evaluation of the proposed algorithms empirically confirming our theoretical findings

Asymptotic optimality of Transductive Confidence Machine

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