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Influential diagnosis is an integral part of data analysis, of which mostexisting methodological frameworks presume a deterministic submodel and aredesigned for low-dimensional data (i.e., the number of predictors p smallerthan the sample size n). However, the stochastic selection of a submodel fromhigh-dimensional data where p exceeds n has become ubiquitous. Thus, methodsfor identifying observations that could exert undue influence on the choice ofa submodel can play an important role in this setting. To date, discussion ofthis topic has been limited, falling short in two domains: (i) constrainedability to detect multiple influential points, and (ii) applicability only inrestrictive settings. After describing the problem, we characterize andformalize the concept of influential observations on variable selection. Then,we propose a generalized diagnostic measure, extended from an available metricaccommodating different model selectors and multiple influential observations,the asymptotic distribution of which is subsequently establish large p, thusproviding guidelines to ascertain influential observations. A high-dimensionalclustering procedure is further incorporated into our proposed scheme to detectmultiple influential points. Simulation is conducted to assess the performancesof various diagnostic approaches. The proposed procedure further demonstratesits value in improving predictive power when analyzing thermal-stimulated painbased on fMRI data.

Assessing Influential Observations in Pain Prediction using fMRI Data