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In large databases, the amount and the complexity of the data calls for data summarization techniques. Such summaries are used to assist fast approximate query answering or query optimization. Histograms are a prominent class of model-free data summaries and are widely used in database systems. So-called self-tuning histograms look at query-execution results to refine themselves. An assumption with such histograms, which has not been questioned so far, is that they can learn the dataset from scratch, that is—starting with an empty bucket configuration. We show that this is not the case. Self-tuning methods are very sensitive to the initial configuration. Three major problems stem from this. Traditional self-tuning is unable to learn projections of multi-dimensional data, is sensitive to the order of queries, and reaches only local optima with high estimation errors. We show how to improve a self-tuning method significantly by starting with a carefully chosen initial configuration. We propose initialization by dense subspace clusters in projections of the data, which improves both accuracy and robustness of self-tuning. Our experiments on different datasets show that the error rate is typically halved compared to the uninitialized version. [ABSTRACT FROM AUTHOR]