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Recent work proposed learned index structures, which learn the distribution of the underlying dataset to improve performance. The initial work on learned indexes has shown that by learning the cumulative distribution function of the data, index structures such as the B-Tree can improve their performance by one order of magnitude while having a smaller memory footprint. In this paper, we present COAX, a learned index for multidimensional data that, instead of learning the distribution of keys, learns the correlations between attributes of the dataset. Our approach is driven by the observation that in many datasets, values of two (or multiple) attributes are correlated. COAX exploits these correlations to reduce the dimensionality of the datasets. More precisely, we learn how to infer one (or multiple) attribute $C_d$ from the remaining attributes and hence no longer need to index attribute $C_d$. This reduces the dimensionality and hence makes the index smaller and more efficient. We theoretically investigate the effectiveness of the proposed technique based on the predictability of the FD attributes. We further show experimentally that by predicting correlated attributes in the data, we can improve the query execution time and reduce the memory overhead of the index. In our experiments, we reduce the execution time by 25% while reducing the memory footprint of the index by four orders of magnitude.