Recent empirical evidence has shown that in many real-world systems, successfully represented as networks, interactions are not limited to dyads, but often involve three or more agents at a time. These data are better described by hypergraphs, where hyperlinks encode higher-order interactions among a group of nodes. In spite of the large number of works on networks, highlighting informative hyperlinks in hypergraphs obtained from real world data is still an open problem. Here we propose an analytic approach to filter hypergraphs by identifying those hyperlinks that are over-expressed with respect to a random null hypothesis, and represent the most relevant higher-order connections. We apply our method to a class of synthetic benchmarks and to several datasets. For all cases, the method highlights hyperlinks that are more informative than those extracted with pairwise approaches. Our method provides a first way to obtain statistically validated hypergraphs, separating informative connections from redundant and noisy ones.