A central problem in the context of the Web of Data, as well as in data integration in general is to identify entities in different data sources that describe the same real-world object. There exists a large body of research on entity resolution. Interestingly, most of the existing research focuses on entity resolution on dense data, meaning data that does not contain too many missing values. This paper sets a different focus and explores learning expressive linkage rules from as well as applying these rules to sparse web data, i.e. data exhibiting a large amount of missing values. Such data is a common challenge in various application domains including e-commerce, online hotel booking, or online recruiting. We propose and compare three entity resolution methods that employ genetic programming to learn expressive linkage rules from sparse data. First, we introduce the GenLinkGL algorithm which learns groups of matching rules and applies specific rules out of these groups depending on which values are missing from a pair of records. Next, we propose GenLinkSA, which employs selective aggregation operators within rules. These operators exclude misleading similarity scores (which result from missing values) from the aggregations, but on the other hand also penalize the uncertainty that results from missing values. Finally, we introduce GenLinkComb, a method which combines the central ideas of the previous two into one integrated method. We evaluate all methods using six benchmark datasets: three of them are e-commerce product datasets, the other datasets describe restaurants, movies, and drugs. We show improvements of up to 16% F-measure compared to handwritten rules, on average 12% F-measure improvement compared to the original GenLink algorithm, 15% compared to EAGLE, 8% compared to FEBRL, and 5% compared to CoSum-P.