Mendelian randomization (MR) is a common tool for identifying causal risk factors underlying diseases. Here, we present a method, MR with automated instrument determination (MRAID), for effective MR analysis. MRAID borrows ideas from fine-mapping analysis to model an initial set of candidate single-nucleotide polymorphisms that are in potentially high linkage disequilibrium with each other and automatically selects among them the suitable instruments for causal inference. MRAID also explicitly models both uncorrelated and correlated horizontal pleiotropic effects that are widespread for complex trait analysis. MRAID achieves both tasks through a joint likelihood framework and relies on a scalable sampling-based algorithm to compute calibrated P values. Comprehensive and realistic simulations show that MRAID can provide calibrated type I error control and reduce false positives while being more powerful than existing approaches. We illustrate the benefits of MRAID for an MR screening analysis across 645 trait pairs in U.K. Biobank, identifying multiple lifestyle causal risk factors of cardiovascular disease-related traits.