Typical RNA sequencing (RNA-seq) experiments uncover hundreds of splicing changes, reflecting underlying changes in splicing factor (SF) activity. Understanding how SF activity influences transcriptomic variation requires elucidating how each SF impacts splicing. Here, we present an interpretable regression model, KATMAP, which models splicing changes throughout the transcriptome by analyzing changes in SF binding and the resulting alterations in RNA processing. To learn a regulatory model, KATMAP requires SF perturbation RNA-seq data and the SF's binding motif as inputs, returning a description of the SF's position-specific regulatory activity and predicted targets. The KATMAP software includes models pretrained on ENCODE SF knockdown data. Learned KATMAP models can be applied to predict SF regulation and cis-elements at individual exons, which can guide the design of splice-switching antisense oligonucleotides. KATMAP can also interpret RNA-seq data by uncovering the factors responsible for transcriptomic changes, distinguishing direct SF targets from indirect effects and inferring relevant SFs from clinical RNA-seq data.