We propose to use a discriminative classifier for outlier detection in large-scale point clouds of cities generated via multi-view stereo (MVS) from densely acquired images. What makes outlier removal hard are varying distributions of inliers and outliers across a scene. Heuristic outlier removal using a specific feature that encodes point distribution often delivers unsatisfying results. Although most outliers can be identified correctly (high recall), many inliers are erroneously removed (low precision), too. This aggravates object 3D reconstruction due to missing data. We thus propose to discriminatively learn class-specific distributions directly from the data to achieve high precision. We apply a standard Random Forest classifier that infers a binary label (inlier or outlier) for each 3D point in the raw, unfiltered point cloud and test two approaches for training. In the first, non-semantic approach, features are extracted without considering the semantic interpretation of the 3D points. The trained model approximates the average distribution of inliers and outliers across all semantic classes. Second, semantic interpretation is incorporated into the learning process, i.e. we train separate inlieroutlier classifiers per semantic class (building facades, roof, ground, vegetation, fields, and water). Performance of learned filtering is evaluated on several large SfM point clouds of cities. We find that results confirm our underlying assumption that discriminatively learning inlier-outlier distributions does improve precision over global heuristics by up to ≈ 12 percent points. Moreover, semantically informed filtering that models class-specific distributions further improves precision by up to ≈ 10 percent points, being able to remove very isolated building, roof, and water points while preserving inliers on building facades and vegetation.