Model interpretability is an increasingly important component of practical machine learning. Some of the most common forms of interpretability systems are example-based, local, and global explanations. One of the main challenges in interpretability is designing explanation systems that can capture aspects of each of these explanation types, in order to develop a more thorough understanding of the model. We address this challenge in a novel model called SLIM that uses local linear modeling techniques along with a dual interpretation of random forests (both as a supervised neighborhood approach and as a feature selection method). SLIM has two fundamental advantages over existing interpretability systems. First, while it is effective as a black-box explanation system, SLIM itself is a highly accurate predictive model that provides faithful self explanations, and thus sidesteps the typical accuracy-interpretability trade-off. Second, SLIM provides both example- based and local explanations and can detect global patterns, which allows it to diagnose limitations in its local explanations.
One of the reasons that local methods are not commonly applied on large-scale problems is that, although their learning rates are minimax optimal, this rate is conservative when not all of the features are involved in the response, as demonstrated empirically in @cite_16 . As a result, we are interested in using a supervised local method. Random forests have two main interpretations towards this: first, as an adaptive method for finding potential nearest neighbors @cite_1 and, second, as a kernel method @cite_9 . Recently, @cite_16 introduced SILO which explicitly uses random forests to define the instance weights for local linear modeling. Empirically, they found that this decreased the bias of the random forest and increased its variance, which is potentially problematic in high dimensional settings.
@cite_9 @cite_16 @cite_1
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Random forests are ensemble methods which grow trees as base learners and combine their predictions by averaging. Random forests are known for their good practical performance, particularly in high-dimensional settings. On the theoretical side, several studies highlight the potentially fruitful connection between the random forests and the kernel methods. In this paper, we work out this connection in detail. In particular, we show that by slightly modifying their definition, random forests can be rewritten as kernel methods (called KeRF for kernel based on random forests) which are more interpretable and easier to analyze. Explicit expressions of KeRF estimates for some specific random forest models are given, together with upper bounds on their rate of consistency. We also show empirically that the KeRF estimates compare favourably to the random forest estimates. In this article we study random forests through their connection with a new framework of adaptive nearest-neighbor methods. We introduce a concept of potential nearest neighbors (k-PNNs) and show that random forests can be viewed as adaptively weighted k-PNN methods. Various aspects of random forests can be studied from this perspective. We study the effect of terminal node sizes on the prediction accuracy of random forests. We further show that random forests with adaptive splitting schemes assign weights to k-PNNs in a desirable way: for the estimation at a given target point, these random forests assign voting weights to the k-PNNs of the target point according to the local importance of different input variables. We propose a new simple splitting scheme that achieves desirable adaptivity in a straightforward fashion. This simple scheme can be combined with existing algorithms. The resulting algorithm is computationally faster and gives comparable results. Other possible aspects of random forests, such...