In this work, we propose a simple but effective method to interpret black-box machine learning models globally. That is, we use a compact binary tree, the interpretation tree, to explicitly represent the most important decision rules that are implicitly contained in the black-box machine learning models. This tree is learned from the contribution matrix which consists of the contributions of input variables to predicted scores for each single prediction. To generate the interpretation tree, a unified process recursively partitions the input variable space by maximizing the difference in the average contribution of the split variable between the divided spaces. We demonstrate the effectiveness of our method in diagnosing machine learning models on multiple tasks. Also, it is useful for new knowledge discovery as such insights are not easily identifiable when only looking at single predictions. In general, our work makes it easier and more efficient for human beings to understand machine learning models.
Recursive partitioning and its resulting tree structure is an intuitive way to present rule sets and model interactions between input variables. It has been used for a long time to analyze heterogeneity for subgroup analysis in survey data @cite_18 . Recently it is applied to study heterogeneous causal or treatment effects @cite_33 @cite_2 . It is a good fit for our global model interpretation task because we want to extract the rules that machine learning model finds and these rules are affected by the interactions between input variables.
@cite_18 @cite_33 @cite_2
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In regression tasks the distribution of the data is often too complex to be fitted by a single model. In contrast, partition-based models are developed where data is divided and fitted by local models. These models partition the input space and do not leverage the input-output dependency of multimodal-distributed data, and strong local models are needed to make good predictions. Addressing these problems, we propose a binary tree-structured hierarchical routing mixture of experts (HRME) model that has classifiers as non-leaf node experts and simple regression models as leaf node experts. The classifier nodes jointly soft-partition the input-output space based on the natural separateness of multimodal data. This enables simple leaf experts to be effective for prediction. Further, we develop a probabilistic framework for the HRME model, and propose a recursive Expectation-Maximization (EM) based algorithm to learn both the tree structure and the expert models. Experiments on a collection of regression tasks validate the effectiveness of our method compared to a variety of other regression models. We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step. In so doing, we extend the recursive bipartitioning methods developed by Newman [M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 103, 8577 (2006); Phys. Rev. E 74, 036104 (2006)] to allow one to consider the best available two-way and three-way divisions at each recursive step. We illustrate the method using simple "bucket brigade" examples and then apply the algorithm to examine the community structures of the coauthorship graph of network scientists and of U. S. Congressional networks inferred from roll call voting similarities. In recursive linear models, the multivariate normal joint distribution of all variables exhibits a dependence structure induced by a recursive (or acyclic) system of linear structural equations. These linear models have a long tradition and appear in seemingly unrelated regressions, structural equation modelling, and approaches to causal inference. They are also related to Gaussian graphical models via a classical representation known as a path diagram. Despite the models' long history, a number of problems remain open. In this paper, we address the problem of computing maximum likelihood estimates in the subclass of 'bow-free' recursive linear models. The term 'bow-free' refers to the condition that the errors for variables i and j be uncorrelated if variable i occurs in the structural equation for variable j. We introduce a new algorithm, termed Residual Iterative Conditional Fitting (RICF), that can be implemented using only least squares computations. In contrast to existing algorithms, RICF has clear convergence properties and yields exact maximum likelihood estimates after the first iteration whenever the MLE is available in closed form. In this paper, we present a novel method to explore semantically meaningful visual information and identify the discriminative spatiotemporal relationships between them for real-time activity recognition. Our approach infers human activities using continuous egocentric (first-person-view) videos of object manipulations in an industrial setup. In order to achieve this goal, we propose a random forest that unifies randomization, discriminative relationships mining and a Markov temporal structure. Discriminative relationships mining helps us to model relations that distinguish different activities, while randomization allows us to handle the large feature space and prevents over-fitting. The Markov temporal structure provides temporally consistent decisions during testing. The proposed random forest uses a discriminative Markov decision tree, where every nonterminal node is a discriminative classifier and the Markov structure is applied at leaf nodes. The proposed approach outperforms the state-of-the-art methods on a new challenging video dataset of assembling a pump system.