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We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…
In regression problems where covariates are naturally organized in a hierarchical tree structure, a central challenge is to select the resolution at which covariates enter the model. Determining this level of feature aggregation is of…
Exploiting the great expressive power of Deep Neural Network architectures, relies on the ability to train them. While current theoretical work provides, mostly, results showing the hardness of this task, empirical evidence usually differs…
Data imputation, the process of filling in missing feature elements for incomplete data sets, plays a crucial role in data-driven learning. A fundamental belief is that data imputation is helpful for learning performance, and it follows…
Decision trees are a popular family of models due to their attractive properties such as interpretability and ability to handle heterogeneous data. Concurrently, missing data is a prevalent occurrence that hinders performance of machine…
We develop Clustered Random Forests, a random forests algorithm for clustered data, arising from independent groups that exhibit within-cluster dependence. The leaf-wise predictions for each decision tree making up clustered random forests…
Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…
Decision forests induce supervised similarities through the partition structure of their trees. Yet forest proximity computation is still often treated as a quadratic operation in the number of samples, which limits scalability and…
Tree-structured neural networks have proven to be effective in learning semantic representations by exploiting syntactic information. In spite of their success, most existing models suffer from the underfitting problem: they recursively use…
Variable trees are a new method for the exploration of discrete multivariate data. They display nested subsets and corresponding frequencies and percentages. Manual calculation of these quantities can be laborious, especially when there are…
Random forest regression is a powerful non-parametric method that adapts to local data characteristics through data-driven partitioning, making it effective across diverse application domains. However, the piecewise constant nature of…
The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights…
Graph kernels are usually defined in terms of simpler kernels over local substructures of the original graphs. Different kernels consider different types of substructures. However, in some cases they have similar predictive performances,…
Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…
Hierarchical tree structures are common in many real-world systems, from tree roots and branches to neuronal dendrites and biologically inspired artificial neural networks, as well as in technological networks for organizing and searching…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
Convolutional neural networks (CNNs) are able to attain better visual recognition performance than fully connected neural networks despite having much fewer parameters due to their parameter sharing principle. Modern architectures usually…
The primary hyperparameter in kernel regression (KR) is the choice of kernel. In most theoretical studies of KR, one assumes the kernel is fixed before seeing the training data. Under this assumption, it is known that the optimal kernel is…