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The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
Simplicial partitions are a fundamental structure in computational geometry, as they form the basis of optimal data structures for range searching and several related problems. Current algorithms are built on very specific spatial…
Tree search is a fundamental tool for planning, as many sequential decision-making problems can be framed as searching over tree-structured spaces. We propose an uncertainty-guided tree search algorithm for settings where the reward…
There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
We extend the herding algorithm to continuous spaces by using the kernel trick. The resulting "kernel herding" algorithm is an infinite memory deterministic process that learns to approximate a PDF with a collection of samples. We show that…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
Two-part models and Tweedie generalized linear models (GLMs) have been used to model loss costs for short-term insurance contract. For most portfolios of insurance claims, there is typically a large proportion of zero claims that leads to…
In processing large quantities of data, a fundamental problem is to obtain a summary which supports approximate query answering. Random sampling yields flexible summaries which naturally support subset-sum queries with unbiased estimators…
We introduce an exact distributed algorithm to train Random Forest models as well as other decision forest models without relying on approximating best split search. We explain the proposed algorithm and compare it to related approaches for…
A scalable graphical method is presented for selecting, and partitioning datasets for the training phase of a classification task. For the heuristic, a clustering algorithm is required to get its computation cost in a reasonable proportion…
We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical…
In this paper we describe an algorithm that embeds a graph metric $(V,d_G)$ on an undirected weighted graph $G=(V,E)$ into a distribution of tree metrics $(T,D_T)$ such that for every pair $u,v\in V$, $d_G(u,v)\leq d_T(u,v)$ and…
We consider the problem of identifying a subset of nodes in a network that will enable the fastest spread of information in a decentralized environment.In a model of communication based on a random walk on an undirected graph, the optimal…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
In order to develop statistical methods for shapes with a tree-structure, we construct a shape space framework for tree-like shapes and study metrics on the shape space. This shape space has singularities, corresponding to topological…
Modern machine learning has achieved impressive prediction performance, but often sacrifices interpretability, a critical consideration in high-stakes domains such as medicine. In such settings, practitioners often use highly interpretable…
We consider a recently introduced class of network construction problems where edges of a transportation network need to be constructed by a server (construction crew). The server has a constant construction speed which is much lower than…
Dealing with datasets of very high dimension is a major challenge in machine learning. In this paper, we consider the problem of feature selection in applications where the memory is not large enough to contain all features. In this…
Sparse decision tree learning provides accurate and interpretable predictive models that are ideal for high-stakes applications by finding the single most accurate tree within a (soft) size limit. Rather than relying on a single "best"…