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We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the goal is to find two leaves of matching color, one in each of…
We introduce a new class of inverse optimization problems in which an input solution is given together with $k$ linear weight functions, and the goal is to modify the weights by the same deviation vector $p$ so that the input solution…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…
This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
Tree ensemble models such as random forests and boosted trees are among the most widely used and practically successful predictive models in applied machine learning and business analytics. Although such models have been used to make…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
Analytic and optimization methods for solving inverse kinematics (IK) problems have been deeply studied throughout the history of robotics. The two strategies have complementary strengths and weaknesses, but developing a unified approach to…
The backpropagation algorithm has experienced remarkable success in training large-scale artificial neural networks; however, its biological plausibility has been strongly criticized, and it remains an open question whether the brain…
Recognition of an adversary's objective is a core problem in physical security and cyber defense. Prior work on target recognition focuses on developing optimal inference strategies given the adversary's operating environment. However, the…
In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…
We propose a constructive algorithm for identifying complete data distributions in graphical models of missing data. The complete data distribution is unrestricted, while the missingness mechanism is assumed to factorize according to a…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
This paper deals with the multiobjective version of the optimal spanning tree problem. More precisely, we are interested in determining the optimal spanning tree according to an Ordered Weighted Average (OWA) of its objective values. We…
We introduce an adaptive tree search algorithm, that can find high-scoring outputs under translation models that make no assumptions about the form or structure of the search objective. This algorithm -- a deterministic variant of Monte…
A plethora of problems in AI, engineering and the sciences are naturally formalized as inference in discrete probabilistic models. Exact inference is often prohibitively expensive, as it may require evaluating the (unnormalized) target…
We present Collaborative Trees, a novel tree model designed for regression prediction, along with its bagging version, which aims to analyze complex statistical associations between features and uncover potential patterns inherent in the…
The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M…
We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…