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The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is…

Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

In this paper, we focus on learning a linear time-invariant (LTI) model with low-dimensional latent variables but high-dimensional observations. We provide an algorithm that recovers the high-dimensional features, i.e. column space of the…

The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms…

Motivated by models for multiway comparison data, we consider the problem of estimating a coordinate-wise isotonic function on the domain $[0, 1]^d$ from noisy observations collected on a uniform lattice, but where the design points have…

For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every…

We consider multi-class classification where the predictor has a hierarchical structure that allows for a very large number of labels both at train and test time. The predictive power of such models can heavily depend on the structure of…

Suppose we label the vertices of a tree by positive integers. The weight of an edge is defined by a monotonically increasing function of the absolute value of the difference of the labels of its endpoints. We define the total cost of the…

This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular…

We propose new methods for Support Vector Machines (SVMs) using tree architecture for multi-class classi- fication. In each node of the tree, we select an appropriate binary classifier using entropy and generalization error estimation, then…

Regression methods for interval-valued data have been increasingly studied in recent years. As most of the existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and therefore…

Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…

We give an algorithm to enumerate the results on trees of monadic second-order (MSO) queries represented by nondeterministic tree automata. After linear time preprocessing (in the input tree), we can enumerate answers with linear delay (in…

For finite integer squares, we consider the problem of learning a classification $I$ that respects Pareto domination. The setup is natural in dynamic programming settings. We show that a generalization of the binary search algorithm…

Decision tree is an important method for both induction research and data mining, which is mainly used for model classification and prediction. ID3 algorithm is the most widely used algorithm in the decision tree so far. In this paper, the…

Linear model trees are regression trees that incorporate linear models in the leaf nodes. This preserves the intuitive interpretation of decision trees and at the same time enables them to better capture linear relationships, which is hard…

The presence of a high number of zero flow trades continues to provide a challenge in identifying gravity parameters to explain international trade using the gravity model. Linear regression with a logarithmic linear equation encounters an…

Learning from the multidimensional data has been an interesting concept in the field of machine learning. However, such learning can be difficult, complex, expensive because of expensive data processing, manipulations as the number of…