Related papers: Inference in Polytrees with Sets of Probabilities

Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…

We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…

We present a simple $O(n^4)$-time algorithm for computing optimal search trees with two-way comparisons. The only previous solution to this problem, by Anderson et al., has the same running time, but is significantly more complicated and is…

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…

Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…

Over the last 10 to 15 years, active inference has helped to explain various brain mechanisms from habit formation to dopaminergic discharge and even modelling curiosity. However, the current implementations suffer from an exponential…

Approximate K-Nearest Neighbor Search (AKNNS) has now become ubiquitous in modern applications, for example, as a fast search procedure with two tower deep learning models. Graph-based methods for AKNNS in particular have received great…

The past two decades have seen a growing interest in combining causal information, commonly represented using causal graphs, with machine learning models. Probability trees provide a simple yet powerful alternative representation of causal…

Graph Retrieval has witnessed continued interest and progress in the past few years. In thisreport, we focus on neural network based approaches for Graph matching and retrieving similargraphs from a corpus of graphs. We explore methods…

Probabilistic dependency graphs (PDGs) are a flexible class of probabilistic graphical models, subsuming Bayesian Networks and Factor Graphs. They can also capture inconsistent beliefs, and provide a way of measuring the degree of this…

There has been a lot of recent work on Bayesian methods for reinforcement learning exhibiting near-optimal online performance. The main obstacle facing such methods is that in most problems of interest, the optimal solution involves…

Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…

Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow…

We consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node $t$ in a given tree $T$. Upon querying a node $v$ of the tree, the strategy receives as a reply an…

Embedding-based retrieval aims to learn a shared semantic representation space for both queries and items, enabling efficient and effective item retrieval through approximate nearest neighbor (ANN) algorithms. In current industrial…

The \emph{Steiner tree} problem is one of the fundamental and classical problems in combinatorial optimization. In this paper, we study this problem in the $\mathcal{CONGESTED}$ $\mathcal{CLIQUE}$ model of distributed computing and present…

Inference methods are often formulated as variational approximations: these approximations allow easy evaluation of statistics by marginalization or linear response, but these estimates can be inconsistent. We show that by introducing…

Nearest neighbor search supports important applications in many domains, such as database, machine learning, computer vision. Since the computational cost for accurate search is too high, the community turned to the research of approximate…