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We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain…
Reachability analysis is a powerful tool when it comes to capturing the behaviour, thus verifying the safety, of autonomous systems. However, general-purpose methods, such as Hamilton-Jacobi approaches, suffer from the curse of…
High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
We consider the optimal conduction path of the one-dimensional variable-range hopping problem. We describe a hierarchical procedure for constructing the path which is in excellent agreement with numerical results obtained from a percolation…
Tree-like structures, such as blood vessels, often express complexity at very fine scales, requiring high-resolution grids to adequately describe their shape. Such sparse morphology can alternately be represented by locations of centreline…
This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions,…
Hierarchical beta process has found interesting applications in recent years. In this paper we present a modified hierarchical beta process prior with applications to hierarchical modeling of multiple data sources. The novel use of the…
This paper presents a nested tracking framework for analyzing cycles in 2D force networks within granular materials. These materials are composed of interacting particles, whose interactions are described by a force network. Understanding…
We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…
A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic…
Previously, we proposed a probabilistic data generation model represented by an unobservable tree and a sequential updating method to calculate a posterior distribution over a set of trees. The set is called a meta-tree. In this paper, we…
This is a discussion of paper "Treelets--An adaptive multi-scale basis for sparse unordered data" [arXiv:0707.0481] by Ann B. Lee, Boaz Nadler and Larry Wasserman. In this paper the authors defined a new type of dimension reduction…
The P\'olya tree (PT) process is a general-purpose Bayesian nonparametric model that has found wide application in a range of inference problems. It has a simple analytic form and the posterior computation boils down to beta-binomial…
Data-intensive platforms such as Hadoop and Spark are routinely used to process massive amounts of data residing on distributed file systems like HDFS. Increasing memory sizes and new hardware technologies (e.g., NVRAM, SSDs) have recently…
We address the problem of building and maintaining distributed spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we…
We present the nested Chinese restaurant process (nCRP), a stochastic process which assigns probability distributions to infinitely-deep, infinitely-branching trees. We show how this stochastic process can be used as a prior distribution in…
Temporal graphs represent interactions between entities over time. Deciding whether entities can reach each other through temporal paths is useful for various applications such as in communication networks and epidemiology. Previous works…
In this paper, we deal with the problem of curves clustering. We propose a nonparametric method which partitions the curves into clusters and discretizes the dimensions of the curve points into intervals. The cross-product of these…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…
Decision trees are widely used for non-linear modeling, as they capture interactions between predictors while producing inherently interpretable models. Despite their popularity, performing inference on the non-linear fit remains largely…