Related papers: Density estimation using cellular binary trees and…
We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the…
For a density $f$ on ${\mathbb R}^d$, a {\it high-density cluster} is any connected component of $\{x: f(x) \geq \lambda\}$, for some $\lambda > 0$. The set of all high-density clusters forms a hierarchy called the {\it cluster tree} of…
Given i.i.d samples from some unknown continuous density on hyper-rectangle $[0, 1]^d$, we attempt to learn a piecewise constant function that approximates this underlying density non-parametrically. Our density estimate is defined on a…
We study the problem of estimating the density $f(\boldsymbol x)$ of a random vector ${\boldsymbol X}$ in $\mathbb R^d$. For a spanning tree $T$ defined on the vertex set $\{1,\dots ,d\}$, the tree density $f_{T}$ is a product of bivariate…
This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) there is a known…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
In order to develop reliable services using machine learning, it is important to understand the uncertainty of the model outputs. Often the probability distribution that the prediction target follows has a complex shape, and a mixture…
Given a (finite) string of zeros and ones, we report a way to determine if the number of ones is less than, greater than, or equal to a prescribed number by applying two sets of cellular automaton rules in succession. Thus, we solve the…
We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to…
Estimating a joint Highest Posterior Density credible set for a multivariate posterior density is challenging as dimension gets larger. Credible intervals for univariate marginals are usually presented for ease of computation and…
Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…
Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on…
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…
Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space…
Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…
Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observations from the two…