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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…

Analysts commonly investigate the data distributions derived from statistical aggregations of data that are represented by charts, such as histograms and binned scatterplots, to visualize and analyze a large-scale dataset. Aggregate queries…

Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…

Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another…

Traditional indexing techniques commonly employed in da\-ta\-ba\-se systems perform poorly on multidimensional array scientific data. Bitmap indices are widely used in commercial databases for processing complex queries, due to their…

In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model…

Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of…

Motivation: The high dimensionality of genomic data calls for the development of specific classification methodologies, especially to prevent over-optimistic predictions. This challenge can be tackled by compression and variable selection,…

In this paper, a new and novel data structure is proposed to dynamically insert and delete segments. Unlike the standard segment trees[3], the proposed data structure permits insertion of a segment with interval range beyond the interval…

The semantic matching capabilities of neural information retrieval can ameliorate synonymy and polysemy problems of symbolic approaches. However, neural models' dense representations are more suitable for re-ranking, due to their…

In data analysis, latent variables play a central role because they help provide powerful insights into a wide variety of phenomena, ranging from biological to human sciences. The latent tree model, a particular type of probabilistic…

Variable trees are a new method for the exploration of discrete multivariate data. They display nested subsets and corresponding frequencies and percentages. Manual calculation of these quantities can be laborious, especially when there are…

Tabular datasets with low-sample-size or many variables are prevalent in biomedicine. Practitioners in this domain prefer linear or tree-based models over neural networks since the latter are harder to interpret and tend to overfit when…

Microbiome compositional data are often high-dimensional, sparse, and exhibit pervasive cross-sample heterogeneity. Generative modeling is a popular approach to analyze such data, and effective generative models must accurately characterize…

Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not…

Random forests are a machine learning method used to automatically classify datasets and consist of a multitude of decision trees. While these random forests often have higher performance and generalize better than a single decision tree,…

We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from…

We propose a novel and computationally efficient approach for nonparametric conditional density estimation in high-dimensional settings that achieves dimension reduction without imposing restrictive distributional or functional form…

This paper presents two approaches to quantifying and visualizing variation in datasets of trees. The first approach localizes subtrees in which significant population differences are found through hypothesis testing and sparse classifiers…

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…