Related papers: A theory of stratification learning

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description - few…

We propose a deep learning approach for discovering kernels tailored to identifying clusters over sample data. Our neural network produces sample embeddings that are motivated by--and are at least as expressive as--spectral clustering. Our…

Model-based clustering is a powerful tool that is often used to discover hidden structure in data by grouping observational units that exhibit similar response values. Recently, clustering methods have been developed that permit…

A solution manifold is the collection of points in a $d$-dimensional space satisfying a system of $s$ equations with $s<d$. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families,…

Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common…

We prove a convergence theorem for stochastic gradient descents on manifolds with adaptive learning rate and apply it to the weighted low-rank approximation problem.

In various applications with large spatial regions, the relationship between the response variable and the covariates is expected to exhibit complex spatial patterns. We propose a spatially clustered varying coefficient model, where the…

Feature selection methods have an important role on the readability of data and the reduction of complexity of learning algorithms. In recent years, a variety of efforts are investigated on feature selection problems based on unsupervised…

We introduce the Neural Collaborative Subspace Clustering, a neural model that discovers clusters of data points drawn from a union of low-dimensional subspaces. In contrast to previous attempts, our model runs without the aid of spectral…

We propose a novel framework for image clustering that incorporates joint representation learning and clustering. Our method consists of two heads that share the same backbone network - a "representation learning" head and a "clustering"…

Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…

Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty…

The proposed method extends upon the representational output of semantic instance segmentation by explicitly including both visible and occluded parts. A fully convolutional network is trained to produce consistent pixel-level embedding…

This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in…

We propose unsupervised representation learning and feature extraction from dendrograms. The commonly used Minimax distance measures correspond to building a dendrogram with single linkage criterion, with defining specific forms of a level…

Subspace clustering is to find underlying low-dimensional subspaces and cluster the data points correctly. In this paper, we propose a novel multi-view subspace clustering method. Most existing methods suffer from two critical issues.…

It has been known for a long time that stratification is one possible strategy to obtain higher convergence rates for the Monte Carlo estimation of integrals over the hyper-cube $[0, 1]^s$ of dimension $s$. However, stratified estimators…