Related papers: Projection Pursuit Density Ratio Estimation
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…
Uncertainty propagation in nonlinear dynamic systems remains an outstanding problem in scientific computing and control. Numerous approaches have been developed, but are limited in their capability to tackle problems with more than a few…
Density Ratio Estimation has attracted attention from the machine learning community due to its ability to compare the underlying distributions of two datasets. However, in some applications, we want to compare distributions of random…
Random Projection (RP) technique has been widely applied in many scenarios because it can reduce high-dimensional features into low-dimensional space within short time and meet the need of real-time analysis of massive data. There is an…
Predictive posterior densities (PPDs) are of interest in approximate Bayesian inference. Typically, these are estimated by simple Monte Carlo (MC) averages using samples from the approximate posterior. We observe that the signal-to-noise…
Estimation of the mixing distribution under a general mixture model is a very difficult problem, especially when the mixing distribution is assumed to have a density. Predictive recursion (PR) is a fast, recursive algorithm for…
Recent results in nonparametric regression show that for deep learning, i.e., for neural network estimates with many hidden layers, we are able to achieve good rates of convergence even in case of high-dimensional predictor variables,…
Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…
Assessing the fidelity and diversity of the generative model is a difficult but important issue for technological advancement. So, recent papers have introduced k-Nearest Neighbor ($k$NN) based precision-recall metrics to break down the…
In many statistical and econometric applications, we gather individual samples from various interconnected populations that undeniably exhibit common latent structures. Utilizing a model that incorporates these latent structures for such…
By integrating two powerful methods of density reduction and intrinsic dimensionality estimation, a new data-driven method, referred to as OLPP-MLE (orthogonal locality preserving projection-maximum likelihood estimation), is introduced for…
In metric learning, the goal is to learn an embedding so that data points with the same class are close to each other and data points with different classes are far apart. We propose a distance-ratio-based (DR) formulation for metric…
Density regression provides a flexible strategy for modeling the distribution of a response variable $Y$ given predictors $\mathbf{X}=(X_1,\ldots,X_p)$ by letting that the conditional density of $Y$ given $\mathbf{X}$ as a completely…
We introduce and analyse a new nonparametric estimator of a multi-dimensional density. Our smooth projection estimator (SPE) is defined by a least squares projection of the sample onto an infinite dimensional mixture class via an…
This study clarifies the relationship between Riesz regression [Chernozhukov et al., 2021] and density ratio estimation (DRE) in causal inference problems, such as average treatment effect estimation. We first show that the Riesz…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Propensity score weighting is widely used to improve the representativeness and correct the selection bias in the voluntary sample. The propensity score is often developed using a model for the sampling probability, which can be subject to…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
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…
Dimensionality reduction methods such as t-SNE are designed to preserve local neighborhood structure but do not explicitly account for how probability mass is distributed, often leading to distortions of data density. We reformulate…