Related papers: Posterior Ratio Estimation of Latent Variables
We propose a Machine Learning approach for optimal macroeconomic density forecasting in a high-dimensional setting where the underlying model exhibits a known group structure. Our approach is general enough to encompass specific forecasting…
Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function…
Latent factor model estimation typically relies on either using domain knowledge to manually pick several observed covariates as factor proxies, or purely conducting multivariate analysis such as principal component analysis. However, the…
We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P\'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's…
We analyze the posterior contraction rates of parameters in Bayesian models via the Langevin diffusion process, in particular by controlling moments of the stochastic process and taking limits. Analogous to the non-asymptotic analysis of…
In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
Models with a large number of latent variables are often used to fully utilize the information in big or complex data. However, they can be difficult to estimate using standard approaches, and variational inference methods are a popular…
Estimating the mixing density of a mixture distribution remains an interesting problem in statistics literature. Using a stochastic approximation method, Newton and Zhang (1999) introduced a fast recursive algorithm for estimating the…
Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…
Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…
It can be difficult to tell whether a trained generative model has learned to generate novel examples or has simply memorized a specific set of outputs. In published work, it is common to attempt to address this visually, for example by…
Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN…
Functions of the ratio of the densities $p/q$ are widely used in machine learning to quantify the discrepancy between the two distributions $p$ and $q$. For high-dimensional distributions, binary classification-based density ratio…
An approach to inference for relative sparsity was developed in prior work, and an adaptive lasso asymptotic normality theorem was given there, but this theorem was not fully used when estimating the variance of the policy coefficients.…