Related papers: SUMO: Unbiased Estimation of Log Marginal Probabil…
We present a new version of the truncated harmonic mean estimator (THAMES) for univariate or multivariate mixture models. The estimator computes the marginal likelihood from Markov chain Monte Carlo (MCMC) samples, is consistent,…
We present general principles for the design and analysis of unbiased Monte Carlo estimators in a wide range of settings. Our estimators posses finite work-normalized variance under mild regularity conditions. We apply our estimators to…
This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
We propose Subsampling MCMC, a Markov Chain Monte Carlo (MCMC) framework where the likelihood function for $n$ observations is estimated from a random subset of $m$ observations. We introduce a highly efficient unbiased estimator of the…
Recent work in scalable approximate Gaussian process regression has discussed a bias-variance-computation trade-off when estimating the log marginal likelihood. We suggest a method that adaptively selects the amount of computation to use…
Latent variable models have been playing a central role in psychometrics and related fields. In many modern applications, the inference based on latent variable models involves one or several of the following features: (1) the presence of…
We show that unconverged stochastic gradient descent can be interpreted as a procedure that samples from a nonparametric variational approximate posterior distribution. This distribution is implicitly defined as the transformation of an…
Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…
We consider an on-line least squares regression problem with optimal solution $\theta^*$ and Hessian matrix H, and study a time-average stochastic gradient descent estimator of $\theta^*$. For $k\ge2$, we provide an unbiased estimator of…
The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…
Models implicitly defined through a random simulator of a process have become widely used in scientific and industrial applications in recent years. However, simulation-based inference methods for such implicit models, like approximate…
Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work (Jang et al.…
Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact…
We consider unbiased estimation of a sparse nonrandom vector corrupted by additive white Gaussian noise. We show that while there are infinitely many unbiased estimators for this problem, none of them has uniformly minimum variance.…
Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…
We utilise a sampler originating from nonequilibrium statistical mechanics, termed here Jarzynski-adjusted Langevin algorithm (JALA), to build statistical estimation methods in latent variable models. We achieve this by leveraging…
To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…
The estimation of categorical response models using bias-reducing adjusted score equations has seen extensive theoretical research and applied use. The resulting estimates have been found to have superior frequentist properties to what…
This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is…