Related papers: Regularized Exponentially Tilted Empirical Likelih…

We introduce an alternative closed form lower bound on the Gaussian process ($\mathcal{GP}$) likelihood based on the R\'enyi $\alpha$-divergence. This new lower bound can be viewed as a convex combination of the Nystr\"om approximation and…

Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…

A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…

Inverse probability weighting (IPW) is widely used in many areas when data are subject to unrepresentativeness, missingness, or selection bias. An inevitable challenge with the use of IPW is that the IPW estimator can be remarkably unstable…

The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…

We propose a new empirical Bayes approach for inference in the $p \gg n$ normal linear model. The novelty is the use of data in the prior in two ways, for centering and regularization. Under suitable sparsity assumptions, we establish a…

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…

The challenges posed by complex stochastic models used in computational ecology, biology and genetics have stimulated the development of approximate approaches to statistical inference. Here we focus on Synthetic Likelihood (SL), a…

The penalized profile sampler for semiparametric inference is an extension of the profile sampler method (Lee, Kosorok and Fine, 2005) obtained by profiling a penalized log-likelihood. The idea is to base inference on the posterior…

We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets. Starting from the classical equivalence between…

The maximum likelihood method is the best-known method for estimating the probabilities behind the data. However, the conventional method obtains the probability model closest to the empirical distribution, resulting in overfitting. Then…

Parameters defined via General Estimating Equations (GEE) can be estimated by maximizing the Empirical Likelihood (EL). Newey and Smith (2004) have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties,…

We propose a two-sample extended empirical likelihood for inference on the difference between two p-dimensional parameters defined by estimating equations. The standard two-sample empirical likelihood for the difference is Bartlett…

Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…

We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…

Heckman selection model is the most popular econometric model in analysis of data with sample selection. However, selection models with Normal errors cannot accommodate heavy tails in the error distribution. Recently, Marchenko and Genton…

The Bayesian Synthetic Likelihood (BSL) method is a widely-used tool for likelihood-free Bayesian inference. This method assumes that some summary statistics are normally distributed, which can be incorrect in many applications. We propose…

Approximate Bayesian computation (ABC) methods, which are applicable when the likelihood is difficult or impossible to calculate, are an active topic of current research. Most current ABC algorithms directly approximate the posterior…