Related papers: Computationally efficient variational-like approxi…
In scientific applications, there often are several competing models that could be fit to the observed data, so quantification of the model uncertainty is of fundamental importance. In this paper, we develop an inferential model (IM)…
The recent explosion in the amount and dimensionality of data has exacerbated the need of trading off computational and statistical efficiency carefully, so that inference is both tractable and meaningful. We propose a framework that…
In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…
This work makes two advances in the study of the (approximate) nonparametric maximum likelihood estimator (NPMLE) for exponential family mixture models. First, we develop a data-compression strategy that reduces the cost of repeated…
Classical mixture models (MMs) are widely used tractable proposals for approximate inference settings such as variational inference (VI) and importance sampling (IS). Recently, mixture models with negative coefficients, called subtractive…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
In this paper, we propose an efficient importance sampling algorithm for rare event simulation under copula models. In the algorithm, the derived optimal probability measure is based on the criterion of minimizing the variance of the…
Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, for a chosen significance level $\varepsilon$, CP…
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…
We propose a novel use of a recent new computational tool for Bayesian inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC is a way to handle models for which the likelihood function may be intractable or even…
We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the…
We propose a family of variational approximations to Bayesian posterior distributions, called $\alpha$-VB, with provable statistical guarantees. The standard variational approximation is a special case of $\alpha$-VB with $\alpha=1$. When…
Inverse Probability Weighting (IPW) is widely used in empirical work in economics and other disciplines. As Gaussian approximations perform poorly in the presence of "small denominators," trimming is routinely employed as a regularization…
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…
Quantifying the influence of infinitesimal changes in training data on model performance is crucial for understanding and improving machine learning models. In this work, we reformulate this problem as a weighted empirical risk minimization…
Computing the conditional mode of a distribution, better known as the $\mathit{maximum\ a\ posteriori}$ (MAP) assignment, is a fundamental task in probabilistic inference. However, MAP estimation is generally intractable, and remains hard…
Variational inference methods often focus on the problem of efficient model optimization, with little emphasis on the choice of the approximating posterior. In this paper, we review and implement the various methods that enable us to…
Diffusion probabilistic models have generated high quality image synthesis recently. However, one pain point is the notorious inference to gradually obtain clear images with thousands of steps, which is time consuming compared to other…