相关论文: Convergence and Loss Bounds for Bayesian Sequence …

When people learn mathematical patterns or sequences, they are able to identify the concepts (or rules) underlying those patterns. Having learned the underlying concepts, humans are also able to generalize those concepts to other numbers,…

We propose a new approach to Bayesian prediction that caters for models with a large number of parameters and is robust to model misspecification. Given a class of high-dimensional (but parametric) predictive models, this new approach…

Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…

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…

Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…

The Laplace approximation is a popular method for constructing a Gaussian approximation to the Bayesian posterior and thereby approximating the posterior mean and variance. But approximation quality is a concern. One might consider using…

We consider the problem of approximating a general Gaussian location mixture by finite mixtures. The minimum order of finite mixtures that achieve a prescribed accuracy (measured by various $f$-divergences) is determined within constant…

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…

This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

Prediction is a central task of statistics and machine learning, yet many inferential settings provide only partial information, typically in the form of moment constraints or estimating equations. We develop a finite, fully Bayesian…

We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growing number of components is a natural one as the degree of…

We study generalized Bayesian inference under misspecification, i.e. when the model is 'wrong but useful'. Generalized Bayes equips the likelihood with a learning rate $\eta$. We show that for generalized linear models (GLMs),…

We examine rules for predicting whether a point in $\mathbb{R}$ generated from a 50-50 mixture of two different probability distributions came from one distribution or the other, given limited (or no) information on the two distributions,…

The paper addresses the problem of estimation of the model parameters of the logistic exponential distribution based on progressive type-I hybrid censored sample. The maximum likelihood estimates are obtained and computed numerically using…

We present some new and explicit error bounds for the approximation of distributions. The approximation error is quantified by the maximal density ratio of the distribution $Q$ to be approximated and its proxy $P$. This non-symmetric…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems.…

We study the convergence properties of a class of data augmentation algorithms targeting posterior distributions of Bayesian lasso models with log-concave likelihoods. Leveraging isoperimetric inequalities, we derive a generic convergence…