Related papers: Universality of Bayesian mixture predictors
We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…
The problem of prediction consists in forecasting the conditional distribution of the next outcome given the past. Assume that the source generating the data is such that there is a stationary ergodic predictor whose error converges to zero…
Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences and consider the question when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain…
Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…
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…
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…
We study the problem of predicting the results of computations that are too expensive to run, via the observation of the results of smaller computations. We model this as an online learning problem with delayed feedback, where the length of…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
We exploit a suitable moment-based characterization of the mixture of Poisson distribution for developing Bayesian inference for the unknown size of a finite population whose units are subject to multiple occurrences during an enumeration…
This paper is a note on the use of Bayesian nonparametric mixture models for continuous time series. We identify a key requirement for such models, and then establish that there is a single type of model which meets this requirement. As it…
The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that…
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…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
The Bayesian framework is ideally suited for induction problems. The probability of observing $x_t$ at time $t$, given past observations $x_1...x_{t-1}$ can be computed with Bayes' rule if the true distribution $\mu$ of the sequences…
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
Even though the forecasting literature agrees that aggregating multiple predictions of some future outcome typically outperforms the individual predictions, there is no general consensus about the right way to do this. Most common…
Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…
A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
Conformal predictors provide set or functional predictions that are valid under the assumption of randomness, i.e., under the assumption of independent and identically distributed data. The question asked in this paper is whether there are…