Related papers: Bayes-optimal performance in a discrete space

Achieving the Bayes optimal binary classification rule subject to group fairness constraints is known to be reducible, in some cases, to learning a group-wise thresholding rule over the Bayes regressor. In this paper, we extend this result…

As machine learning is increasingly used to make real-world decisions, recent research efforts aim to define and ensure fairness in algorithmic decision making. Existing methods often assume a fixed set of observable features to define…

We efficiently solve the optimal multi-dimensional mechanism design problem for independent bidders with arbitrary demand constraints when either the number of bidders is a constant or the number of items is a constant. In the first…

Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…

Identifying optimal values for a high-dimensional set of hyperparameters is a problem that has received growing attention given its importance to large-scale machine learning applications such as neural architecture search. Recently…

Evaluation of treatment effects and more general estimands is typically achieved via parametric modelling, which is unsatisfactory since model misspecification is likely. Data-adaptive model building (e.g. statistical/machine learning) is…

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…

Discrete latent variables are considered important for real world data, which has motivated research on Variational Autoencoders (VAEs) with discrete latents. However, standard VAE training is not possible in this case, which has motivated…

We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…

Unsupervised ensemble learning emerged to address the challenge of combining multiple learners' predictions without access to ground truth labels or additional data. This paradigm is crucial in scenarios where evaluating individual…

The surface area of a set which is only observed as a binary pixel image is often estimated by a weighted sum of pixel configurations counts. In this paper we examine these estimators in a design based setting -- we assume that the observed…

In this paper, we consider the problem of parametric empirical Bayes estimation of an i.i.d. prior in high-dimensional Bayesian linear regression, with random design. We obtain the asymptotic distribution of the variational Empirical Bayes…

This paper describes a new form of unsupervised learning, whose input is a set of unlabeled points that are assumed to be local maxima of an unknown value function v in an unknown subset of the vector space. Two functions are learned: (i) a…

In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of…

This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the…

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

Recently, there has been much interest in finding globally optimal Bayesian network structures. These techniques were developed for generative scores and can not be directly extended to discriminative scores, as desired for classification.…

In a smooth semiparametric estimation problem, the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior. It is…

Inference in the presence of outliers is an important field of research as outliers are ubiquitous and may arise across a variety of problems and domains. Bayesian optimization is method that heavily relies on probabilistic inference. This…

Bayesian optimization is a methodology for global optimization of unknown and expensive objectives. It combines a surrogate Bayesian regression model with an acquisition function to decide where to evaluate the objective. Typical regression…