Related papers: An Oracle Inequality for Quasi-Bayesian Non-Negati…

The model averaging problem is to average multiple models to achieve a prediction accuracy not much worse than that of the best single model in terms of mean squared error. It is known that if the models are misspecified, model averaging is…

In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation…

Bateni et al. has recently introduced the weak-strong distance oracle model to study clustering problems in settings with limited distance information. Given query access to the strong-oracle and weak-oracle in the weak-strong oracle model,…

An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle…

Quantum amplitude amplification and estimation have shown quadratic speedups to unstructured search and estimation tasks. We show that a coherent combination of these quantum algorithms also provides a quadratic speedup to calculating the…

The double oracle algorithm is a popular method of solving games, because it is able to reduce computing equilibria to computing a series of best responses. However, its theoretical properties are not well understood. In this paper, we…

In this paper we study the problem of bilinear regression and we further address the case when the response matrix contains missing data that referred as the problem of inductive matrix completion. We propose a quasi-Bayesian approach first…

The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…

The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the…

Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…

Interference arises when the treatment assigned to one individual affects the outcomes of other individuals. Commonly, individuals are naturally grouped into clusters, and interference occurs only among individuals within the same cluster,…

Quasiprobability representation is an important tool for analyzing a quantum system, such as a quantum state or a quantum circuit. In this work, we propose classical algorithms specialized for approximating outcome probabilities of a linear…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…

This paper proposes a novel method to estimate large panel data error-correction models with stationary/non-stationary covariates and spatially dependent errors, which allows for known/unknown group-specific patterns of slope heterogeneity.…

Relational quantum queries are sometimes capable to effectively decide between collections of mutually exclusive elementary cases without completely resolving and determining those individual instances. Thereby the set of mutually exclusive…

Bayesian modelling allows for the quantification of predictive uncertainty which is crucial in safety-critical applications. Yet for many machine learning (ML) algorithms, it is difficult to construct or implement their Bayesian…

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Current solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and…

We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We…

We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…

Score based approaches to sampling have shown much success as a generative algorithm to produce new samples from a target density given a pool of initial samples. In this work, we consider if we have no initial samples from the target…