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Deterministic solutions are becoming more critical for interpretability. Weighted Least-Squares (WLS) has been widely used as a deterministic batch solution with a specific weight design. In the online settings of WLS, exact reweighting is…

Machine Learning · Computer Science 2023-01-24 Se-In Jang

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

Quantum Physics · Physics 2021-09-22 Samuel P. Nolan , Augusto Smerzi , Luca Pezzè

In a variety of problems originating in supervised, unsupervised, and reinforcement learning, the loss function is defined by an expectation over a collection of random variables, which might be part of a probabilistic model or the external…

Machine Learning · Computer Science 2016-01-06 John Schulman , Nicolas Heess , Theophane Weber , Pieter Abbeel

We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…

Methodology · Statistics 2026-05-26 Panagiotis Papastamoulis , Konstantinos Perrakis

A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…

Artificial Intelligence · Computer Science 2018-11-14 Zhenyu A. Liao , Charupriya Sharma , James Cussens , Peter van Beek

We introduce ensembles of stochastic neural networks to approximate the Bayesian posterior, combining stochastic methods such as dropout with deep ensembles. The stochastic ensembles are formulated as families of distributions and trained…

Machine Learning · Computer Science 2024-01-04 Oleksandr Balabanov , Bernhard Mehlig , Hampus Linander

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

Machine Learning · Statistics 2026-05-06 Nan Feng , Xun Huan

We present a modular approach to reinforcement learning that uses a Bayesian representation of the uncertainty over models. The approach, BOSS (Best of Sampled Set), drives exploration by sampling multiple models from the posterior and…

Machine Learning · Computer Science 2012-05-14 John Asmuth , Lihong Li , Michael L. Littman , Ali Nouri , David Wingate

Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly sub-optimal, solutions. The extent to which these algorithms approximate Bayesian…

Statistics Theory · Mathematics 2026-02-18 Sandra Fortini , Sonia Petrone

Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…

Applications · Statistics 2018-11-06 Cheng Zhang , Frederick A. Matsen

In this paper, we study the generalization properties of online learning based stochastic methods for supervised learning problems where the loss function is dependent on more than one training sample (e.g., metric learning, ranking). We…

Machine Learning · Computer Science 2013-05-14 Purushottam Kar , Bharath K Sriperumbudur , Prateek Jain , Harish C Karnick

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…

Machine Learning · Computer Science 2022-03-31 Andrew Gordon Wilson , Pavel Izmailov

Aggregating multiple learners through an ensemble of models aim to make better predictions by capturing the underlying distribution of the data more accurately. Different ensembling methods, such as bagging, boosting, and stacking/blending,…

Machine Learning · Statistics 2020-11-03 Mohsen Shahhosseini , Guiping Hu , Hieu Pham

Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…

Machine Learning · Statistics 2024-07-03 Tommy Rochussen

The posterior in probabilistic programs with stochastic support decomposes as a weighted sum of the local posterior distributions associated with each possible program path. We show that making predictions with this full posterior…

Machine Learning · Computer Science 2024-04-15 Tim Reichelt , Luke Ong , Tom Rainforth

We consider a Bayesian approach to offline model-based inverse reinforcement learning (IRL). The proposed framework differs from existing offline model-based IRL approaches by performing simultaneous estimation of the expert's reward…

Machine Learning · Computer Science 2024-04-09 Ran Wei , Siliang Zeng , Chenliang Li , Alfredo Garcia , Anthony McDonald , Mingyi Hong

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection. The resulting algorithm has key advantages over previous work: it provides provable robustness by leveraging the generalised Bayesian…

Machine Learning · Statistics 2023-05-15 Matias Altamirano , François-Xavier Briol , Jeremias Knoblauch

This chapter introduces the Bayesian reflex -- an analogy with the autonomic nervous system -- as a unifying framework for online learning in AI. Bayesian online algorithms automatically maintain equilibrium in dynamic environments via…

Methodology · Statistics 2026-05-05 Durba Bhattacharya , Sucharita Roy , Sourabh Bhattacharya

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

Methodology · Statistics 2020-07-15 Shintaro Hashimoto , Shonosuke Sugasawa