Prior specification via prior predictive matching: Poisson matrix factorization and beyond

Silva, Eliezer de Souza da; Kuśmierczyk, Tomasz; Hartmann, Marcelo; Klami, Arto

doi:10.48550/arxiv.1910.12263

Cited by 2 publications

(2 citation statements)

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“…The optimisation problem of minimising Equation ( 1) is often underspecified. Specifically, there are many optimal values λ * that yield values of D(λ * | X) that are practically indistinguishable (noted by da Silva et al, 2019), and yet the prior distributions P(θ | λ * , X) and the corresponding marginals for components of θ can differ immensely. In terms of our desiderata, there are many equally faithful priors (which immediately implies a lack of uniqueness), thus we have an optimisation problem with solutions that are difficult to replicate due to nonuniqueness.…”

Section: Regularising Estimates Of λ * By Promoting the Marginal Stan...mentioning

confidence: 99%

Translating predictive distributions into informative priors

Manderson¹,

Goudie²

2023

Preprint

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When complex Bayesian models exhibit implausible behaviour, one solution is to assemble available information into an informative prior. Challenges arise as prior information is often only available for the observable quantity, or some model-derived marginal quantity, rather than directly pertaining to the natural parameters in our model. We propose a method for translating available prior information, in the form of an elicited distribution for the observable or model-derived marginal quantity, into an informative joint prior. Our approach proceeds given a parametric class of prior distributions with as yet undetermined hyperparameters, and minimises the difference between the supplied elicited distribution and corresponding prior predictive distribution. We employ a global, multi-stage Bayesian optimisation procedure to locate optimal values for the hyperparameters. Three examples illustrate our approach: a nonlinear regression model; a setting in which prior information pertains to R 2 -a model-derived quantity; and a cure-fraction survival model, where censoring implies that the observable quantity is a priori a mixed discrete/continuous quantity.

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Section: Regularising Estimates Of λ * By Promoting the Marginal Stan...mentioning

confidence: 99%

Translating predictive distributions into informative priors

Manderson¹,

Goudie²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Conventional probabilistic factor models [26], [27], [28], [29] construct the likelihood function over the rating matrix. However, in our model, the likelihood function is given over only observed user-item interactions, and the benefit is that we can incorporate additional information into the model, such as biases, attributes of a user.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Latent Factor Model for Collaborative Filtering with Bayesian Inference

Fang,

Zhang,

et al. 2020

Preprint

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Latent Factor Model (LFM) is one of the most successful methods for Collaborative filtering (CF) in the recommendation system, in which both users and items are projected into a joint latent factor space. Base on matrix factorization applied usually in pattern recognition, LFM models user-item interactions as inner products of factor vectors of user and item in that space and can be efficiently solved by least square methods with optimal estimation. However, such optimal estimation methods are prone to overfitting due to the extreme sparsity of useritem interactions. In this paper, we propose a Bayesian treatment for LFM, named Bayesian Latent Factor Model (BLFM). Based on observed user-item interactions, we build a probabilistic factor model in which the regularization is introduced via placing prior constraint on latent factors, and the likelihood function is established over observations and parameters. Then we draw samples of latent factors from the posterior distribution with Variational Inference (VI) to predict expected value. We further make an extension to BLFM, called BLFMBias, incorporating user-dependent and item-dependent biases into the model for enhancing performance. Extensive experiments on the movie rating dataset show the effectiveness of our proposed models by compared with several strong baselines.

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Prior specification via prior predictive matching: Poisson matrix factorization and beyond

Cited by 2 publications

References 0 publications

Translating predictive distributions into informative priors

Translating predictive distributions into informative priors

Probabilistic Latent Factor Model for Collaborative Filtering with Bayesian Inference

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