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Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…

In various practical situations, matrix factorization methods suffer from poor data quality, such as high data sparsity and low signal-to-noise ratio (SNR). Here, we consider a matrix factorization problem by utilizing auxiliary…

Gaussian random fields (GFs) are fundamental tools in spatial modeling and can be represented flexibly and efficiently as solutions to stochastic partial differential equations (SPDEs). The SPDEs depend on specific parameters, which enforce…

Latent Gaussian Models (LGMs) are a subset of Bayesian Hierarchical models where Gaussian priors, conditional on variance parameters, are assigned to all effects in the model. LGMs are employed in many fields for their flexibility and…

Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…

In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian…

Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…

Very often features come with their own vectorial descriptions which provide detailed information about their properties. We refer to these vectorial descriptions as feature side-information. In the standard learning scenario, input is…

Embedding methods have achieved success in face recognition by comparing facial features in a latent semantic space. However, in a fully unconstrained face setting, the facial features learned by the embedding model could be ambiguous or…

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…

There has recently been considerable interest in completing a low-rank matrix or tensor given only a small fraction (or few linear combinations) of its entries. Related approaches have found considerable success in the area of recommender…

Nonnegative matrix factorization (NMF) has an established reputation as a useful data analysis technique in numerous applications. However, its usage in practical situations is undergoing challenges in recent years. The fundamental factor…

Matrix factorization (MF) is one of the most efficient methods for rating predictions. MF learns user and item representations by factorizing the user-item rating matrix. Further, textual contents are integrated to conventional MF to…

Computer simulations often involve both qualitative and numerical inputs. Existing Gaussian process (GP) methods for handling this mainly assume a different response surface for each combination of levels of the qualitative factors and…

We introduce stochastic variational inference for Gaussian process models. This enables the application of Gaussian process (GP) models to data sets containing millions of data points. We show how GPs can be vari- ationally decomposed to…

In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…

Although latent factor models (e.g., matrix factorization) obtain good performance in predictions, they suffer from several problems including cold-start, non-transparency, and suboptimal recommendations. In this paper, we employ text with…

Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and…

We develop a Bayesian Poisson matrix factorization model for forming recommendations from sparse user behavior data. These data are large user/item matrices where each user has provided feedback on only a small subset of items, either…

Beta process is the standard nonparametric Bayesian prior for latent factor model. In this paper, we derive a structured mean-field variational inference algorithm for a beta process non-negative matrix factorization (NMF) model with…