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Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
Predictive mean matching (PMM) is a popular imputation strategy that imputes missing values by borrowing observed values from other cases with similar expectations. We show that, unlike other imputation strategies, PMM is not guaranteed to…
Gaussian processes (GPs) are nonparametric priors over functions. Fitting a GP implies computing a posterior distribution of functions consistent with the observed data. Similarly, deep Gaussian processes (DGPs) should allow us to compute a…
Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…
The essence of the challenges cold start and sparsity in Recommender Systems (RS) is that the extant techniques, such as Collaborative Filtering (CF) and Matrix Factorization (MF), mainly rely on the user-item rating matrix, which sometimes…
In this paper we introduce a novel online time series forecasting model we refer to as the pM-GP filter. We show that our model is equivalent to Gaussian process regression, with the advantage that both online forecasting and online…
Factorization machines (FMs) are widely used in recommender systems due to their adaptability and ability to learn from sparse data. However, for the ubiquitous non-interactive features in sparse data, existing FMs can only estimate the…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
Factorization-based models have gained popularity since the Netflix challenge {(2007)}. Since that, various factorization-based models have been developed and these models have been proven to be efficient in predicting users' ratings…
Survivors of childhood cancer need lifelong monitoring for side effects from radiotherapy. However, longitudinal data from routine monitoring is often infrequently and irregularly sampled, and subject to inaccuracies. Due to this,…
This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…
Nonnegative matrix factorization (NMF) is a powerful tool in data exploratory analysis by discovering the hidden features and part-based patterns from high-dimensional data. NMF and its variants have been successfully applied into diverse…
In this paper, we analyze Gaussian processes using statistical mechanics. Although the input is originally multidimensional, we simplify our model by considering the input as one-dimensional for statistical mechanical analysis. Furthermore,…
Collaborative filtering is an effective recommendation approach in which the preference of a user on an item is predicted based on the preferences of other users with similar interests. A big challenge in using collaborative filtering…
Collaborative filtering is one of the most popular techniques in designing recommendation systems, and its most representative model, matrix factorization, has been wildly used by researchers and the industry. However, this model suffers…
Poisson factorization is a probabilistic model of users and items for recommendation systems, where the so-called implicit consumer data is modeled by a factorized Poisson distribution. There are many variants of Poisson factorization…
In network science, researchers often use mutual information to understand the difference between network partitions produced by community detection methods. Here we extend the use of mutual information to covers, that is, the cases where a…
Polytopic matrix factorization (PMF) is a recently introduced matrix decomposition method in which the data vectors are modeled as linear transformations of samples from a polytope. The successful recovery of the original factors in the…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
In this paper, we explore the application of Gaussian Processes (GPs) for predicting mean-reverting time series with an underlying structure, using relatively unexplored functional and augmented data structures. While many conventional…