Related papers: Fast Non-Parametric Bayesian Inference on Infinite…

We propose a novel Bayesian neural network architecture that can learn invariances from data alone by inferring a posterior distribution over different weight-sharing schemes. We show that our model outperforms other non-invariant…

Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov-Smirnov and Cramer-von-Mises tests do not scale well as the dimensionality increases and…

A Bayesian nonparametric approach to the study of species diversity based on choosing a random discrete distribution as a prior model for the unknown relative abundances of species has been recently introduced in Lijoi et al. (2007, 2008).…

Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…

Predicting the winner of an election is of importance to multiple stakeholders. To formulate the problem, we consider an independent sequence of categorical data with a finite number of possible outcomes in each. The data is assumed to be…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…

Bayesian Neural Networks provide a principled framework for uncertainty quantification by modeling the posterior distribution of network parameters. However, exact posterior inference is computationally intractable, and widely used…

Density estimation plays a crucial role in many data analysis tasks, as it infers a continuous probability density function (PDF) from discrete samples. Thus, it is used in tasks as diverse as analyzing population data, spatial locations in…

Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…

A Bayesian network is a directed acyclic graph that represents statistical dependencies between variables of a joint probability distribution. A fundamental task in data science is to learn a Bayesian network from observed data.…

Bayesian networks are popular probabilistic models that capture the conditional dependencies among a set of variables. Inference in Bayesian networks is a fundamental task for answering probabilistic queries over a subset of variables in…

Performing exact posterior inference in complex generative models is often difficult or impossible due to an expensive to evaluate or intractable likelihood function. Approximate Bayesian computation (ABC) is an inference framework that…

Bayes' theorem incorporates distinct types of information through the likelihood and prior. Direct observations of state variables enter the likelihood and modify posterior probabilities through consistent updating. Information in terms of…

Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…

Distribution regression, where the goal is to predict a scalar response from a distribution-valued predictor, arises naturally in settings where observations are grouped and outcomes depend on group-level characteristics rather than on…

Random forests are a scheme proposed by Leo Breiman in the 2000's for building a predictor ensemble with a set of decision trees that grow in randomly selected subspaces of data. Despite growing interest and practical use, there has been…

The context tree source is a source model in which the occurrence probability of symbols is determined from a finite past sequence, and is a broader class of sources that includes i.i.d. and Markov sources. The proposed source model in this…

To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…

Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…