Related papers: Bayesian machine learning via category theory
The problem of sequentially maximizing the expectation of a function seeks to maximize the expected value of a function of interest without having direct control on its features. Instead, the distribution of such features depends on a given…
A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…
We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…
We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric…
This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate…
Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…
Latent class analysis is used to perform model based clustering for multivariate categorical responses. Selection of the variables most relevant for clustering is an important task which can affect the quality of clustering considerably.…
In reinforcement learning, conducting task composition by forming cohesive, executable sequences from multiple tasks remains challenging. However, the ability to (de)compose tasks is a linchpin in developing robotic systems capable of…
We present a novel, yet rather simple construction within the traditional framework of Scott domains to provide semantics to probabilistic programming, thus obtaining a solution to a long-standing open problem in this area. Unlike current…
Quantifying spatial and/or temporal associations in multivariate geolocated data of different types is achievable via spatial random effects in a Bayesian hierarchical model, but severe computational bottlenecks arise when spatial…
State space models have long played an important role in signal processing. The Gaussian case can be treated algorithmically using the famous Kalman filter. Similarly since the 1970s there has been extensive application of Hidden Markov…
Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…
Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…
Markov categories are the central framework for categorical probability theory. Many important concepts from probability theory can be formalized in terms of Markov categories. In particular, conditional probability distributions and Bayes'…
We comment on some conceptual and and technical problems related to computational mechanics, point out some errors in several papers, and straighten out some wrong priority claims. We present explicitly the correct algorithm for…
We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…
Multivariate categorical data are common in many fields. We are motivated by election polls studies assessing evidence of changes in voters opinions with their candidates preferences in the 2016 United States Presidential primaries or…
In this paper, we are interested in optimal decisions in a partially observable Markov universe. Our viewpoint departs from the dynamic programming viewpoint: we are directly approximating an optimal strategic tree depending on the…
We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…