25 papers · ranked by Valyu relevance
Kirk Sturtz
Using the symmetric monoidal closed category structure of the category of measurable spaces, in conjunction with the Giry monad which we show is a strong monad, we analyze Bayesian inference maps and their construction in relation to the tensor product probability. This perspective permits the inference maps to be seen…
Yeowon Kim, Yul H. R. Kang
Navigation requires perception: location must be inferred from noisy and ambiguous egocentric sensory inputs, as in visual estimation of distance. However, many classical models of spatial representation implicitly assume that allocentric location is directly observable, thereby neglecting perceptual uncertainty. Here…
Changhe Yuan, Tsai-Ching Lu, Marek J. Drużdżel
Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22], even for constrained networks, such as polytrees [18]. Hence, previous…
Noah C. Benson, Jonathan Winawer
A major question in human neuroscience is how cortical function is mapped onto surface anatomy. Retinotopic maps, which tile about a quarter of the cortical surface, have served as a testbed to address this question. Prior work has shown that the location and retinotopic organization of posterior visual field maps…
M. Rule, P. Chaudhuri-Vayalambrone, M. Krstulovic, M. Bauza + 2 more
We present practical solutions to applying Gaussian-process methods to calculate spatial statistics for grid cells in large environments. Gaussian processes are a data efficient approach to inferring neural tuning as a function of time, space, and other variables. We discuss how to design appropriate kernels for grid…
Michael Evans, Gun Ho Jang
Consider a sampling model for data x, given by a collection of densities {f(· | θ) : θ ∈ Θ} with respect to a support measure µ on sample space X, and a proper prior, given by density π with respect to support measure ν on Θ. When the data x ∈ X is observed these ingredients lead to the posterior distribution on Θ with…
Yumi Shikauchi, Makoto Miyakoshi, Scott Makeig, John R. Iversen
We investigated Bayesian modelling of human whole-body motion capture data recorded during an exploratory real-space navigation task in an “Audiomaze” environment (see the companion paper by Miyakoshi et al. in the same volume) to study the effect of map learning on navigation behaviour. There were three models, a…
Ruohai Di, Peng Wang, Chuchao He, Zhigao Guo
Maximum a posteriori estimation (MAP) with Dirichlet prior has been shown to be effective in improving the parameter learning of Bayesian networks when the available data are insufficient. Given no extra domain knowledge, uniform prior is often considered for regularization. However, when the underlying parameter…
Kevin Linka, Gerhard A Holzapfel, Ellen Kuhl
Understanding uncertainty is critical, especially when data are sparse and variations are large. Bayesian neural networks offer a powerful strategy to build predictable models from sparse data, and inherently quantify both, aleatoric uncertainties of the data and epistemic uncertainties of the model. Yet, classical…
David C. Schneider, Roy Thompson
In 1755 Thomas Bayes expressed an interest in the problem of combining repeated measurements of the location of a star. Bayes described a tandem set-up of a ball thrown on a table, followed by repeated throws of a second ball. Bayes' table has long been taken as a billiard table, for which there is no evidence. We…
Natalya Denisova
The Bayesian approach Maximum a Posteriori (MAP) provides a common basis for developing statistical methods for solving ill-posed image reconstruction problems. MAP solutions are dependent on a priori model. Approaches developed in literature are based on prior models that describe the properties of the expected image…
Sanggyun Kim, Diego Mesa, Rui Ma, Todd P. Coleman
We consider the problem of transforming samples from one continuous source distribution into samples from another target distribution. We demonstrate with optimal transport theory that when the source distribution can be easily sampled from and the target distribution is log-concave, this can be tractably solved with…
Marcelo Pereyra
Maximum-a-posteriori (MAP) estimation is the main Bayesian estimation methodology in imaging sciences, where high dimensionality is often addressed by using Bayesian models that are log-concave and whose posterior mode can be computed efficiently by convex optimisation. However, despite its success and wide adoption…
Oliver Lüdtke, Esther Ulitzsch, Alexander Robitzsch
With small to modest sample sizes and complex models, maximum likelihood (ML) estimation of confirmatory factor analysis (CFA) models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators…
Hexuan Liu, Jimin Kim, Eli Shlizerman
We propose a data-driven approach to represent neuronal network dynamics as a Probabilistic Graphical Model (PGM). Our approach learns the PGM structure by employing dimension reduction to network response dynamics evoked by stimuli applied to each neuron separately. The outcome model captures how stimuli propagate…
Jonas Verhellen
In recent years, there have been considerable academic and industrial research efforts to develop novel generative models for high-performing, small molecules. Traditional, rules-based algorithms such as genetic algorithms [Jensen, Chem. Sci., 2019, 12, 3567-3572] have, however, been shown to rival deep learning…
Brandon S. Coventry, Edward L. Bartlett
Typical statistical practices in the biological sciences have been increasingly called into question due to difficulties in the replication of an increasing number of studies, many of which are confounded by the relative difficulty of null significance hypothesis testing designs and interpretation of p-values. Bayesian…
Chenxi Sui, Ziyang Jiang, Genesis Higueros, David Carlson + 1 more
High-performance batteries are poised for electrification of vehicles and therefore mitigate greenhouse gas emissions, which, in turn, promote a sustainable future. However, the design of optimized batteries is challenging due to the nonlinear governing physics and electrochemistry. Recent advancements have…
Konstantinos Bakas, John Kornak, Hernando Ombao
Bayesian methods are commonly applied to solve image analysis problems such as noise-reduction, feature enhancement and object detection. A primary limitation of these approaches is the computational complexity due to the interdependence of neighboring pixels which limits the ability to perform full posterior sampling…
Julia Sirock, Markus Vogel, Tina Seufert
Solving Bayesian problems poses many challenges, such as identifying relevant numerical information, classifying and translating it into mathematical formula language, and forming a mental representation. This triggers research on how to support the solving of Bayesian problems. The facilitating effect of using…
Julia Sirock, Markus Vogel, Tina Seufert
Solving Bayesian problems poses many challenges, such as identifying relevant numerical information, classifying, and translating it into mathematical formula language, and forming a mental representation. This triggers research on how to support the solving of Bayesian problems. The facilitating effect of using…
Lucian Chan, Geoffrey Hutchison, Garrett Morris
Generating low-energy molecular conformers is a key task for many areas of computational chemistry, molecular modeling and cheminformatics. Most current conformer generation methods primarily focus on generating geometrically diverse conformers rather than finding the most probable or energetically lowest minima. Here…
Lucian Chan, Geoffrey Hutchison, Garrett Morris
Generating low-energy molecular conformers is a key task for many areas of computational chemistry, molecular modeling and cheminformatics. Most current conformer generation methods primarily focus on generating geometrically diverse conformers rather than finding the most probable or energetically lowest minima. Here…
Yifan Wu, Aron Walsh, Alex Ganose
What is the minimum number of experiments, or calculations, required to find an optimal solution? Relevant chemical problems range from identifying a compound with target functionality within a given phase space to controlling materials synthesis and device fabrication conditions. A common feature in this application…
Authors not listed
Solving optimization problems, especially for nonlinear and constrained systems, is a challenge. Decades of specialized algorithms have been developed for general and special cases of root finding, minimization (including constraints), for parameter estimation, and mapping connected spaces. These approaches typically…