Related papers: Bayesian inference of grid cell firing patterns us…
Decades of research on the neural code underlying spatial navigation have revealed a diverse set of neural response properties. The Entorhinal Cortex (EC) of the mammalian brain contains a rich set of spatial correlates, including grid…
We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…
In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…
In this paper we provide an overview of a new framework for robot perception, real-world modelling, and navigation that uses a stochastic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a…
We propose a new cellular network model that captures both deterministic and random aspects of base station deployments. Namely, the base station locations are modeled as the superposition of two independent stationary point processes: a…
Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…
In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…
Grid cells in the medial entorhinal cortex (MEC) of the mammalian brain exhibit a strikingly regular hexagonal firing field over space. These cells are learned after birth and are thought to support spatial navigation but also more abstract…
This paper considers neural representation through the lens of active inference, a normative framework for understanding brain function. It delves into how living organisms employ generative models to minimize the discrepancy between…
The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed,…
Patterns of microcircuitry suggest that the brain has an array of repeated canonical computational units. Yet neural representations are distributed, so the relevant computations may only be related indirectly to single-neuron…
To gain a deeper understanding of the behavior and learning dynamics of (deep) artificial neural networks, it is valuable to employ mathematical abstractions and models. These tools provide a simplified perspective on network performance…
The Bayesian view of the brain hypothesizes that the brain constructs a generative model of the world, and uses it to make inferences via Bayes' rule. Although many types of approximate inference schemes have been proposed for hierarchical…
This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is…
Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected…
Recent advances in local models for point processes have highlighted the need for flexible methodologies to account for the spatial heterogeneity of external covariates influencing process intensity. In this work, we introduce tessellated…
A central question in multimodal neuroimaging analysis is to understand the association between two imaging modalities and to identify brain regions where such an association is statistically significant. In this article, we propose a…
Sequences of neuronal activation have long been implicated in a variety of brain functions. In particular, these sequences have been tied to memory formation and spatial navigation in the hippocampus, a region of mammalian brains.…
Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way…
Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains…