Related papers: Simulations of Gaussian Processes and Neuronal Mod…
In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of this paper is to deal with an infinite number of components.…
The brain constantly turns large flows of sensory information into selective representations of the environment. It, therefore, needs to learn to process those sensory inputs that are most relevant for behaviour. It is not well understood…
One major impediment to the wider use of deep learning for clinical decision making is the difficulty of assigning a level of confidence to model predictions. Currently, deep Bayesian neural networks and sparse Gaussian processes are the…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often…
When a program is loaded into memory for execution, the relative position of its basic blocks is crucial, since loading basic blocks that are unlikely to be executed first places them high in the instruction-memory hierarchy only to be…
Numerical simulation of continuous-time Markovian processes is an essential and widely applied tool in the investigation of epidemic spreading on complex networks. Due to the high heterogeneity of the connectivity structure through which…
Gaussian Processes (GPs) are Bayesian models that provide uncertainty estimates associated to the predictions made. They are also very flexible due to their non-parametric nature. Nevertheless, GPs suffer from poor scalability as the number…
In this paper we present a novel analysis of variance Gaussian process (ANOVA-GP) emulator for models governed by partial differential equations (PDEs) with high-dimensional random inputs. Gaussian process (GP) is a widely used surrogate…
Graph convolutional neural networks~(GCNs) have recently demonstrated promising results on graph-based semi-supervised classification, but little work has been done to explore their theoretical properties. Recently, several deep neural…
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene…
With the significant advancement in quantum computation in the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used…
Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…
A neural network (NN) is a parameterised function that can be tuned via gradient descent to approximate a labelled collection of data with high precision. A Gaussian process (GP), on the other hand, is a probabilistic model that defines a…
Filtered shot noise processes have proven to be very effective in modelling the evolution of systems exposed to stochastic shot noise sources, and have been applied to a wide variety of fields ranging from electronics through biology. In…
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…
There are so many models in the literature that it is difficult for practitioners to decide which combinations are likely to be effective for a new task. This paper attempts to address this question by capturing relationships among…
The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the…
Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising…
In this paper, we study random subsampling of Gaussian process regression, one of the simplest approximation baselines, from a theoretical perspective. Although subsampling discards a large part of training data, we show provable guarantees…