Related papers: Statistical physics approaches to subnetwork dynam…
Nature presents multiple intriguing examples of processes which proceed at high precision and regularity. This remarkable stability is frequently counter to modelers' experience with the inherent stochasticity of chemical reactions in the…
There is increasing interest in learning how human brain networks vary as a function of a continuous trait, but flexible and efficient procedures to accomplish this goal are limited. We develop a Bayesian semiparametric model, which…
In this paper, we consider the problem of model order reduction of stochastic biochemical networks. In particular, we reduce the order of (the number of equations in) the Linear Noise Approximation of the Chemical Master Equation, which is…
Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real…
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…
Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses,…
For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set…
Gaussian process regression is a powerful Bayesian nonlinear regression method. Recent research has enabled the capture of many types of observations using non-Gaussian likelihoods. To deal with various tasks in spatial modeling, we benefit…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that…
Network theory has proven invaluable in unraveling complex protein interactions. Previous studies have employed statistical methods rooted in network theory, including the Gaussian graphical model, to infer networks among proteins,…
Inference in Gaussian process (GP) models is computationally challenging for large data, and often difficult to approximate with a small number of inducing points. We explore an alternative approximation that employs stochastic inference…
The network inference problem arises in biological research when one needs to quantitatively choose the best protein-interaction model for explaining a phenotype. The diverse nature of the data and nonlinear dynamics pose significant…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…
One of the focus areas of modern scientific research is to reveal mysteries related to genes and their interactions. The dynamic interactions between genes can be encoded into a gene regulatory network (GRN), which can be used to gain…
Stochastic Gumbel graph networks are proposed to learn high-dimensional time series, where the observed dimensions are often spatially correlated. To that end, the observed randomness and spatial-correlations are captured by learning the…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…