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Found 45 papers, 7 papers with code
A Convergence Analysis of Approximate Message Passing with Non-Separable Functions and Applications to Multi-Class Classification
Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et.
Variational Inference for SDEs Driven by Fractional Noise
In this paper, building upon the Markov approximation of fBM, we derive the evidence lower bound essential for efficient variational inference of posterior path measures, drawing from the well-established field of stochastic analysis.
Analysis of Random Sequential Message Passing Algorithms for Approximate Inference
We analyze the dynamics of a random sequential message passing algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario.
Adaptive Inducing Points Selection For Gaussian Processes
Gaussian Processes (\textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation.
Nonlinear Hawkes Process with Gaussian Process Self Effects
We continue the line of work of Bayesian inference for Hawkes processes, and our approach dispenses with the necessity of estimating a branching structure for the posterior, as we perform inference on an aggregated sum of Gaussian Processes.
Exact solution to the random sequential dynamics of a message passing algorithm
We analyze the random sequential dynamics of a message passing algorithm for Ising models with random interactions in the large system limit.
Gaussian Density Parametrization Flow: Particle and Stochastic Approaches
Bayesian inference is intractable for most practical problems and requires approximation schemes with several trade-offs.
Evidence Estimation by Kullback-Leibler Integration for Flow-Based Methods
Flow-based methods such as Stein Variational Gradient Descent caught a lot of interest due to their flexibility and the strong theory going with them.
A Dynamical Mean-Field Theory for Learning in Restricted Boltzmann Machines
We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations.
A Mathematical Model of Local and Global Attention in Natural Scene Viewing
Thus, the main contribution of our modeling approach is two--fold; first, we propose a new model for saccade generation in scene viewing.
Neurons and Cognition
Automated Augmented Conjugate Inference for Non-conjugate Gaussian Process Models
Building on the conjugate structure of the augmented model, we develop two inference methods.
Understanding the dynamics of message passing algorithms: a free probability heuristics
We use freeness assumptions of random matrix theory to analyze the dynamical behavior of inference algorithms for probabilistic models with dense coupling matrices in the limit of large systems.
Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach
We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario.
Tightening Bounds for Variational Inference by Revisiting Perturbation Theory
In this paper, we revisit perturbation theory as a powerful way of improving the variational approximation.
Multi-Class Gaussian Process Classification Made Conjugate: Efficient Inference via Data Augmentation
We propose a new scalable multi-class Gaussian process classification approach building on a novel modified softmax likelihood function.
Memory-free dynamics for the TAP equations of Ising models with arbitrary rotation invariant ensembles of random coupling matrices
We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices.
Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes
We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function.
Efficient Bayesian Inference for a Gaussian Process Density Model
We reconsider a nonparametric density model based on Gaussian processes.
Efficient Gaussian Process Classification Using Polya-Gamma Data Augmentation
We propose a scalable stochastic variational approach to GP classification building on Polya-Gamma data augmentation and inducing points.
Expectation Propagation for Approximate Inference: Free Probability Framework
We study asymptotic properties of expectation propagation (EP) -- a method for approximate inference originally developed in the field of machine learning.
Perturbative Black Box Variational Inference
Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences.
Inverse Ising problem in continuous time: A latent variable approach
For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.
A statistical physics approach to learning curves for the Inverse Ising problem
Assuming that the data are generated from a true Ising model, we compute the reconstruction error of the couplings using a combination of the replica method with the cavity approach for densely connected systems.
Approximate Bayes learning of stochastic differential equations
We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector.
Optimal Encoding and Decoding for Point Process Observations: an Approximate Closed-Form Filter
The process of dynamic state estimation (filtering) based on point process observations is in general intractable.
Self-Averaging Expectation Propagation
Our approach extends the framework of (generalized) approximate message passing -- assumes zero-mean iid entries of the measurement matrix -- to a general class of random matrix ensembles.
Variational perturbation and extended Plefka approaches to dynamics on random networks: the case of the kinetic Ising model
We first briefly consider the variational approach based on minimizing the Kullback-Leibler divergence between independent trajectories and the real ones and note that this approach only coincides with the mean field equations from the saddle point approximation to the generating functional when the dynamics is defined through a logistic link function, which is the case for the kinetic Ising model with parallel update.
Expectation propagation for continuous time stochastic processes
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints.
A Tractable Approximation to Optimal Point Process Filtering: Application to Neural Encoding
The process of dynamic state estimation (filtering) based on point process observations is in general intractable.
An Analytically Tractable Bayesian Approximation to Optimal Point Process Filtering
The process of dynamic state estimation (filtering) based on point process observations is in general intractable.
Optimal Neural Codes for Control and Estimation
Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations.
Poisson Process Jumping between an Unknown Number of Rates: Application to Neural Spike Data
We introduce a model where the rate of an inhomogeneous Poisson process is modified by a Chinese restaurant process.
Expectation Propagation
Variational inference is a powerful concept that underlies many iterative approximation algorithms; expectation propagation, mean-field methods and belief propagations were all central themes at the school that can be perceived from this unifying framework.
Optimal Population Codes for Control and Estimation
Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations.
Approximate Gaussian process inference for the drift function in stochastic differential equations
We introduce a nonparametric approach for estimating drift functions in systems of stochastic differential equations from incomplete observations of the state vector.
Approximate inference in latent Gaussian-Markov models from continuous time observations
We propose an approximate inference algorithm for continuous time Gaussian-Markov process models with both discrete and continuous time likelihoods.
Visualizing the Effects of a Changing Distance on Data Using Continuous Embeddings
The right scale is hard to pin down and it is preferable when results do not depend too tightly on the exact value one picked.
Temporal Autoencoding Improves Generative Models of Time Series
This leads to a significant improvement in the performance of both models in a filling-in-frames task across a number of datasets.
Perturbative Corrections for Approximate Inference in Gaussian Latent Variable Models
A perturbative expansion is made of the exact but intractable correction, and can be applied to the model's partition function and other moments of interest.
Inference in continuous-time change-point models
We consider the problem of Bayesian inference for continuous time multi-stable stochastic systems which can change both their diffusion and drift parameters at discrete times.
Analytical Results for the Error in Filtering of Gaussian Processes
Bayesian filtering of stochastic stimuli has received a great deal of attention re- cently.
Approximate inference in continuous time Gaussian-Jump processes
We present a novel approach to inference in conditionally Gaussian continuous time stochastic processes, where the latent process is a Markovian jump process.
Improving on Expectation Propagation
We develop as series of corrections to Expectation Propagation (EP), which is one of the most popular methods for approximate probabilistic inference.
Variational Inference for Diffusion Processes
Diffusion processes are a family of continuous-time continuous-state stochastic processes that are in general only partially observed.
Variational inference for Markov jump processes
Markov jump processes play an important role in a large number of application domains.
