27,033 research outputs found
Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging
In this paper we present an optimization-based view of distributed parameter
estimation and observational social learning in networks. Agents receive a
sequence of random, independent and identically distributed (i.i.d.) signals,
each of which individually may not be informative about the underlying true
state, but the signals together are globally informative enough to make the
true state identifiable. Using an optimization-based characterization of
Bayesian learning as proximal stochastic gradient descent (with
Kullback-Leibler divergence from a prior as a proximal function), we show how
to efficiently use a distributed, online variant of Nesterov's dual averaging
method to solve the estimation with purely local information. When the true
state is globally identifiable, and the network is connected, we prove that
agents eventually learn the true parameter using a randomized gossip scheme. We
demonstrate that with high probability the convergence is exponentially fast
with a rate dependent on the KL divergence of observations under the true state
from observations under the second likeliest state. Furthermore, our work also
highlights the possibility of learning under continuous adaptation of network
which is a consequence of employing constant, unit stepsize for the algorithm.Comment: 6 pages, To appear in Conference on Decision and Control 201
The Neural Particle Filter
The robust estimation of dynamically changing features, such as the position
of prey, is one of the hallmarks of perception. On an abstract, algorithmic
level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing
signals based on the history of observations, provides a mathematical framework
for dynamic perception in real time. Since the general, nonlinear filtering
problem is analytically intractable, particle filters are considered among the
most powerful approaches to approximating the solution numerically. Yet, these
algorithms prevalently rely on importance weights, and thus it remains an
unresolved question how the brain could implement such an inference strategy
with a neuronal population. Here, we propose the Neural Particle Filter (NPF),
a weight-less particle filter that can be interpreted as the neuronal dynamics
of a recurrently connected neural network that receives feed-forward input from
sensory neurons and represents the posterior probability distribution in terms
of samples. Specifically, this algorithm bridges the gap between the
computational task of online state estimation and an implementation that allows
networks of neurons in the brain to perform nonlinear Bayesian filtering. The
model captures not only the properties of temporal and multisensory integration
according to Bayesian statistics, but also allows online learning with a
maximum likelihood approach. With an example from multisensory integration, we
demonstrate that the numerical performance of the model is adequate to account
for both filtering and identification problems. Due to the weightless approach,
our algorithm alleviates the 'curse of dimensionality' and thus outperforms
conventional, weighted particle filters in higher dimensions for a limited
number of particles
Bayesian Policy Gradients via Alpha Divergence Dropout Inference
Policy gradient methods have had great success in solving continuous control
tasks, yet the stochastic nature of such problems makes deterministic value
estimation difficult. We propose an approach which instead estimates a
distribution by fitting the value function with a Bayesian Neural Network. We
optimize an -divergence objective with Bayesian dropout approximation
to learn and estimate this distribution. We show that using the Monte Carlo
posterior mean of the Bayesian value function distribution, rather than a
deterministic network, improves stability and performance of policy gradient
methods in continuous control MuJoCo simulations.Comment: Accepted to Bayesian Deep Learning Workshop at NIPS 201
Distributed Learning with Infinitely Many Hypotheses
We consider a distributed learning setup where a network of agents
sequentially access realizations of a set of random variables with unknown
distributions. The network objective is to find a parametrized distribution
that best describes their joint observations in the sense of the
Kullback-Leibler divergence. Apart from recent efforts in the literature, we
analyze the case of countably many hypotheses and the case of a continuum of
hypotheses. We provide non-asymptotic bounds for the concentration rate of the
agents' beliefs around the correct hypothesis in terms of the number of agents,
the network parameters, and the learning abilities of the agents. Additionally,
we provide a novel motivation for a general set of distributed Non-Bayesian
update rules as instances of the distributed stochastic mirror descent
algorithm.Comment: Submitted to CDC201
A Factor Graph Approach to Automated Design of Bayesian Signal Processing Algorithms
The benefits of automating design cycles for Bayesian inference-based
algorithms are becoming increasingly recognized by the machine learning
community. As a result, interest in probabilistic programming frameworks has
much increased over the past few years. This paper explores a specific
probabilistic programming paradigm, namely message passing in Forney-style
factor graphs (FFGs), in the context of automated design of efficient Bayesian
signal processing algorithms. To this end, we developed "ForneyLab"
(https://github.com/biaslab/ForneyLab.jl) as a Julia toolbox for message
passing-based inference in FFGs. We show by example how ForneyLab enables
automatic derivation of Bayesian signal processing algorithms, including
algorithms for parameter estimation and model comparison. Crucially, due to the
modular makeup of the FFG framework, both the model specification and inference
methods are readily extensible in ForneyLab. In order to test this framework,
we compared variational message passing as implemented by ForneyLab with
automatic differentiation variational inference (ADVI) and Monte Carlo methods
as implemented by state-of-the-art tools "Edward" and "Stan". In terms of
performance, extensibility and stability issues, ForneyLab appears to enjoy an
edge relative to its competitors for automated inference in state-space models.Comment: Accepted for publication in the International Journal of Approximate
Reasonin
A Bayesian Network View on Acoustic Model-Based Techniques for Robust Speech Recognition
This article provides a unifying Bayesian network view on various approaches
for acoustic model adaptation, missing feature, and uncertainty decoding that
are well-known in the literature of robust automatic speech recognition. The
representatives of these classes can often be deduced from a Bayesian network
that extends the conventional hidden Markov models used in speech recognition.
These extensions, in turn, can in many cases be motivated from an underlying
observation model that relates clean and distorted feature vectors. By
converting the observation models into a Bayesian network representation, we
formulate the corresponding compensation rules leading to a unified view on
known derivations as well as to new formulations for certain approaches. The
generic Bayesian perspective provided in this contribution thus highlights
structural differences and similarities between the analyzed approaches
- …