2,622 research outputs found
Information-Geometric Optimization Algorithms: A Unifying Picture via Invariance Principles
We present a canonical way to turn any smooth parametric family of
probability distributions on an arbitrary search space into a
continuous-time black-box optimization method on , the
\emph{information-geometric optimization} (IGO) method. Invariance as a design
principle minimizes the number of arbitrary choices. The resulting \emph{IGO
flow} conducts the natural gradient ascent of an adaptive, time-dependent,
quantile-based transformation of the objective function. It makes no
assumptions on the objective function to be optimized.
The IGO method produces explicit IGO algorithms through time discretization.
It naturally recovers versions of known algorithms and offers a systematic way
to derive new ones. The cross-entropy method is recovered in a particular case,
and can be extended into a smoothed, parametrization-independent maximum
likelihood update (IGO-ML). For Gaussian distributions on , IGO
is related to natural evolution strategies (NES) and recovers a version of the
CMA-ES algorithm. For Bernoulli distributions on , we recover the
PBIL algorithm. From restricted Boltzmann machines, we obtain a novel algorithm
for optimization on . All these algorithms are unified under a
single information-geometric optimization framework.
Thanks to its intrinsic formulation, the IGO method achieves invariance under
reparametrization of the search space , under a change of parameters of the
probability distributions, and under increasing transformations of the
objective function.
Theory strongly suggests that IGO algorithms have minimal loss in diversity
during optimization, provided the initial diversity is high. First experiments
using restricted Boltzmann machines confirm this insight. Thus IGO seems to
provide, from information theory, an elegant way to spontaneously explore
several valleys of a fitness landscape in a single run.Comment: Final published versio
On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions
Game theory offers an interpretable mathematical framework for modeling
multi-agent interactions. However, its applicability in real-world robotics
applications is hindered by several challenges, such as unknown agents'
preferences and goals. To address these challenges, we show a connection
between differential games, optimal control, and energy-based models and
demonstrate how existing approaches can be unified under our proposed
Energy-based Potential Game formulation. Building upon this formulation, this
work introduces a new end-to-end learning application that combines neural
networks for game-parameter inference with a differentiable game-theoretic
optimization layer, acting as an inductive bias. The experiments using
simulated mobile robot pedestrian interactions and real-world automated driving
data provide empirical evidence that the game-theoretic layer improves the
predictive performance of various neural network backbones.Comment: International Conference on Machine Learning, Workshop on New
Frontiers in Learning, Control, and Dynamical Systems (ICML 2023
Frontiers4LCD
Mixing and non-mixing local minima of the entropy contrast for blind source separation
In this paper, both non-mixing and mixing local minima of the entropy are
analyzed from the viewpoint of blind source separation (BSS); they correspond
respectively to acceptable and spurious solutions of the BSS problem. The
contribution of this work is twofold. First, a Taylor development is used to
show that the \textit{exact} output entropy cost function has a non-mixing
minimum when this output is proportional to \textit{any} of the non-Gaussian
sources, and not only when the output is proportional to the lowest entropic
source. Second, in order to prove that mixing entropy minima exist when the
source densities are strongly multimodal, an entropy approximator is proposed.
The latter has the major advantage that an error bound can be provided. Even if
this approximator (and the associated bound) is used here in the BSS context,
it can be applied for estimating the entropy of any random variable with
multimodal density.Comment: 11 pages, 6 figures, To appear in IEEE Transactions on Information
Theor
Procedural function-based modelling of volumetric microstructures
We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parameterised models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented
Quantifying the Evolutionary Self Structuring of Embodied Cognitive Networks
We outline a possible theoretical framework for the quantitative modeling of
networked embodied cognitive systems. We notice that: 1) information self
structuring through sensory-motor coordination does not deterministically occur
in Rn vector space, a generic multivariable space, but in SE(3), the group
structure of the possible motions of a body in space; 2) it happens in a
stochastic open ended environment. These observations may simplify, at the
price of a certain abstraction, the modeling and the design of self
organization processes based on the maximization of some informational
measures, such as mutual information. Furthermore, by providing closed form or
computationally lighter algorithms, it may significantly reduce the
computational burden of their implementation. We propose a modeling framework
which aims to give new tools for the design of networks of new artificial self
organizing, embodied and intelligent agents and the reverse engineering of
natural ones. At this point, it represents much a theoretical conjecture and it
has still to be experimentally verified whether this model will be useful in
practice.
Extraction of Audio Features Specific to Speech using Information Theory and Differential Evolution
We present a method that exploits an information theoretic framework to extract optimized audio features using the video information. A simple measure of mutual information (MI) between the resulting audio features and the video ones allows to detect the active speaker among different candidates. Our method involves the optimization of an MI-based objective function. No approximation is introduced to solve this optimization problem, neither concerning the estimation of the probability density functions (pdf) of the features, nor the cost function itself. The pdf are estimated from the samples using a non-parametric approach. As far as concern the optimization process itself, three different optimization methods (one local and two globals) are compared in this paper. The Differential Evolution algorithm is shown to be outstanding performant for our problem and is threrefore eventually retains. Two information theoretic optimization criteria are compared and their ability to extract audio features specific to speeh is discussed. As a result, our method achieves a speaker detection rate of 100% on our test sequences, and of 95% on a state-of-the-art sequence
Extraction of audio features specific to speech production for multimodal speaker detection
A method that exploits an information theoretic framework to extract optimized audio features using video information is presented. A simple measure of mutual information (MI) between the resulting audio and video features allows the detection of the active speaker among different candidates. This method involves the optimization of an MI-based objective function. No approximation is needed to solve this optimization problem, neither for the estimation of the probability density functions (pdf) of the features, nor for the cost function itself. The pdf are estimated from the samples using a non-parametric approach. The challenging optimization problem is solved using a global method: the Differential Evolution algorithm. Two information theoretic optimization criteria are compared and their ability to extract audio features specific to speech is discussed. Using these specific speech audio features, candidates video features are then classified as membership of the "speaker" or "non-speaker" class, resulting in a speaker detection scheme. As a result, our method achieves a speaker detection rate of 100% on home- grown test sequences, and of 85% on most commonly used sequences
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