40,773 research outputs found
Learning coupled forward-inverse models with combined prediction errors
Challenging tasks in unstructured environments require robots to learn complex models. Given a large amount of information, learning multiple simple models can offer an efficient alternative to a monolithic complex network. Training multiple models—that is, learning their parameters and their responsibilities—has been shown to be prohibitively hard as optimization is prone to local minima. To efficiently learn multiple models for different contexts, we thus develop a new algorithm based on expectation maximization (EM). In contrast to comparable concepts, this algorithm trains multiple modules of paired forward-inverse models by using the prediction errors of both forward and inverse models simultaneously. In particular, we show that our method yields a substantial improvement over only considering the errors of the forward models on tasks where the inverse space contains multiple solution
Learning Coupled Forward-Inverse Models with Combined Prediction Errors
Challenging tasks in unstructured environments require robots to learn complex models. Given a large amount of information, learning multiple simple models can offer an efficient alternative to a monolithic complex network. Training multiple models-that is, learning their parameters and their responsibilities-has been shown to be prohibitively hard as optimization is prone to local minima. To efficiently learn multiple models for different contexts, we thus develop a new algorithm based on expectation maximization (EM). In contrast to comparable concepts, this algorithm trains multiple modules of paired forward-inverse models by using the prediction errors of both forward and inverse models simultaneously. In particular, we show that our method yields a substantial improvement over only considering the errors of the forward models on tasks where the inverse space contains multiple solutions
Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography
We study the feasibility of data based machine learning applied to ultrasound
tomography to estimate water-saturated porous material parameters. In this
work, the data to train the neural networks is simulated by solving wave
propagation in coupled poroviscoelastic-viscoelastic-acoustic media. As the
forward model, we consider a high-order discontinuous Galerkin method while
deep convolutional neural networks are used to solve the parameter estimation
problem. In the numerical experiment, we estimate the material porosity and
tortuosity while the remaining parameters which are of less interest are
successfully marginalized in the neural networks-based inversion. Computational
examples confirms the feasibility and accuracy of this approach
Probabilistic Models of Motor Production
N. Bernstein defined the ability of the central neural system (CNS) to control many degrees of freedom of a physical body with all its redundancy and flexibility as the main problem in motor control. He pointed at that man-made mechanisms usually have one, sometimes two degrees of freedom (DOF); when the number of DOF increases further, it becomes prohibitively hard to control them. The brain, however, seems to perform such control effortlessly. He suggested the way the brain might deal with it: when a motor skill is being acquired, the brain artificially limits the degrees of freedoms, leaving only one or two. As the skill level increases, the brain gradually "frees" the previously fixed DOF, applying control when needed and in directions which have to be corrected, eventually arriving to the control scheme where all the DOF are "free". This approach of reducing the dimensionality of motor control remains relevant even today.
One the possibles solutions of the Bernstetin's problem is the hypothesis of motor primitives (MPs) - small building blocks that constitute complex movements and facilitite motor learnirng and task completion. Just like in the visual system, having a homogenious hierarchical architecture built of similar computational elements may be beneficial.
Studying such a complicated object as brain, it is important to define at which level of details one works and which questions one aims to answer. David Marr suggested three levels of analysis: 1. computational, analysing which problem the system solves; 2. algorithmic, questioning which representation the system uses and which computations it performs; 3. implementational, finding how such computations are performed by neurons in the brain. In this thesis we stay at the first two levels, seeking for the basic representation of motor output.
In this work we present a new model of motor primitives that comprises multiple interacting latent dynamical systems, and give it a full Bayesian treatment. Modelling within the Bayesian framework, in my opinion, must become the new standard in hypothesis testing in neuroscience. Only the Bayesian framework gives us guarantees when dealing with the inevitable plethora of hidden variables and uncertainty.
The special type of coupling of dynamical systems we proposed, based on the Product of Experts, has many natural interpretations in the Bayesian framework. If the dynamical systems run in parallel, it yields Bayesian cue integration. If they are organized hierarchically due to serial coupling, we get hierarchical priors over the dynamics. If one of the dynamical systems represents sensory state, we arrive to the sensory-motor primitives. The compact representation that follows from the variational treatment allows learning of a motor primitives library. Learned separately, combined motion can be represented as a matrix of coupling values.
We performed a set of experiments to compare different models of motor primitives. In a series of 2-alternative forced choice (2AFC) experiments participants were discriminating natural and synthesised movements, thus running a graphics Turing test. When available, Bayesian model score predicted the naturalness of the perceived movements. For simple movements, like walking, Bayesian model comparison and psychophysics tests indicate that one dynamical system is sufficient to describe the data. For more complex movements, like walking and waving, motion can be better represented as a set of coupled dynamical systems. We also experimentally confirmed that Bayesian treatment of model learning on motion data is superior to the simple point estimate of latent parameters. Experiments with non-periodic movements show that they do not benefit from more complex latent dynamics, despite having high kinematic complexity.
By having a fully Bayesian models, we could quantitatively disentangle the influence of motion dynamics and pose on the perception of naturalness. We confirmed that rich and correct dynamics is more important than the kinematic representation.
There are numerous further directions of research. In the models we devised, for multiple parts, even though the latent dynamics was factorized on a set of interacting systems, the kinematic parts were completely independent. Thus, interaction between the kinematic parts could be mediated only by the latent dynamics interactions. A more flexible model would allow a dense interaction on the kinematic level too.
Another important problem relates to the representation of time in Markov chains. Discrete time Markov chains form an approximation to continuous dynamics. As time step is assumed to be fixed, we face with the problem of time step selection. Time is also not a explicit parameter in Markov chains. This also prohibits explicit optimization of time as parameter and reasoning (inference) about it. For example, in optimal control boundary conditions are usually set at exact time points, which is not an ecological scenario, where time is usually a parameter of optimization. Making time an explicit parameter in dynamics may alleviate this
The cerebellum could solve the motor error problem through error increase prediction
We present a cerebellar architecture with two main characteristics. The first
one is that complex spikes respond to increases in sensory errors. The second
one is that cerebellar modules associate particular contexts where errors have
increased in the past with corrective commands that stop the increase in error.
We analyze our architecture formally and computationally for the case of
reaching in a 3D environment. In the case of motor control, we show that there
are synergies of this architecture with the Equilibrium-Point hypothesis,
leading to novel ways to solve the motor error problem. In particular, the
presence of desired equilibrium lengths for muscles provides a way to know when
the error is increasing, and which corrections to apply. In the context of
Threshold Control Theory and Perceptual Control Theory we show how to extend
our model so it implements anticipative corrections in cascade control systems
that span from muscle contractions to cognitive operations.Comment: 34 pages (without bibliography), 13 figure
Multivariate Bayesian Predictive Synthesis in Macroeconomic Forecasting
We develop the methodology and a detailed case study in use of a class of
Bayesian predictive synthesis (BPS) models for multivariate time series
forecasting. This extends the recently introduced foundational framework of BPS
to the multivariate setting, with detailed application in the topical and
challenging context of multi-step macroeconomic forecasting in a monetary
policy setting. BPS evaluates-- sequentially and adaptively over time-- varying
forecast biases and facets of miscalibration of individual forecast densities,
and-- critically-- of time-varying inter-dependencies among them over multiple
series. We develop new BPS methodology for a specific subclass of the dynamic
multivariate latent factor models implied by BPS theory. Structured dynamic
latent factor BPS is here motivated by the application context-- sequential
forecasting of multiple US macroeconomic time series with forecasts generated
from several traditional econometric time series models. The case study
highlights the potential of BPS to improve of forecasts of multiple series at
multiple forecast horizons, and its use in learning dynamic relationships among
forecasting models or agents
Research and Education in Computational Science and Engineering
Over the past two decades the field of computational science and engineering
(CSE) has penetrated both basic and applied research in academia, industry, and
laboratories to advance discovery, optimize systems, support decision-makers,
and educate the scientific and engineering workforce. Informed by centuries of
theory and experiment, CSE performs computational experiments to answer
questions that neither theory nor experiment alone is equipped to answer. CSE
provides scientists and engineers of all persuasions with algorithmic
inventions and software systems that transcend disciplines and scales. Carried
on a wave of digital technology, CSE brings the power of parallelism to bear on
troves of data. Mathematics-based advanced computing has become a prevalent
means of discovery and innovation in essentially all areas of science,
engineering, technology, and society; and the CSE community is at the core of
this transformation. However, a combination of disruptive
developments---including the architectural complexity of extreme-scale
computing, the data revolution that engulfs the planet, and the specialization
required to follow the applications to new frontiers---is redefining the scope
and reach of the CSE endeavor. This report describes the rapid expansion of CSE
and the challenges to sustaining its bold advances. The report also presents
strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie
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