Streaming covariance selection with applications to adaptive querying in sensor networks

Sensor networks can be naturally represented as graphical models, where the edge set encodes the presence of sparsity in the correlation structure between sensors. Such graphical representations can be valuable for information mining purposes as well as for optimizing bandwidth and battery usage with minimal loss of estimation accuracy. We use a computationally efficient technique for estimating sparse graphical models which fits a sparse linear regression locally at each node of the graph via the Lasso estimator. Using a recently suggested online, temporally adaptive implementation of the Lasso, we propose an algorithm for streaming graphical model selection over sensor networks. With battery consumption minimization applications in mind, we use this algorithm as the basis of an adaptive querying scheme. We discuss implementation issues in the context of environmental monitoring using sensor networks, where the objective is short-term forecasting of local wind direction. The algorithm is tested against real UK weather data and conclusions are drawn about certain tradeoffs inherent in decentralized sensor networks data analysis. © 2010 The Author. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved.

Filtering via approximate Bayesian computation

Approximate Bayesian computation (ABC) has become a popular technique to facilitate Bayesian inference from complex models. In this article we present an ABC approximation designed to perform biased filtering for a Hidden Markov Model when the likelihood function is intractable. We use a sequential Monte Carlo (SMC) algorithm to both fit and sample from our ABC approximation of the target probability density. This approach is shown to, empirically, be more accurate w.r.t.~the original filter than competing methods. The theoretical bias of our method is investigated; it is shown that the bias goes to zero at the expense of increased computational effort. Our approach is illustrated on a constrained sequential lasso for portfolio allocation to 15 constituents of the FTSE 100 share index.

Optimal control predicts human performance on objects with internal degrees of freedom.

On a daily basis, humans interact with a vast range of objects and tools. A class of tasks, which can pose a serious challenge to our motor skills, are those that involve manipulating objects with internal degrees of freedom, such as when folding laundry or using a lasso. Here, we use the framework of optimal feedback control to make predictions of how humans should interact with such objects. We confirm the predictions experimentally in a two-dimensional object manipulation task, in which subjects learned to control six different objects with complex dynamics. We show that the non-intuitive behavior observed when controlling objects with internal degrees of freedom can be accounted for by a simple cost function representing a trade-off between effort and accuracy. In addition to using a simple linear, point-mass optimal control model, we also used an optimal control model, which considers the non-linear dynamics of the human arm. We find that the more realistic optimal control model captures aspects of the data that cannot be accounted for by the linear model or other previous theories of motor control. The results suggest that our everyday interactions with objects can be understood by optimality principles and advocate the use of more realistic optimal control models for the study of human motor neuroscience.

Convex approaches to model wavelet sparsity patterns

Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees (HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence of a sensing or observation matrix produces a linear mixing of the simple Markovian dependency structure. This leads to reconstruction problems that are non-convex optimizations. Past work has dealt with this issue by resorting to greedy or suboptimal iterative reconstruction methods. In this paper, we propose new modeling approaches based on group-sparsity penalties that leads to convex optimizations that can be solved exactly and efficiently. We show that the methods we develop perform significantly better in de-convolution and compressed sensing applications, while being as computationally efficient as standard coefficient-wise approaches such as lasso. © 2011 IEEE.

ℓasso MPC: Smart regulation of over-actuated systems

In this paper, a novel MPC strategy is proposed, and referred to as asso MPC. The new paradigm features an 1-regularised least squares loss function, in which the control error variance competes with the sum of input channels magnitude (or slew rate) over the whole horizon length. This cost choice is motivated by the successful development of LASSO theory in signal processing and machine learning. In the latter fields, sum-of-norms regularisation have shown a strong capability to provide robust and sparse solutions for system identification and feature selection. In this paper, a discrete-time dual-mode asso MPC is formulated, and its stability is proven by application of standard MPC arguments. The controller is then tested for the problem of ship course keeping and roll reduction with rudder and fins, in a directional stochastic sea. Simulations show the asso MPC to inherit positive features from its corresponding regressor: extreme reduction of decision variables' magnitude, namely, actuators' magnitude (or variations), with a finite energy error, being particularly promising for over-actuated systems. © 2012 AACC American Automatic Control Council).

Stabilising terminal cost and terminal controller for ℓasso- MPC: Enhanced optimality and region of attraction

In recent literature, ℓ1-regularised MPC, or ℓasso-MPC, has been recommended for control tasks involving complex requirements on the control signals, for instance, the simultaneous solution of regulation and sharp control allocation for redundantly-actuated systems. This is due to the implicit thresholding ability of LASSO regression. In this paper, a stabilising terminal cost featuring a mixed ℓ1/ℓ2 2 penalty is presented. Then, a candidate terminal controller is computed, with the aim of enlarging the region of attraction. © 2013 EUCA.