In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories. In particular, we focus on equivalent representations of the systems in the two frameworks for the problem of simulating a future nonlinear system trajectory starting from a given set of noisy data. The goal also includes extending some existing results from the deterministic to the stochastic setting.

The network control theory framework holds great potential to inform neurostimulation experiments aimed at inducing desired activity states in the brain. However, the current applicability of the framework is limited by inappropriate modeling of brain dynamics, and an overly ambitious focus on whole-brain activity control. In this work, we leverage recent progress in linear modeling of brain dynamics (effective connectivity) and we exploit the concept of target controllability to focus on the control of a single region or a small subnetwork of nodes. We discuss when control may be possible with a reasonably low energy cost and few stimulation loci, and give general predictions on where to stimulate depending on the subset of regions one wishes to control. Importantly, using the robustly asymmetric effective connectome instead of the symmetric structural connectome (as in previous research), we highlight the fundamentally different roles in- and out-hubs have in the control problem, and the relevance of inhibitory connections. The large degree of inter-individual variation in the effective connectome implies that the control problem is best formulated at the individual level, but we discuss to what extent group results may still prove useful.

In texture synthesis and classification, algorithms require a small texture to be provided as an input, which is assumed to be representative of a larger region to be re-synthesized or categorized. We focus on how to characterize such textures and automatically retrieve them. Most works generate these small input textures manually by cropping, which does not ensure maximal compression, nor that the selection is the best representative of the original. We construct a new representation that compactly summarizes a texture, while using less storage, that can be used for texture compression and synthesis. We also demonstrate how the representation can be integrated in our proposed video texture synthesis algorithm to generate novel instances of textures and video hole-filling. Finally, we propose a novel criterion that measures structural and statistical dissimilarity between textures.

Inference of three-dimensional motion from the fusion of inertial and visual sensory data has to contend with the preponderance of outliers in the latter. Robust filtering deals with the joint inference and classification task of selecting which data fits the model, and estimating its state. We derive the optimal discriminant and propose several approximations, some used in the literature, others new. We compare them analytically, by pointing to the assumptions underlying their approximations, and empirically. We show that the best performing method improves the performance of state-of-the-art visual-inertial sensor fusion systems, while retaining the same computational complexity.

We characterize ``visual textures'' as realizations of a stationary, ergodic, Markovian process, and propose using its approximate minimal sufficient statistics for compressing texture images. We propose inference algorithms for estimating the ``state'' of such process and its ``variability''. These represent the encoding stage. We also propose a non-parametric sampling scheme for decoding, by synthesizing textures from their encoding. While these are not faithful reproductions of the original textures (so they would fail a comparison test based on PSNR), they capture the statistical properties of the underlying process, as we demonstrate empirically. We also quantify the tradeoff between fidelity (measured by a proxy of a perceptual score) and complexity.

We describe the tradeoff between the performance in a visual recognition problem and the control authority that the agent can exercise on the sensing process. We focus on the problem of “visual search” of an object in an otherwise known and static scene, propose a measure of control authority, and relate it to the expected risk and its proxy (conditional entropy of the posterior density). We show this analytically, as well as empirically by simulation using the simplest known model that captures the phenomenology of image formation, including scaling and occlusions. We show that a “passive” agent given a training set can provide no guarantees on performance beyond what is afforded by the priors, and that an “omnipotent” agent, capable of infinite control authority, can achieve arbitrarily good performance (asymptotically).

Summary form only given. In this article the simplest task (binary decision) for channels subject to scaling and occlusion phenomena, ubiquitous in remote sensing and imaging data is discussed. In order to extend Rate-Distortion theory, the tradeoff between decision performance (expected risk) and resources ("rate") is characterized. In the presence of scaling and occlusions, in order to trade off the expected risk, it is necessary to exercise control on the sensing process. Thus the natural generalization of "rate" is not the volume of the data provided by the sensor, but the amount of control authority that can be exercised on it, measured by the volume of the reachable set and the energy of the input.

We introduce a new Bayesian nonparametric approach to identification of sparse dynamic linear systems. The impulse responses are modeled as Gaussian processes whose autocovariances encode the BIBO stability constraint, as defined by the recently introduced “Stable Spline kernel”. Sparse solutions are obtained by placing exponential hyperpriors on the scale factors of such kernels. Numerical experiments regarding estimation of ARMAX models show that this technique provides a definite advantage over a group LAR algorithm and state-of-the-art parametric identification techniques based on prediction error minimization.

In this paper, we consider the problem of estimating the state of a dynamical system from distributed noisy measurements. Each agent constructs a local estimate based on its own measurements and on the estimates from its neighbors. Estimation is performed via a two stage strategy, the first being a Kalman-like measurement update which does not require communication, and the second being an estimate fusion using a consensus matrix. In particular we study the interaction between the consensus matrix, the number of messages exchanged per sampling time, and the Kalman gain for scalar systems. We prove that optimizing the consensus matrix for fastest convergence and using the centralized optimal gain is not necessarily the optimal strategy if the number of exchanged messages per sampling time is small. Moreover, we show that although the joint optimization of the consensus matrix and the Kalman gain is in general a non-convex problem, it is possible to compute them under some relevant scenarios. We also provide some numerical examples to clarify some of the analytical results and compare them with alternative estimation strategies.

We address the problem of performing decision tasks, and in particular classification and recognition, in the space of dynamical models in order to compare time series of data. Motivated by the application of recognition of human motion in image sequences, we consider a class of models that include linear dynamics, both stable and marginally stable (periodic), both minimum and non-minimum phase, driven by non-Gaussian processes. This requires extending existing learning and system identification algorithms to handle periodic modes and nonminimum phase behavior, while taking into account higher-order statistics of the data. Once a model is identified, we define a kernel-based cord distance between models that includes their dynamics, their initial conditions as well as input distribution. This is made possible by a novel kernel defined between two arbitrary (non-Gaussian) distributions, which is computed by efficiently solving an optimal transport problem. We validate our choice of models, inference algorithm, and distance on the tasks of human motion synthesis (sample paths of the learned models), and recognition (nearest-neighbor classification in the computed distance). However, our work can be applied more broadly where one needs to compare historical data while taking into account periodic trends, non-minimum phase behavior, and non-Gaussian input distributions.

We describe an algorithm for reconstructing three-dimensional structure and motion causally, in real time from monocular sequences of images. We prove that the algorithm is minimal and stable, in the sense that the estimation error remains bounded with probability one throughout a sequence of arbitrary length. We discuss a scheme for handling occlusions (point features appearing and disappearing) and drift in the scale factor. These issues are crucial for the algorithm to operate in real time on real scenes. We describe in detail the implementation of the algorithm, which runs on a personal computer and has been made available to the community. We report the performance of our implementation on a few representative long sequences of real and synthetic images. The algorithm, which has been tested extensively over the course of the past few years, exhibits honest performance when the scene contains at least 20-40 points with high contrast, when the relative motion is "slow" compared to the sampling frequency of the frame grabber (30 Hz), and the lens aperture is "large enough" (typically more than 30/spl deg/ of visual field).

We pose the problem of recognizing different types of human gait in the space of dynamical systems where each gait is represented Established techniques are employed to track a kinematic model of a human body in motion, and the trajectories of the parameters are used to learn a representation of a dynamical system, which defines a gait. Various types of distance between models are then computed These computations are non trivial due to the fact that, even for the case of linear systems, the space of canonical realizations is not linear.