Monthly Archives: February 2016

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Using multiple RANSACs for tracking

Peter C. Niedfeldt and Randal W. Beard, Convergence and Complexity Analysis of Recursive-RANSAC: A New Multiple Target Tracking Algorithm, in IEEE Transactions on Automatic Control , vol.61, no.2, pp.456-461, Feb. 2016, DOI: 10.1109/TAC.2015.2437518.

The random sample consensus (RANSAC) algorithm was developed as a regression algorithm that robustly estimates the parameters of a single signal in clutter by forming many simple hypotheses and computing how many measurements support that hypothesis. In essence, RANSAC estimates the data association problem of a single target in clutter by identifying the hypothesis with the most supporting measurements. The newly developed recursive-RANSAC (R-RANSAC) algorithm extends the traditional RANSAC algorithm to track multiple targets recursively by storing a set of hypotheses between time steps. In this technical note we show that R-RANSAC converges to the minimum mean-squared solution for well-spaced targets. We also show that the worst-case computational complexity of R-RANSAC is quadratic in the number of new measurements and stored models.

Limitations of the simulation of physical systems when used in AI reasoning processes for prediction

Ernest Davis, Gary Marcus, The scope and limits of simulation in automated reasoning, Artificial Intelligence, Volume 233, April 2016, Pages 60-72, ISSN 0004-3702, DOI: 10.1016/j.artint.2015.12.003.

In scientific computing and in realistic graphic animation, simulation – that is, step-by-step calculation of the complete trajectory of a physical system – is one of the most common and important modes of calculation. In this article, we address the scope and limits of the use of simulation, with respect to AI tasks that involve high-level physical reasoning. We argue that, in many cases, simulation can play at most a limited role. Simulation is most effective when the task is prediction, when complete information is available, when a reasonably high quality theory is available, and when the range of scales involved, both temporal and spatial, is not extreme. When these conditions do not hold, simulation is less effective or entirely inappropriate. We discuss twelve features of physical reasoning problems that pose challenges for simulation-based reasoning. We briefly survey alternative techniques for physical reasoning that do not rely on simulation.

It seems that the human motor cortex not only contains a map of motions but a map of basic behaviors (compositions of motions)

Michael S.A. Graziano, Ethological Action Maps: A Paradigm Shift for the Motor Cortex, Trends in Cognitive Sciences, Volume 20, Issue 2, February 2016, Pages 121-132, ISSN 1364-6613, DOI: 10.1016/j.tics.2015.10.008.

The map of the body in the motor cortex is one of the most iconic images in neuroscience. The map, however, is not perfect. It contains overlaps, reversals, and fractures. The complex pattern suggests that a body plan is not the only organizing principle. Recently a second organizing principle was discovered: an action map. The motor cortex appears to contain functional zones, each of which emphasizes an ethologically relevant category of behavior. Some of these complex actions can be evoked by cortical stimulation. Although the findings were initially controversial, interest in the ethological action map has grown. Experiments on primates, mice, and rats have now confirmed and extended the earlier findings with a range of new methods.

A method to predict the grading of students during a course

Yannick Meier, Jie Xu, Onur Atan, and Mihaela van der Schaar, Predicting Grades, in IEEE Transactions on Signal Processing , vol.64, no.4, pp.959-972, Feb.15, 2016, DOI: 10.1109/TSP.2015.2496278.


To increase efficacy in traditional classroom courses as well as in Massive Open Online Courses (MOOCs), automated systems supporting the instructor are needed. One important problem is to automatically detect students that are going to do poorly in a course early enough to be able to take remedial actions. Existing grade prediction systems focus on maximizing the accuracy of the prediction while overseeing the importance of issuing timely and personalized predictions. This paper proposes an algorithm that predicts the final grade of each student in a class. It issues a prediction for each student individually, when the expected accuracy of the prediction is sufficient. The algorithm learns online what is the optimal prediction and time to issue a prediction based on past history of students’ performance in a course. We derive a confidence estimate for the prediction accuracy and demonstrate the performance of our algorithm on a dataset obtained based on the performance of approximately 700 UCLA undergraduate students who have taken an introductory digital signal processing over the past seven years. We demonstrate that for 85% of the students we can predict with 76% accuracy whether they are going do well or poorly in the class after the fourth course week. Using data obtained from a pilot course, our methodology suggests that it is effective to perform early in-class assessments such as quizzes, which result in timely performance prediction for each student, thereby enabling timely interventions by the instructor (at the student or class level) when necessary.

Efficient computation of determinant and inversion of gaussian covariance matrices in the context of gaussian processes

Sivaram Ambikasaran, Daniel Foreman-Mackey, Leslie Greengard, David W. Hogg, and Michael O’Neil, Fast Direct Methods for Gaussian Processes, in IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.38, no.2, pp.252-265, Feb. 1 2016, DOI: 10.1109/TPAMI.2015.2448083

A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation of the corresponding Gaussian density. In the n-dimensional setting, however, it requires the inversion of an n x n covariance matrix, C, as well as the evaluation of its determinant, det(C). In many cases, such as regression using Gaussian processes, the covariance matrix is of the form C = σ2I + K, where K is computed using a specified covariance kernel which depends on the data and additional parameters (hyperparameters). The matrix C is typically dense, causing standard direct methods for inversion and determinant evaluation to require O(n3) work. This cost is prohibitive for large-scale modeling. Here, we show that for the most commonly used covariance functions, the matrix C can be hierarchically factored into a product of block low-rank updates of the identity matrix, yielding an O(n log2 n) algorithm for inversion. More importantly, we show that this factorization enables the evaluation of the determinant det(C), permitting the direct calculation of probabilities in high dimensions under fairly broad assumptions on the kernel defining K. Our fast algorithm brings many problems in marginalization and the adaptation of hyperparameters within practical reach using a single CPU core. The combination of nearly optimal scaling in terms of problem size with high-performance computing resources will permit the modeling of previously intractable problems. We illustrate the performance of the scheme on standard covariance kernels.

Interesting approach to PF-based localization and active localization when the map contains semantic information

Nikolay Atanasov, Menglong Zhu, Kostas Daniilidis, and George J. Pappas, Localization from semantic observations via the matrix permanent, The International Journal of Robotics Research January–March 2016 35: 73-99, first published on October 6, 2015, DOI: 10.1177/0278364915596589.

Most approaches to robot localization rely on low-level geometric features such as points, lines, and planes. In this paper, we use object recognition to obtain semantic information from the robot’s sensors and consider the task of localizing the robot within a prior map of landmarks, which are annotated with semantic labels. As object recognition algorithms miss detections and produce false alarms, correct data association between the detections and the landmarks on the map is central to the semantic localization problem. Instead of the traditional vector-based representation, we propose a sensor model, which encodes the semantic observations via random finite sets and enables a unified treatment of missed detections, false alarms, and data association. Our second contribution is to reduce the problem of computing the likelihood of a set-valued observation to the problem of computing a matrix permanent. It is this crucial transformation that allows us to solve the semantic localization problem with a polynomial-time approximation to the set-based Bayes filter. Finally, we address the active semantic localization problem, in which the observer’s trajectory is planned in order to improve the accuracy and efficiency of the localization process. The performance of our approach is demonstrated in simulation and in real environments using deformable-part-model-based object detectors. Robust global localization from semantic observations is demonstrated for a mobile robot, for the Project Tango phone, and on the KITTI visual odometry dataset. Comparisons are made with the traditional lidar-based geometric Monte Carlo localization.

Using the Bingham distribution of probability, which is defined on a d-dimensional sphere to be antipodally symmetric, to address the problem of angle periodicity in [0,2pi] when estimating orientation in a recursive filter

Gilitschenski, I.; Kurz, G.; Julier, S.J.; Hanebeck, U.D., Unscented Orientation Estimation Based on the Bingham Distribution, in Automatic Control, IEEE Transactions on , vol.61, no.1, pp.172-177, Jan. 2016, DOI: 10.1109/TAC.2015.2423831.

In this work, we develop a recursive filter to estimate orientation in 3D, represented by quaternions, using directional distributions. Many closed-form orientation estimation algorithms are based on traditional nonlinear filtering techniques, such as the extended Kalman filter (EKF) or the unscented Kalman filter (UKF). These approaches assume the uncertainties in the system state and measurements to be Gaussian-distributed. However, Gaussians cannot account for the periodic nature of the manifold of orientations and thus small angular errors have to be assumed and ad hoc fixes must be used. In this work, we develop computationally efficient recursive estimators that use the Bingham distribution. This distribution is defined on the hypersphere and is inherently more suitable for periodic problems. As a result, these algorithms are able to consistently estimate orientation even in the presence of large angular errors. Furthermore, handling of nontrivial system functions is performed using an entirely deterministic method which avoids any random sampling. A scheme reminiscent of the UKF is proposed for the nonlinear manifold of orientations. It is the first deterministic sampling scheme that truly reflects the nonlinear manifold of orientations.

How mood influcences learning, concretely perception of rewards in the context of reinforcement learning

Eran Eldar, Robb B. Rutledge, Raymond J. Dolan, Yael Niv, Mood as Representation of Momentum, Trends in Cognitive Sciences, Volume 20, Issue 1, January 2016, Pages 15-24, ISSN 1364-6613, DOI: j.tics.2015.07.010.

Experiences affect mood, which in turn affects subsequent experiences. Recent studies suggest two specific principles. First, mood depends on how recent reward outcomes differ from expectations. Second, mood biases the way we perceive outcomes (e.g., rewards), and this bias affects learning about those outcomes. We propose that this two-way interaction serves to mitigate inefficiencies in the application of reinforcement learning to real-world problems. Specifically, we propose that mood represents the overall momentum of recent outcomes, and its biasing influence on the perception of outcomes ‘corrects’ learning to account for environmental dependencies. We describe potential dysfunctions of this adaptive mechanism that might contribute to the symptoms of mood disorders.