The two-thirds power law, an empirical law stating an inverse nonlinear relationship between the tangential hand speed and the curvature of its trajectory during curved motion, is widely acknowledged to be an invariant of upper-limb movement. It has also been shown to exist in eyemotion, locomotion and was even demonstrated in motion perception and prediction. This ubiquity has fostered various attempts to uncover the origins of this empirical relationship. In these it was generally attributed either to smoothness in hand-or joint-space or to the result of mechanisms that damp noise inherent in the motor system to produce the smooth trajectories evident in healthy human motion. We show here that white Gaussian noise also obeys this power-law. Analysis of signal and noise combinations shows that trajectories that were synthetically created not to comply with the power-law are transformed to power-law compliant ones after combination with low levels of noise. Furthermore, there exist colored noise types that drive non-power-law trajectories to power-law compliance and are not affected by smoothing. These results suggest caution when running experiments aimed at verifying the power-law or assuming its underlying existence without proper analysis of the noise. Our results could also suggest that the power-law might be derived not from smoothness or smoothness-inducing mechanisms operating on the noise inherent in our motor system but rather from the correlated noise which is inherent in this motor system.

We propose a new Bayesian method for spatial cluster detection, the "Bayesian spatial scan statistic," and compare this method to the standard (frequentist) scan statistic approach. We demonstrate that the Bayesian statistic has several advantages over the frequentist approach, including increased power to detect clusters and (since randomization testing is unnecessary) much faster runtime. We evaluate the Bayesian and frequentist methods on the task of prospective disease surveillance: detecting spatial clusters of disease cases resulting from emerging disease outbreaks. We demonstrate that our Bayesian methods are successful in rapidly detecting outbreaks while keeping number of false positives low.

This paper presents a novel technique for analyzing electromagnetic imaging data obtained using the stimulus evoked experimental paradigm. The technique is based on a probabilistic graphical model, which describes the data in terms of underlying evoked and interference sources, and explicitly models the stimulus evoked paradigm.

The Octopus arm is a highly versatile and complex limb. How the Octopus controls such a hyper-redundant arm (not to mention eight of them!) is as yet unknown. Robotic arms based on the same mechanical principles may render present day robotic arms obsolete. In this paper, we tackle this control problem using an online reinforcement learning algorithm, based on a Bayesian approach to policy evaluation known as Gaussian process temporal difference (GPTD) learning. Our substitute for the real arm is a computer simulation of a 2-dimensional model of an Octopus arm. Even with the simplifications inherent to this model, the state space we face is a high-dimensional one. We apply a GPTDbased algorithm to this domain, and demonstrate its operation on several learning tasks of varying degrees of difficulty.

Sets", we consider the problem of retrieving items from a concept or cluster, given a query consisting of a few items from that cluster. We formulate this as a Bayesian inference problem and describe a very simple algorithm for solving it. Our algorithm uses a modelbased concept of a cluster and ranks items using a score which evaluates the marginal probability that each item belongs to a cluster containing the query items. For exponential family models with conjugate priors this marginal probability is a simple function of sufficient statistics. We focus on sparse binary data and show that our score can be evaluated exactly using a single sparse matrix multiplication, making it possible to apply our algorithm to very large datasets. We evaluate our algorithm on three datasets: retrieving movies from EachMovie, finding completions of author sets from the NIPS dataset, and finding completions of sets of words appearing in the Grolier encyclopedia.

Linear text classification algorithms work by computing an inner product between a test document vector and a parameter vector. In many such algorithms, including naive Bayes and most TFIDF variants, the parameters are determined by some simple, closed-form, function of training set statistics; we call this mapping mapping from statistics to parameters, the parameter function. Much research in text classification over the last few decades has consisted of manual efforts to identify better parameter functions. In this paper, we propose an algorithm for automatically learning this function from related classification problems. The parameter function found by our algorithm then defines a new learning algorithm for text classification, which we can apply to novel classification tasks. We find that our learned classifier outperforms existing methods on a variety of multiclass text classification tasks.

Sparse PCA seeks approximate sparse "eigenvectors" whose projections capture the maximal variance of data. As a cardinality-constrained and non-convex optimization problem, it is NPhard and is encountered in a wide range of applied fields, from bio-informatics to finance. Recent progress has focused mainly on continuous approximation and convex relaxation of the hard cardinality constraint. In contrast, we consider an alternative discrete spectral formulation based on variational eigenvalue bounds and provide an effective greedy strategy as well as provably optimal solutions using branch-and-bound search. Moreover, the exact methodology used reveals a simple renormalization step that improves approximate solutions obtained by any continuous method. The resulting performance gain of discrete algorithms is demonstrated on real-world benchmark data and in extensive Monte Carlo evaluation trials.

We derive a Bayesian Ideal Observer (BIO) for detecting motion and solving the correspondence problem. We obtain Barlow and Tripathy's classic model as an approximation. Our psychophysical experiments show that the trends of human performance are similar to the Bayesian Ideal, but overall human performance is far worse. We investigate ways to degrade the Bayesian Ideal but show that even extreme degradations do not approach human performance. Instead we propose that humans perform motion tasks using generic, general purpose, models of motion. We perform more psychophysical experiments which are consistent with humans using a Slow-and-Smooth model and which rule out an alternative model using Slowness.

We describe a vision-based obstacle avoidance system for off-road mobile robots. The system is trained from end to end to map raw input images to steering angles. It is trained in supervised mode to predict the steering angles provided by a human driver during training runs collected in a wide variety of terrains, weather conditions, lighting conditions, and obstacle types. The robot is a 50cm off-road truck, with two forwardpointing wireless color cameras. A remote computer processes the video and controls the robot via radio. The learning system is a large 6-layer convolutional network whose input is a single left/right pair of unprocessed low-resolution images. The robot exhibits an excellent ability to detect obstacles and navigate around them in real time at speeds of 2 m/s.

Probabilistic temporal planning attempts to find good policies for acting in domains with concurrent durative tasks, multiple uncertain outcomes, and limited resources. These domains are typically modelled as Markov decision problems and solved using dynamic programming methods. This paper demonstrates the application of reinforcement learning -- in the form of a policy-gradient method -- to these domains. Our emphasis is large domains that are infeasible for dynamic programming. Our approach is to construct simple policies, or agents, for each planning task. The result is a general probabilistic temporal planner, named the Factored Policy-Gradient Planner (FPG-Planner), which can handle hundreds of tasks, optimising for probability of success, duration, and resource use.