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 Statistics , 2015, Abstract: We provide scientific foundations for athletic performance prediction on an individual level, exposing the phenomenology of individual athletic running performance in the form of a low-rank model dominated by an individual power law. We present, evaluate, and compare a selection of methods for prediction of individual running performance, including our own, \emph{local matrix completion} (LMC), which we show to perform best. We also show that many documented phenomena in quantitative sports science, such as the form of scoring tables, the success of existing prediction methods including Riegel's formula, the Purdy points scheme, the power law for world records performances and the broken power law for world record speeds may be explained on the basis of our findings in a unified way.
 Statistics , 2014, Abstract: We introduce statistical methods for predicting the types of human activity at sub-second resolution using triaxial accelerometry data. The major innovation is that we use labeled activity data from some subjects to predict the activity labels of other subjects. To achieve this, we normalize the data across subjects by matching the standing up and lying down portions of triaxial accelerometry data. This is necessary to account for differences between the variability in the position of the device relative to gravity, which are induced by body shape and size as well as by the ambiguous definition of device placement. We also normalize the data at the device level to ensure that the magnitude of the signal at rest is similar across devices. After normalization we use overlapping movelets (segments of triaxial accelerometry time series) extracted from some of the subjects to predict the movement type of the other subjects. The problem was motivated by and is applied to a laboratory study of 20 older participants who performed different activities while wearing accelerometers at the hip. Prediction results based on other people's labeled dictionaries of activity performed almost as well as those obtained using their own labeled dictionaries. These findings indicate that prediction of activity types for data collected during natural activities of daily living may actually be possible.
 Journal of NeuroEngineering and Rehabilitation , 2007, DOI: 10.1186/1743-0003-4-8 Abstract: Here we assume that motor recovery from a neurologic injury can be modelled as a process of learning a novel sensory motor transformation, which allows us to study a simplified experimental protocol amenable to mathematical description. Specifically, we use a robotic force field paradigm to impose a virtual impairment on the left leg of unimpaired subjects walking on a treadmill. We then derive an "assist-as-needed" robotic training algorithm to help subjects overcome the virtual impairment and walk normally. The problem is posed as an optimization of performance error and robotic assistance. The optimal robotic movement trainer becomes an error-based controller with a forgetting factor that bounds kinematic errors while systematically reducing its assistance when those errors are small. As humans have a natural range of movement variability, we introduce an error weighting function that causes the robotic trainer to disregard this variability.We experimentally validated the controller with ten unimpaired subjects by demonstrating how it helped the subjects learn the novel sensory motor transformation necessary to counteract the virtual impairment, while also preventing them from experiencing large kinematic errors. The addition of the error weighting function allowed the robot assistance to fade to zero even though the subjects' movements were variable. We also show that in order to assist-as-needed, the robot must relax its assistance at a rate faster than that of the learning human.The assist-as-needed algorithm proposed here can limit error during the learning of a dynamic motor task. The algorithm encourages learning by decreasing its assistance as a function of the ongoing progression of movement error. This type of algorithm is well suited for helping people learn dynamic tasks for which large kinematic errors are dangerous or discouraging, and thus may prove useful for robot-assisted movement training of walking or reaching following neurologic injury.Robot-
 Computer Science , 2015, Abstract: We present and test a sequential learning algorithm for the short-term prediction of human mobility. This novel approach pairs the Exponential Weights forecaster with a very large ensemble of experts. The experts are individual sequence prediction algorithms constructed from the mobility traces of 10 million roaming mobile phone users in a European country. Average prediction accuracy is significantly higher than that of individual sequence prediction algorithms, namely constant order Markov models derived from the user's own data, that have been shown to achieve high accuracy in previous studies of human mobility prediction. The algorithm uses only time stamped location data, and accuracy depends on the completeness of the expert ensemble, which should contain redundant records of typical mobility patterns. The proposed algorithm is applicable to the prediction of any sufficiently large dataset of sequences.
 PLOS ONE , 2011, DOI: 10.1371/journal.pone.0022795 Abstract: Understanding animal movement and resource selection provides important information about the ecology of the animal, but an animal's movement and behavior are not typically constant in time. We present a velocity-based approach for modeling animal movement in space and time that allows for temporal heterogeneity in an animal's response to the environment, allows for temporal irregularity in telemetry data, and accounts for the uncertainty in the location information. Population-level inference on movement patterns and resource selection can then be made through cluster analysis of the parameters related to movement and behavior. We illustrate this approach through a study of northern fur seal (Callorhinus ursinus) movement in the Bering Sea, Alaska, USA. Results show sex differentiation, with female northern fur seals exhibiting stronger response to environmental variables.
 Statistics , 2015, Abstract: The monitoring of animal movement patterns provides insights into animals decision-making behaviour. It is generally assumed that high-resolution data are needed to extract meaningful behavioural patterns, which potentially limits the application of this approach. Obtaining high-resolution movement data continues to be an economic and technical challenge, particularly for animals that live in social groups. Here, we test whether accurate movement behaviour can be extracted from data that possesses increasingly lower temporal resolution. To do so, we use a modified version of force matching, in which simulated forces acting on a focal animal are compared to observed movement data. We show that useful information can be extracted from sparse data. We apply this approach to a sparse movement dataset collected on the adult members of a troop of baboons in the DeHoop Nature Reserve, South Africa. We use these data to test the hypothesis that individuals are sensitive to isolation from the group as a whole or, alternatively, whether they are sensitive to the location of specific individuals within the group. Using data from a focal animal, our data provide support for both hypothesis, with stronger support for the latter. Although the focal animal was found to be sensitive to the group, this occurred only on a small number of occasions when the group as a whole was highly clustered as a single entity away from the focal animal. We suggest that specific social interactions may thus drive overall group cohesion. Given that sparse movement data is informative about individual movement behaviour, we suggest that both high (~seconds) and relatively low (~minutes) resolution datasets are valuable for the study of how individuals react to and manipulate their local social and ecological environments.
 Mathematics , 2013, Abstract: Is it a good idea to use the frequency of events in the past, as a guide to their frequency in the future (as we all do anyway)? In this paper the question is attacked from the perspective of universal prediction of individual sequences. It is shown that there is a universal sequential probability assignment, such that for a large class loss functions (optimization goals), the predictor minimizing the expected loss under this probability, is a good universal predictor. The proposed probability assignment is based on randomly dithering the empirical frequencies of states in the past, and it is easy to show that randomization is essential. This yields a very simple universal prediction scheme which is similar to Follow-the-Perturbed-Leader (FPL) and works for a large class of loss functions, as well as a partial justification for using probabilistic assumptions.
 Mathematics , 2005, Abstract: Motivated by the evident success of context-tree based methods in lossless data compression, we explore, in this paper, methods of the same spirit in universal prediction of individual sequences. By context-tree prediction, we refer to a family of prediction schemes, where at each time instant $t$, after having observed all outcomes of the data sequence $x_1,...,x_{t-1}$, but not yet $x_t$, the prediction is based on a context'' (or a state) that consists of the $k$ most recent past outcomes $x_{t-k},...,x_{t-1}$, where the choice of $k$ may depend on the contents of a possibly longer, though limited, portion of the observed past, $x_{t-k_{\max}},...x_{t-1}$. This is different from the study reported in [1], where general finite-state predictors as well as Markov'' (finite-memory) predictors of fixed order, were studied in the regime of individual sequences. Another important difference between this study and [1] is the asymptotic regime. While in [1], the resources of the predictor (i.e., the number of states or the memory size) were kept fixed regardless of the length $N$ of the data sequence, here we investigate situations where the number of contexts or states is allowed to grow concurrently with $N$. We are primarily interested in the following fundamental question: What is the critical growth rate of the number of contexts, below which the performance of the best context-tree predictor is still universally achievable, but above which it is not? We show that this critical growth rate is linear in $N$. In particular, we propose a universal context-tree algorithm that essentially achieves optimum performance as long as the growth rate is sublinear, and show that, on the other hand, this is impossible in the linear case.
 Modern Applied Science , 2009, DOI: 10.5539/mas.v3n12p28 Abstract: Ability to predict direction of stock/index price accurately is crucial for market dealers or investors to maximize their profits. Data mining techniques have been successfully shown to generate high forecasting accuracy of stock price movement. Nowadays, in stead of a single method, traders need to use various forecasting techniques to gain multiple signals and more information about the future of the markets. In this paper, ten different techniques of data mining are discussed and applied to predict price movement of Hang Seng index of Hong Kong stock market. The approaches include Linear discriminant analysis (LDA), Quadratic discriminant analysis (QDA), K-nearest neighbor classification, Na ve Bayes based on kernel estimation, Logit model, Tree based classification, neural network, Bayesian classification with Gaussian process, Support vector machine (SVM) and Least squares support vector machine (LS-SVM). Experimental results show that the SVM and LS-SVM generate superior predictive performances among the other models. Specifically, SVM is better than LS-SVM for in-sample prediction but LS-SVM is, in turn, better than the SVM for the out-of-sample forecasts in term of hit rate and error rate criteria.
 Journal of NeuroEngineering and Rehabilitation , 2006, DOI: 10.1186/1743-0003-3-20 Abstract: Healthy subjects (n = 20) attempted to reproduce a novel three-dimensional path after practicing it with mechanical guidance from a robot. Subjects viewed their arm as the robot guided it, so this "haptic guidance" training condition provided both somatosensory and visual input. Learning was compared to reproducing the movement following only visual observation of the robot moving along the path, with the hand in the lap (the "visual demonstration" training condition). Retention was assessed periodically by instructing the subjects to reproduce the path without robotic demonstration.Subjects improved in ability to reproduce the path following practice in the haptic guidance or visual demonstration training conditions, as evidenced by a 30–40% decrease in spatial error across 126 movement attempts in each condition. Performance gains were not significantly different between the two techniques, but there was a nearly significant trend for the visual demonstration condition to be better than the haptic guidance condition (p = 0.09). The 95% confidence interval of the mean difference between the techniques was at most 25% of the absolute error in the last cycle. When asked to reproduce the path repeatedly following either training condition, the subjects' performance degraded significantly over the course of a few trials. The tracing errors were not random, but instead were consistent with a systematic evolution toward another path, as if being drawn to an "attractor path".These results indicate that both forms of robotic demonstration can improve short-term performance of a novel desired path. The availability of both haptic and visual input during the haptic guidance condition did not significantly improve performance compared to visual input alone in the visual demonstration condition. Further, the motor system is inclined to repeat its previous mistakes following just a few movements without robotic demonstration, but these systematic errors can be reduced with peri
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