Additive opportunistic capture explains group hunting benefits in African wild dogs

African wild dogs (Lycaon pictus) are described as highly collaborative endurance pursuit hunters based on observations derived primarily from the grass plains of East Africa. However, the remaining population of this endangered species mainly occupies mixed woodland savannah where hunting strategies appear to differ from those previously described. We used high-resolution GPS and inertial technology to record fine-scale movement of all members of a single pack of six adult African wild dogs in northern Botswana. The dogs used multiple short-distance hunting attempts with a low individual kill rate (15.5%), but high group feeding rate due to the sharing of prey. Use of high-level cooperative chase strategies (coordination and collaboration) was not recorded. In the mixed woodland habitats typical of their current range, simultaneous, opportunistic, short-distance chasing by dogs pursuing multiple prey (rather than long collaborative pursuits of single prey by multiple individuals) could be the key to their relative success in these habitats

Modelling a response as a function of high frequency count data: the association between physical activity and fat mass

We present a new statistical modelling approach where the response is a function of high frequency count data. Our application is about investigating the relationship between the health outcome fat mass and physical activity (PA) measured by accelerometer. The accelerometer quantifies the intensity of physical activity as counts per epoch over a given period of time. We use data from the Avon longitudinal study of parents and children (ALSPAC) where accelerometer data is available as a time series of accelerometer counts per minute over seven days for a subset of children. In order to compare accelerometer profiles between individuals and to reduce the high dimension a functional summary of the profiles is used. We use the histogram as a functional summary due to its simplicity, suitability and ease of interpretation. Our model is an extension of generalised regression of scalars on functions or signal regression. It allows also multi-dimensional functional predictors and additive non-linear predictors for metric covariates. The additive multidimensional functional predictors allow investigating specific questions about whether the effect of PA varies over its intensity, by gender, by time of day or by day of the week. The key feature of the model is that it utilises the full profile of measured PA without requiring cut-points defining intensity levels for light, moderate and vigorous activity. We show that the (not necessarily causal) effect of PA is not linear and not constant over the activity intensity. Also, there is little evidence to suggest that the effect of PA intensity varies by gender or whether it happens on weekdays or on weekends

Movement activity based classification of animal behaviour with an application to data from cheetah (Acinonyx jubatus).

We propose a new method, based on machine learning techniques, for the analysis of a combination of continuous data from dataloggers and a sampling of contemporaneous behaviour observations. This data combination provides an opportunity for biologists to study behaviour at a previously unknown level of detail and accuracy; however, continuously recorded data are of little use unless the resulting large volumes of raw data can be reliably translated into actual behaviour. We address this problem by applying a Support Vector Machine and a Hidden-Markov Model that allows us to classify an animal's behaviour using a small set of field observations to calibrate continuously recorded activity data. Such classified data can be applied quantitatively to the behaviour of animals over extended periods and at times during which observation is difficult or impossible. We demonstrate the usefulness of the method by applying it to data from six cheetah (Acinonyx jubatus) in the Okavango Delta, Botswana. Cumulative activity data scores were recorded every five minutes by accelerometers embedded in GPS radio-collars for around one year on average. Direct behaviour sampling of each of the six cheetah were collected in the field for comparatively short periods. Using this approach we are able to classify each five minute activity score into a set of three key behaviour (feeding, mobile and stationary), creating a continuous behavioural sequence for the entire period for which the collars were deployed. Evaluation of our classifier with cross-validation shows the accuracy to be 83%-94%, but that the accuracy for individual classes is reduced with decreasing sample size of direct observations. We demonstrate how these processed data can be used to study behaviour identifying seasonal and gender differences in daily activity and feeding times. Results given here are unlike any that could be obtained using traditional approaches in both accuracy and detail

A non-stationary copula-based spike count model

Recently, detailed dependencies of spike counts were successfully modeled with the help of copulas [1, 2, 3]. Copulas can be used to couple arbitrary single neuron distributions to form joint distributions with various dependencies. This approach has so far been restricted to stationary spike rates and dependencies. It is known, however, that spike counts of recorded neurons can exhibit non-stationary behavior within trials. In this work, we extend the copula approach to capture non-stationary rates and dependence strengths which are on the order of several hundred milliseconds. We use Poisson marginals for the single neuron statistics and several copula families with and without tail dependencies to couple these marginals. The rates of the Poisson marginals and the dependence strengths of the copula families are time-dependent and fitted to overlapping 100 ms time bins using the inference for margins procedure. To reduce the model complexity we then use regularized least-squares fits of polynomial basis functions for the time-dependent rates and dependence strengths. The approach is applied to data that were recorded from macaque prefrontal cortex during a visual delayed match-to-sample task. Spike trains were recorded using a micro-tetrode array and post-processed using a PCA-based spike sorting method. We compare the cross-validated log likelihoods of the non-stationary models to the corresponding stationary models that have the same marginals and copula families. We find that taking non-stationarities into account increases the likelihood of the test set trials. The approach thereby widens the applicability of detailed dependence models of spike counts. This work was supported by BMBF grant 01GQ0410

An evaluation of different copula models for the short-term noise dependence of spike counts

Correlations between spike counts are often used to analyze neural coding. Traditionally, multivariate Gaussian distributions are frequently used to model the correlation structure of these spike-counts [1]. However, this approximation is not realistic for short time intervals. In this study, as an alternative approach we introduce dependencies by means of copulas of several families. Copulas are functions that can be used to couple marginal cumulative distribution functions to form a joint distribution function with the same margins [2]. We can thus use arbitrary marginal distributions such as Poisson or negative binomial that are better suited for modeling noise distributions of spike counts. Furthermore, copulas place a wide range of dependence structures at our disposal and can be used to analyze higher order interactions. We develop a framework to analyze spike count data by means of such copulas. Methods for parameter inference based on maximum likelihood estimates and for computation of Shannon entropy are provided. The methods are evaluated on a data set of simultaneously measured spike-counts on 100 ms intervals of up to three neurons in macaque MT responding to stochastic dot stimuli [3] and of up to six neurons recorded from macaque prefrontal cortex. Parameters are estimated by the inference-for margins method: first the margin likelihoods are separately maximized and then the coupling parameters are estimated given the parameterized margins. Resulting parameters are close to the maximum likelihood estimation with the advantage that the approach is also tractable for moderate dimensions. Goodness-of-fit is evaluated by cross-validation for the likelihoods. The data analysis leads to three significant findings: (1) copula-based distributions provide better fits than discretized multivariate normal distributions; (2) negative binomial margins fit the data better than Poisson margins; and (3) a dependence model that includes only pairwise interactions overestimates the information entropy by at least 19% compared to the model with higher order interactions

M.: Conditional mean embeddings as regressors

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings minimise, providing an intuitive understanding of the embeddings and a justification for their use. Furthermore, the equivalence allows the application of vector-valued regression methods and results to the problem of learning conditional distributions. Using this link we derive a sparse version of the embedding by considering alternative formulations. Further, by applying convergence results for vector-valued regression to the embedding problem we derive minimax convergence rates which are O(log(n)/n) – compared to current state of the art rates of O(n−1/4) – and are valid under milder and more intuitive assumptions. These minimax upper rates coincide with lower rates up to a logarithmic factor, showing that the embedding method achieves nearly optimal rates. We study our sparse embedding algorithm in a reinforcement learning task where the algorithm shows significant improvement in sparsity over an incomplete Cholesky decomposition. 1. Introduction/Motivation In recent years a framework for embedding probability distributions into reproducing kernel Hilbert spaces (RKHS