Recent research has shown that surprisingly rich models of human activity can be learned from GPS (positional) data. However, most effort to date has concentrated on modeling single individuals or statistical properties of groups of people. Moreover, prior work focused solely on modeling actual successful executions (and not failed or attempted executions) of the activities of interest. We, in contrast, take on the task of understanding human interactions, attempted interactions, and intentions from noisy sensor data in a fully relational multi-agent setting. We use a real-world game of capture the flag to illustrate our approach in a well-defined domain that involves many distinct cooperative and competitive joint activities. We model the domain using Markov logic, a statistical-relational language, and learn a theory that jointly denoises the data and infers occurrences of high-level activities, such as a player capturing an enemy. Our unified model combines constraints imposed by the geometry of the game area, the motion model of the players, and by the rules and dynamics of the game in a probabilistically and logically sound fashion. We show that while it may be impossible to directly detect a multi-agent activity due to sensor noise or malfunction, the occurrence of the activity can still be inferred by considering both its impact on the future behaviors of the people involved as well as the events that could have preceded it. Further, we show that given a model of successfully performed multi-agent activities, along with a set of examples of failed attempts at the same activities, our system automatically learns an augmented model that is capable of recognizing success and failure, as well as goals of people's actions with high accuracy. We compare our approach with other alternatives and show that our unified model, which takes into account not only relationships among individual players, but also relationships among activities over the entire length of a game, although more computationally costly, is significantly more accurate. Finally, we demonstrate that explicitly modeling unsuccessful attempts boosts performance on other important recognition tasks.

We apply kernel-based methods to solve the difficult reinforcement learning problem of 3vs2 keepaway in RoboCup simulated soccer. Key challenges in keepaway are the high-dimensionality of the state space (rendering conventional discretization-based function approximation like tilecoding infeasible), the stochasticity due to noise and multiple learning agents needing to cooperate (meaning that the exact dynamics of the environment are unknown) and real-time learning (meaning that an efficient online implementation is required). We employ the general framework of approximate policy iteration with least-squares-based policy evaluation. As underlying function approximator we consider the family of regularization networks with subset of regressors approximation. The core of our proposed solution is an efficient recursive implementation with automatic supervised selection of relevant basis functions. Simulation results indicate that the behavior learned through our approach clearly outperforms the best results obtained earlier with tilecoding by Stone et al. (2005).

Feature selection in reinforcement learning (RL), i.e. choosing basis functions such that useful approximations of the unkown value function can be obtained, is one of the main challenges in scaling RL to real-world applications. Here we consider the Gaussian process based framework GPTD for approximate policy evaluation, and propose feature selection through marginal likelihood optimization of the associated hyperparameters. Our approach has two appealing benefits: (1) given just sample transitions, we can solve the policy evaluation problem fully automatically (without looking at the learning task, and, in theory, independent of the dimensionality of the state space), and (2) model selection allows us to consider more sophisticated kernels, which in turn enable us to identify relevant subspaces and eliminate irrelevant state variables such that we can achieve substantial computational savings and improved prediction performance.

This paper develops generalizations of empowerment to continuous states. Empowerment is a recently introduced information-theoretic quantity motivated by hypotheses about the efficiency of the sensorimotor loop in biological organisms, but also from considerations stemming from curiosity-driven learning. Empowemerment measures, for agent-environment systems with stochastic transitions, how much influence an agent has on its environment, but only that influence that can be sensed by the agent sensors. It is an information-theoretic generalization of joint controllability (influence on environment) and observability (measurement by sensors) of the environment by the agent, both controllability and observability being usually defined in control theory as the dimensionality of the control/observation spaces. Earlier work has shown that empowerment has various interesting and relevant properties, e.g., it allows us to identify salient states using only the dynamics, and it can act as intrinsic reward without requiring an external reward. However, in this previous work empowerment was limited to the case of small-scale and discrete domains and furthermore state transition probabilities were assumed to be known. The goal of this paper is to extend empowerment to the significantly more important and relevant case of continuous vector-valued state spaces and initially unknown state transition probabilities. The continuous state space is addressed by Monte-Carlo approximation; the unknown transitions are addressed by model learning and prediction for which we apply Gaussian processes regression with iterated forecasting. In a number of well-known continuous control tasks we examine the dynamics induced by empowerment and include an application to exploration and online model learning.

A standard approach in pattern recognition is to estimate the first two moments of each class-conditional distribution from training samples, and then assume the unknown distributions are Gaussians. Depending on the exact assumptions, this approach is called linear or quadratic discriminant analysis (QDA) [1], [2]. Gaussians are known to maximize entropy given the first two moments [3] and to have other nice mathematical properties, but how robust are they with respect to maximizing the Bayes error? To answer that, in this paper we investigate the more general question: "What is the maximum possible Bayes error given moment constraints on the class-conditional distributions?" We present both a lower bound and an upper bound for the maximum possible Bayes error.

In many situations where the interest lies in identifying clusters one might expect that not all available variables carry information about these groups. Furthermore, data quality (e.g. outliers or missing entries) might present a serious and sometimes hard-to-assess problem for large and complex datasets. In this paper we show that a small proportion of atypical observations might have serious adverse effects on the solutions found by the sparse clustering algorithm of Witten and Tibshirani (2010). We propose a robustification of their sparse K-means algorithm based on the trimmed K-means algorithm of Cuesta-Albertos et al. (1997) Our proposal is also able to handle datasets with missing values. We illustrate the use of our method on microarray data for cancer patients where we are able to identify strong biological clusters with a much reduced number of genes. Our simulation studies show that, when there are outliers in the data, our robust sparse K-means algorithm performs better than other competing methods both in terms of the selection of features and also the identified clusters. This robust sparse K-means algorithm is implemented in the R package RSKC which is publicly available from the CRAN repository.

In medical risk modeling, typical data are "scarce": they have relatively small number of training instances (N), censoring, and high dimensionality (M). We show that the problem may be effectively simplified by reducing it to bipartite ranking, and introduce new bipartite ranking algorithm, Smooth Rank, for robust learning on scarce data. The algorithm is based on ensemble learning with unsupervised aggregation of predictors. The advantage of our approach is confirmed in comparison with two "gold standard" risk modeling methods on 10 real life survival analysis datasets, where the new approach has the best results on all but two datasets with the largest ratio N/M. For systematic study of the effects of data scarcity on modeling by all three methods, we conducted two types of computational experiments: on real life data with randomly drawn training sets of different sizes, and on artificial data with increasing number of features. Both experiments demonstrated that Smooth Rank has critical advantage over the popular methods on the scarce data; it does not suffer from overfitting where other methods do.

Feature selection is an important problem in high-dimensional data analysis and classification. Conventional feature selection approaches focus on detecting the features based on a redundancy criterion using learning and feature searching schemes. In contrast, we present an approach that identifies the need to select features based on their discriminatory ability among classes. Area of overlap between inter-class and intra-class distances resulting from feature to feature comparison of an attribute is used as a measure of discriminatory ability of the feature. A set of nearest attributes in a pattern having the lowest area of overlap within a degree of tolerance defined by a selection threshold is selected to represent the best available discriminable features. State of the art recognition results are reported for pattern classification problems by using the proposed feature selection scheme with the nearest neighbour classifier. These results are reported with benchmark databases having high dimensional feature vectors in the problems involving images and micro array data.

Many performance metrics have been introduced for the evaluation of classification performance, with different origins and niches of application: accuracy, macro-accuracy, area under the ROC curve, the ROC convex hull, the absolute error, and the Brier score (with its decomposition into refinement and calibration). One way of understanding the relation among some of these metrics is the use of variable operating conditions (either in the form of misclassification costs or class proportions). Thus, a metric may correspond to some expected loss over a range of operating conditions. One dimension for the analysis has been precisely the distribution we take for this range of operating conditions, leading to some important connections in the area of proper scoring rules. However, we show that there is another dimension which has not received attention in the analysis of performance metrics. This new dimension is given by the decision rule, which is typically implemented as a threshold choice method when using scoring models. In this paper, we explore many old and new threshold choice methods: fixed, score-uniform, score-driven, rate-driven and optimal, among others. By calculating the loss of these methods for a uniform range of operating conditions we get the 0-1 loss, the absolute error, the Brier score (mean squared error), the AUC and the refinement loss respectively. This provides a comprehensive view of performance metrics as well as a systematic approach to loss minimisation, namely: take a model, apply several threshold choice methods consistent with the information which is (and will be) available about the operating condition, and compare their expected losses. In order to assist in this procedure we also derive several connections between the aforementioned performance metrics, and we highlight the role of calibration in choosing the threshold choice method.

Data collection at a massive scale is becoming ubiquitous in a wide variety of settings, from vast offline databases to streaming real-time information. Learning algorithms deployed in such contexts must rely on single-pass inference, where the data history is never revisited. In streaming contexts, learning must also be temporally adaptive to remain up-to-date against unforeseen changes in the data generating mechanism. Although rapidly growing, the online Bayesian inference literature remains challenged by massive data and transient, evolving data streams. Non-parametric modelling techniques can prove particularly ill-suited, as the complexity of the model is allowed to increase with the sample size. In this work, we take steps to overcome these challenges by porting standard streaming techniques, like data discarding and downweighting, into a fully Bayesian framework via the use of informative priors and active learning heuristics. We showcase our methods by augmenting a modern non-parametric modelling framework, dynamic trees, and illustrate its performance on a number of practical examples. The end product is a powerful streaming regression and classification tool, whose performance compares favourably to the state-of-the-art.