We state and analyze the first active learning algorithm which works in the presence of arbitrary forms of noise. The algorithm, A2 (for Agnostic Active), relies only upon the assumption that the samples are drawn i.i.d. from a fixed distribution. We show that A2 achieves an exponential improvement (i.e., requires only O � ln 1 ɛ samples to find an ɛ-optimal classifier) over the usual sample complexity of supervised learning, for several settings considered before in the realizable case. These include learning threshold classifiers and learning homogeneous linear separators with respect to an input distribution which is uniform over the unit sphere. 1.

Abstract. This paper aims to shed light on achievable limits in active learning. Using minimax analysis techniques, we study the achievable rates of classification error convergence for broad classes of distributions characterized by decision boundary regularity and noise conditions. The results clearly indicate the conditions under which one can expect significant gains through active learning. Furthermore we show that the learning rates derived are tight for “boundary fragment ” classes in ddimensional feature spaces when the feature marginal density is bounded from above and below. 1

In this paper we address the theoretical capabilities of active sampling for estimating functions in noise. Specifically, the problem we consider is that of estimating a function from noisy point-wise samples, that is, the measurements which are collected at various points over the domain of the function. In the classical (passive) setting the sampling locations are chosen a priori, meaning that the choice of the sample locations precedes the gathering of the function observations. In the active sampling setting, on the other hand, the sample locations are chosen in an online fashion: the decision of where to sample next depends on all the observations made up to that point, in the spirit of the twenty questions game (as opposed to passive sampling where all the questions need to be asked before any answers are given). This extra degree of flexibility leads to improved signal reconstruction in comparison to the performance of classical (passive) methods. We present results characterizing the fundamental limits of active learning for various nonparametric function classes, as well as practical algorithms capable of exploiting the extra flexibility of the active setting and provably improving on classical techniques. In particular, significantly faster rates of convergence are achievable in cases involving functions whose complexity (in a the Kolmogorov sense) is highly concentrated in small regions of space (e.g., piecewise constant functions). Our active learning theory and methods show promise in a number of applications, including field estimation using wireless sensor networks and fault line detection. 1

Compressive Sampling (CS), also called Compressed Sensing, entails making observations of an unknown signal by projecting it onto random vectors. Recent theoretical results show that if the signal is sparse (or nearly sparse) in some basis, then with high probability such observations essentially encode the salient information in the signal. Further, the signal can be reconstructed from these “random projections,” even when the number of observations is far less than the ambient signal dimension. The provable success of CS for signal reconstruction motivates the study of its potential in other applications. This paper investigates the utility of CS projection observations for signal classification (more specifically, mary hypothesis testing). Theoretical error bounds are derived and verified with several simulations.

This paper investigates data-adaptive path planning schemes for wireless networks of mobile sensor platforms. We focus on applications of environmental monitoring, in which the goal is to reconstruct a spatial map of environmental factors of interest. Traditional sampling theory deals with data collection processes that are completely independent of the target map to be estimated, aside from possible a priori specifications reflective of assumed properties of the target. We refer to such processes as passive learning methods. Alternatively, one can envision sequential, adaptive data collection procedures that use information gleaned from previous observations to guide the process. We refer to such feedbackdriven processes as active learning methods. Active learning is naturally suited to mobile path planning, in which previous samples are used to guide the motion of the mobiles for further sampling. This paper presents some of the most encouraging theoretical results to date that support the effectiveness of active over passive learning, and focuses on new results regarding the capabilities of active learning methods for mobile sensing. Tradeoffs between latency, path lengths, and accuracy are carefully assessed using our theory. Adaptive path planning methods are developed to guide mobiles in order to focus attention in interesting regions of the sensing domain, thus conducting spatial surveys much more rapidly while maintaining the accuracy of the estimated map. The theory and methods are illustrated in the application of water current mapping in a freshwater lake.

We investigate a topic at the interface of machine learning and cognitive science. Human active learning, where learners can actively query the world for information, is contrasted with passive learning from random examples. Furthermore, we compare human active learning performance with predictions from statistical learning theory. We conduct a series of human category learning experiments inspired by a machine learning task for which active and passive learning error bounds are well understood, and dramatically distinct. Our results indicate that humans are capable of actively selecting informative queries, and in doing so learn better and faster than if they are given random training data, as predicted by learning theory. However, the improvement over passive learning is not as dramatic as that achieved by machine active learning algorithms. To the best of our knowledge, this is the first quantitative study comparing human category learning in active versus passive settings. 1

Abstract — This paper presents greedy gossip with eavesdropping (GGE), a new average consensus algorithm for wireless sensor network applications. Consensus algorithms have recently received much attention in the sensor network community because of their simplicity and completely decentralized nature which makes them robust to changes in the network topology and unreliable wireless networking environments. In the sensor network, each node has a measurement value and the aim of average consensus is computing the average of these node values in the absence of a central authority. We prove that GGE converges to the average consensus with probability one. We also illustrate the performance of the algorithm via simulations and conclude that GGE provides a significant performance improvement compared to existing average consensus algorithms such as randomized gossip and geographic gossip.

This thesis develops and analyzes theoretical frameworks for new emerging paradigms of Machine Learning including Semi-supervised, Active, and Similarity-based Learning. These are areas of significant practical importance and significant activity in Machine Learning, and a number of different algorithmic approaches have been developed for each of them. Standard Learning Theory frameworks such as PAC or Statistical Learning Theory models tend to not capture these learning approaches, hence developing sound and rigorous models that provide a thorough understanding of these new paradigms is desirable. The purpose of this thesis is to propose and to study new theoretical frameworks and algorithms for better understanding and extending some of these learning approaches. In addition, this dissertation also presents new applications of techniques from Machine Learning Theory to new emerging areas of Computer Science at large, such as Auction and Mechanism Design. In Machine Learning, there has been growing interest in using unlabeled data together with labeled data due to the availability of large amounts of unlabeled data in many applications. As a result, a number of different algorithmic approaches have been developed for this

Multi-armed bandit (MAB) problems are a class of sequential resource allocation problems concerned with allocating one or more resources among several alternative (competing) projects. Such problems are paradigms of a fundamental conflict between making decisions (allocating resources) that yield

We develop unified information-theoretic machinery for deriving lower bounds for passive and active learning schemes. Our bounds involve the so-called Alexander’s capacity function. The supremum of this function has been recently rediscovered by Hanneke in the context of active learning under the name of “disagreement coefficient. ” For passive learning, our lower bounds match the upper bounds of Giné and Koltchinskii up to constants and generalize analogous results of Massart and Nédélec. For active learning, we provide first known lower bounds based on the capacity function rather than the disagreement coefficient. 1