We consider online prediction of a binary sequence with expert advice. For this setting, we devise label-efficient forecasting algorithms, which use a selective sampling scheme that enables collecting much fewer labels than standard procedures. For the general case without a perfect expert, we prove best-of-both-worlds guarantees, demonstrating that the proposed forecasting algorithm always queries sufficiently many labels in the worst case to obtain optimal regret guarantees, while simultaneously querying much fewer labels in more benign settings. Specifically, for a scenario where one expert is strictly better than the others in expectation, we show that the label complexity of the label-efficient forecaster is roughly upper-bounded by the square root of the number of rounds. Finally, we present numerical experiments empirically showing that the normalized regret of the label-efficient forecaster can asymptotically match known minimax rates for pool-based active learning, suggesting it can optimally adapt to benign settings.

Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its effects on the dynamics of social networks. In this paper, we propose a statistical model for dynamically evolving networks, together with a variational inference approach. Our model, Neural Latent Space Model with Variational Inference, encodes edge dependencies across different time snapshots. It represents nodes via latent vectors and uses interaction matrices to model the presence of edges. These matrices can be used to incorporate multiple relations in heterogeneous networks by having a separate matrix for each of the relations. To capture the temporal dynamics, both node vectors and interaction matrices are allowed to evolve with time. Existing network analysis methods use representation learning techniques for modelling networks. These techniques are different for homogeneous and heterogeneous networks because heterogeneous networks can have multiple types of edges and nodes as opposed to a homogeneous network. Unlike these, we propose a unified model for homogeneous and heterogeneous networks in a variational inference framework. Moreover, the learned node latent vectors and interaction matrices may be interpretable and therefore provide insights on the mechanisms behind network evolution. We experimented with a single step and multi-step link forecasting on real-world networks of homogeneous, bipartite, and heterogeneous nature, and demonstrated that our model significantly outperforms existing models.

This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering such sets through compressive measurements, while simultaneously providing adaptive support recovery protocols that perform near optimally for these classes. We show that by adaptively designing the sensing matrix, we can attain significant performance gains over non-adaptive protocols. These gains arise from the fact that adaptive sensing can: 1) better mitigate the effects of noise and 2) better capitalize on the structure of the support sets.

In many practical settings one can sequentially and adaptively guide the collection of future data, based on information extracted from data collected previously. These sequential data collection procedures are known by different names, such as sequential experimental design, active learning, or adaptive sensing/sampling. The intricate relation between data analysis and acquisition in adaptive sensing paradigms can be extremely powerful, and often allows for reliable signal estimation and detection in situations where nonadaptive sensing would fail dramatically. In this paper, we investigate the problem of estimating the support of a structured sparse signal from coordinate-wise observations under the adaptive sensing paradigm. We present a general procedure for support set estimation that is optimal in a variety of cases and shows that through the use of adaptive sensing one can: 1) mitigate the effect of observation noise when compared with nonadaptive sensing and 2) capitalize on structural information to a much larger extent than possible with nonadaptive sensing. In addition to a general procedure to perform adaptive sensing in structured settings, we present both performance upper bounds, and corresponding lower bounds for both sensing paradigms.

The problem of detecting correlations from samples of a high-dimensional Gaussian vector has recently received a lot of attention. In most existing work, detection procedures are provided with a full sample. However, following common wisdom in experimental design, the experimenter may have the capacity to make targeted measurements in an on-line and adaptive manner. In this paper, we investigate such adaptive sensing procedures for detecting positive correlations. It is shown that, using the same number of measurements, adaptive procedures are able to detect significantly weaker correlations than their nonadaptive counterparts. We also establish minimax lower bounds that show the limitations of any procedure.

Cognitive radios process their sensed information collectively in order to opportunistically identify and access underutilized spectrum segments (spectrum holes). Due to the transient and rapidly varying nature of the spectrum occupancy, the cognitive radios (secondary users) must be agile in identifying the spectrum holes in order to enhance their spectral efficiency. We propose a novel adaptive procedure to reinforce the agility of the secondary users for identifying multiple spectrum holes simultaneously over a wide spectrum band. This is accomplished by successively exploring the set of potential spectrum holes and progressively allocating the sensing resources to the most promising areas of the spectrum. Such exploration and resource allocation results in conservative spending of the sensing resources and translates into very agile spectrum monitoring. The proposed successive and adaptive sensing procedure is in contrast to the more conventional approaches that distribute the sampling resources equally over the entire spectrum. Besides improved agility, the adaptive procedure requires less-stringent constraints on the power of the primary users to guarantee that they remain distinguishable from the environment noise and renders more reliable spectrum hole detection.

Adaptive sampling results in significant improvements in the recovery of sparse signals in white Gaussian noise. A sequential adaptive sampling-and-refinement procedure called Distilled Sensing (DS) is proposed and analyzed. DS is a form of multistage experimental design and testing. Because of the adaptive nature of the data collection, DS can detect and localize far weaker signals than possible from non-adaptive measurements. In particular, reliable detection and localization (support estimation) using non-adaptive samples is possible only if the signal amplitudes grow logarithmically with the problem dimension. Here it is shown that using adaptive sampling, reliable detection is possible provided the amplitude exceeds a constant, and localization is possible when the amplitude exceeds any arbitrarily slowly growing function of the dimension.

Vast segments of the frequency spectrum are licensed to specific users for particular applications. These legacy users, however, often under-utilize their designated spectrum segments. Unlicensed (secondary) users can benefit from this fact and opportunistically exploit the vacant spectrum segments (spectral holes). Due to the transient nature of the spectrum occupancy it becomes imperative for secondary users to quickly identify such spectral holes. To accomplish this, we propose a novel sequential and adaptive spectrum sensing procedure. The underlying notion of this procedure is to progressively allocate the sensing resources to only the most promising areas of the spectrum. This translates in a reduction of sensing resources and time needed to accurately identify spectrum holes, in contrast with more conventional approaches that allocate the sensing budget over the entire spectrum uniformly. The proposed method is theoretically sound and further supported by simulation results.

It is shown here that adaptivity in sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. An adaptive sampling-and-refinement procedure called distilled sensing is discussed and analyzed, resulting in fundamental new asymptotic scaling relationships in terms of the minimum feature strength required for reliable signal detection or localization (support recovery). In particular, reliable detection and localization using non-adaptive samples is possible only if the feature strength grows logarithmically in the problem dimension. Here it is shown that using adaptive sampling, reliable detection is possible provided the feature strength exceeds a constant, and localization is possible when the feature strength exceeds any (arbitrarily slowly) growing function of the problem dimension.

The theory of compressed sensing shows that samples in the form of random projections are optimal for recovering sparse signals in high-dimensional spaces (i.e., finding needles in haystacks), provided the measurements are noiseless. However, noise is almost always present in applications, and compressed sensing suffers from it. The signal to noise ratio per dimension using random projections is very poor, since sensing energy is equally distributed over all dimensions. Consequently, the ability of compressed sensing to locate sparse components degrades significantly as noise increases. It is possible, in principle, to improve performance by "shaping" the projections to focus sensing energy in proper dimensions. The main question addressed here is, can projections be adaptively shaped to achieve this focusing effect? The answer is yes, and we demonstrate a simple, computationally efficient procedure that does so.

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.

This paper analyzes the potential advantages and theoretical challenges of "active learning" algorithms. Active learning involves sequential sampling procedures that use information gleaned from previous samples in order to focus the sampling and accelerate the learning process relative to "passive learning" algorithms, which are based on nonadaptive (usually random) samples. There are a number of empirical and theoretical results suggesting that in certain situations active learning can be significantly more effective than passive learning. However, the fact that active learning algorithms are feedback systems makes their theoretical analysis very challenging. 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 d-dimensional feature spaces when the feature marginal density is bounded from above and below.

Compressive sampling (CS), or Compressed Sensing, has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning, uses information gleaned from previous observations (e.g., feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of compressive and adaptive sampling in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near-optimal. This result is remarkable since it is the first evidence that shows that compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in presence of noise.

This paper presents a rigorous statistical analysis characterizing regimes in which active learning significantly outperforms classical passive learning. Active learning algorithms are able to make queries or select sample locations in an online fashion, depending on the results of the previous queries. In some regimes, this extra flexibility leads to significantly faster rates of error decay than those possible in classical passive learning settings. The nature of these regimes is explored by studying fundamental performance limits of active and passive learning in two illustrative nonparametric function classes. In addition to examining the theoretical potential of active learning, this paper describes a practical algorithm capable of exploiting the extra flexibility of the active setting and provably improving upon the classical passive techniques. Our active learning theory and methods show promise in a number of applications, including field estimation using wireless sensor networks and fault line detection.

In this paper we consider a sequential, coarse-to-fine estimation of a piecewise constant function with smooth boundaries. Accurate detection and localization of the boundary (a manifold) is the key aspect of this problem. In general, algorithms capable of achieving optimal performance require exhaustive searches over large dictionaries that grow exponentially with the dimension of the observation domain. The computational burden of the search hinders the use of such techniques in practice, and motivates our work. We consider a sequential, coarse-to-fine approach that involves first examining the data on a coarse grid, and then refining the analysis and approximation in regions of interest. Our estimators involve an almost linear-time (in two dimensions) sequential search over the dictionary, and converge at the same near-optimal rate as estimators based on exhaustive searches. Specifically, for two dimensions, our algorithm requires O(n/sup 7/6/) operations for an n-pixel image, much less than the traditional wedgelet approaches, which require O(n/sup 11/6/) operations.

Network tomography is a process for inferring "internal" link-level delay and loss performance information based on end-to-end (edge) network measurements. These methods require knowledge of the network topology; therefore a first crucial step in the tomography process is topology identification. This paper considers the problem of discovering network topology solely from host-based, unicast measurements, without internal network cooperation. First, we introduce a novel delay-based measurement scheme that does not require clock synchronization, making it more practical than other previous proposals. In contrast to methods that rely on network cooperation , our methodology has the potential to identify layer two elements (provided they are logical topology branching points and induce some measurable delay). Second, we propose a maximum penalized likelihood criterion for topology identification. This is a global optimality criterion, in contrast to other recent proposals for topology identification that employ suboptimal, pair-merging strategies. We develop a novel Markov Chain Monte Carlo (MCMC) procedure for rapid determination of the most likely topologies. The performance of our new probing scheme and identification algorithm is explored through simulation and Internet experiments.