Distributed Algorithms for Learning and Cognitive Medium Access with Logarithmic Regret

The problem of distributed learning and channel access is considered in a cognitive network with multiple secondary users. The availability statistics of the channels are initially unknown to the secondary users and are estimated using sensing decisions. There is no explicit information exchange or prior agreement among the secondary users. We propose policies for distributed learning and access which achieve order-optimal cognitive system throughput (number of successful secondary transmissions) under self play, i.e., when implemented at all the secondary users. Equivalently, our policies minimize the regret in distributed learning and access. We first consider the scenario when the number of secondary users is known to the policy, and prove that the total regret is logarithmic in the number of transmission slots. Our distributed learning and access policy achieves order-optimal regret by comparing to an asymptotic lower bound for regret under any uniformly-good learning and access policy. We then consider the case when the number of secondary users is fixed but unknown, and is estimated through feedback. We propose a policy in this scenario whose asymptotic sum regret which grows slightly faster than logarithmic in the number of transmission slots.Comment: Submitted to IEEE JSAC on Advances in Cognitive Radio Networking and Communications, Dec. 2009, Revised May 201

Active Learning of Multiple Source Multiple Destination Topologies

We consider the problem of inferring the topology of a network with $M$ sources and $N$ receivers (hereafter referred to as an $M$-by-$N$ network), by sending probes between the sources and receivers. Prior work has shown that this problem can be decomposed into two parts: first, infer smaller subnetwork components (i.e., $1$-by-$N$'s or $2$-by-$2$'s) and then merge these components to identify the $M$-by-$N$ topology. In this paper, we focus on the second part, which had previously received less attention in the literature. In particular, we assume that a $1$-by-$N$ topology is given and that all $2$-by-$2$ components can be queried and learned using end-to-end probes. The problem is which $2$-by-$2$'s to query and how to merge them with the given $1$-by-$N$, so as to exactly identify the $2$-by-$N$ topology, and optimize a number of performance metrics, including the number of queries (which directly translates into measurement bandwidth), time complexity, and memory usage. We provide a lower bound, $\lceil \frac{N}{2} \rceil$, on the number of $2$-by-$2$'s required by any active learning algorithm and propose two greedy algorithms. The first algorithm follows the framework of multiple hypothesis testing, in particular Generalized Binary Search (GBS), since our problem is one of active learning, from $2$-by-$2$ queries. The second algorithm is called the Receiver Elimination Algorithm (REA) and follows a bottom-up approach: at every step, it selects two receivers, queries the corresponding $2$-by-$2$, and merges it with the given $1$-by-$N$; it requires exactly $N-1$ steps, which is much less than all $\binom{N}{2}$ possible $2$-by-$2$'s. Simulation results over synthetic and realistic topologies demonstrate that both algorithms correctly identify the $2$-by-$N$ topology and are near-optimal, but REA is more efficient in practice

Differentially Private Video Activity Recognition

In recent years, differential privacy has seen significant advancements in image classification; however, its application to video activity recognition remains under-explored. This paper addresses the challenges of applying differential privacy to video activity recognition, which primarily stem from: (1) a discrepancy between the desired privacy level for entire videos and the nature of input data processed by contemporary video architectures, which are typically short, segmented clips; and (2) the complexity and sheer size of video datasets relative to those in image classification, which render traditional differential privacy methods inadequate. To tackle these issues, we propose Multi-Clip DP-SGD, a novel framework for enforcing video-level differential privacy through clip-based classification models. This method samples multiple clips from each video, averages their gradients, and applies gradient clipping in DP-SGD without incurring additional privacy loss. Moreover, we incorporate a parameter-efficient transfer learning strategy to make the model scalable for large-scale video datasets. Through extensive evaluations on the UCF-101 and HMDB-51 datasets, our approach exhibits impressive performance, achieving 81% accuracy with a privacy budget of epsilon=5 on UCF-101, marking a 76% improvement compared to a direct application of DP-SGD. Furthermore, we demonstrate that our transfer learning strategy is versatile and can enhance differentially private image classification across an array of datasets including CheXpert, ImageNet, CIFAR-10, and CIFAR-100

DETECTION OF GAUSS-MARKOV RANDOM FIELD ON NEAREST-NEIGHBOR GRAPH

The problem of hypothesis testing against independence for a Gauss-Markov random field (GMRF) with nearest-neighbor dependency graph is analyzed. The sensors measuring samples from the signal field are placed IID according to the uniform distribution. The asymptotic performance of Neyman-Pearson detection is characterized through the largedeviation theory. An expression for the error exponent is derived using a special law of large numbers for graph functionals. The exponent is analyzed for different values of the variance ratio and correlation. It is found that a more correlated GMRF has a higher exponent (improved detection performance) at low values of the variance ratio, whereas the opposite is true at high values of the ratio

Opportunistic Spectrum Access with Multiple Users: Learning under Competition

Abstract—The problem of cooperative allocation among multiple secondary users to maximize cognitive system throughput is considered. The channel availability statistics are initially unknown to the secondary users and are learnt via sensing samples. Two distributed learning and allocation schemes which maximize the cognitive system throughput or equivalently minimize the total regret in distributed learning and allocation are proposed. The first scheme assumes minimal prior information in terms of pre-allocated ranks for secondary users while the second scheme is fully distributed and assumes no such prior information. The two schemes have sum regret which is provably logarithmic in the number of sensing time slots. A lower bound is derived for any learning scheme which is asymptotically logarithmic in the number of slots. Hence, our schemes achieve asymptotic order optimality in terms of regret in distributed learning and allocation. Index Terms—Cognitive medium access, learning, multi-armed bandits, logarithmic regret, distributed algorithms. I

Type-Based Random Access for Distributed Detection Over Multiaccess Fading Channels

Abstract—The problem of distributed detection in a sensor network over multiaccess fading channels is considered. A random-access transmission scheme referred to as the type-based random access (TBRA) is proposed and analyzed. Error exponents of TBRA under noncoherent detection are characterized with respect to the mean transmission rate and the channel-coherence index. For the zero-mean multiaccess fading channels, it is shown that there exists an optimal mean-transmission rate that maximizes the detection-error exponents. The optimal mean-transmission rate can be calculated numerically or estimated using the Gaussian approximation, and it gives a sensor-activation strategy that achieves an optimal allocation of transmission energy to spatial and temporal domains. Numerical examples and simulations are used to compare TBRA with the conventional centralized time-division multiple access (TDMA) scheme. It is shown that for the zero-mean multiaccess fading channels, TBRA gives substantial improvement in the low signal-to-noise ratio (SNR) regime whereas for the nonzero mean fading channels, TBRA performs better over a wide range of SNR. Index Terms—Distributed detection, multisensor systems, performance analysis, signal processing for communications. I

ROBUST RATE-MAXIMIZATION GAME UNDER BOUNDED CHANNEL UNCERTAINTY

The problem of decentralized power allocation for competitive rate maximization in a frequency-selective Gaussian interference channel is considered. In the absence of perfect knowledge of channel state information (CSI), a distribution-free robust game is formulated. A robust-optimization equilibrium (RE) is proposed where each player formulates a best response to the worst-case interference. The conditions for existence, uniqueness and convergence of the RE are derived. It is shown that the convergence reduces as the uncertainty increases. Simulations show an interesting phenomenon where the proposed RE moves closer to a Pareto-optimal solution as the CSI uncertainty bound increases, when compared to the classical Nash equilibrium under perfect CSI. Thus, the robust-optimization equilibrium successfully counters bounded channel uncertainty and increases system sum-rate due to users being more conservative about causing interference to other users. Index Terms — Rate maximization, robust games, waterfilling, decentralized power control, Gaussian interference channe

Minimum Cost Data Aggregation with Localized Processing for Statistical Inference

The problem of minimum cost in-network fusion of measurements, collected from distributed sensors via multihop routing is considered. A designated fusion center performs an optimal statistical-inference test on the correlated measurements, drawn from a Markov random field. Conditioned on the delivery of a sufficient statistic for inference to the fusion center, the structure of optimal routing and fusion is shown to be a Steiner tree on a transformed graph. This Steiner-tree reduction preserves the approximation ratio, which implies that any Steinertree heuristic can be employed for minimum cost fusion with the same approximation ratio. The proposed fusion scheme involves routing packets of two types viz., raw measurements sent for local processing, and aggregates obtained on combining these processed values. The performance of heuristics for minimum cost fusion are evaluated through theory and simulations, showing a significant saving in routing costs, when compared to routing all the raw measurements to the fusion center. Index Terms — Sensor networks, in-network processing and aggregation, statistical inference, cost minimization I