Support Vector Machines (SVMs) are one of the most popular algorithms for classification and regression analysis. Despite their popularity, even efficient implementations have proven to be computationally expensive to train at a large-scale, especially in streaming settings. In this paper, we propose a novel coreset construction algorithm for efficiently generating compact representations of massive data sets to speed up SVM training. A coreset is a weighted subset of the original data points such that SVMs trained on the coreset are provably competitive with those trained on the original (massive) data set. We provide both lower and upper bounds on the number of samples required to obtain accurate approximations to the SVM problem as a function of the complexity of the input data. Our analysis also establishes sufficient conditions on the existence of sufficiently compact and representative coresets for the SVM problem. We empirically evaluate the practical effectiveness of our algorithm against synthetic and real-world data sets.
We present a provable, sampling-based approach for generating compact Convolutional Neural Networks (CNNs) by identifying and removing redundant filters from an over-parameterized network. Our algorithm uses a small batch of input data points to assign a saliency score to each filter and constructs an importance sampling distribution where filters that highly affect the output are sampled with correspondingly high probability. In contrast to existing filter pruning approaches, our method is simultaneously data-informed, exhibits provable guarantees on the size and performance of the pruned network, and is widely applicable to varying network architectures and data sets. Our analytical bounds bridge the notions of compressibility and importance of network structures, which gives rise to a fully-automated procedure for identifying and preserving filters in layers that are essential to the network's performance. Our experimental evaluations on popular architectures and data sets show that our algorithm consistently generates sparser and more efficient models than those constructed by existing filter pruning approaches.
We introduce a pruning algorithm that provably sparsifies the parameters of a trained model in a way that approximately preserves the model's predictive accuracy. Our algorithm uses a small batch of input points to construct a data-informed importance sampling distribution over the network's parameters, and adaptively mixes a sampling-based and deterministic pruning procedure to discard redundant weights. Our pruning method is simultaneously computationally efficient, provably accurate, and broadly applicable to various network architectures and data distributions. Our empirical comparisons show that our algorithm reliably generates highly compressed networks that incur minimal loss in performance relative to that of the original network. We present experimental results that demonstrate our algorithm's potential to unearth essential network connections that can be trained successfully in isolation, which may be of independent interest.
In this paper, we address the problem of determining whether a bottleneck router on a given network path is using an AQM or a drop-tail scheme. We assume that we are given a source-to-sink path of interest -along which a bottleneck router exists- and data regarding the Round-Trip Times (RTT) and Congestion Window (CWND) sizes with respect to this flow. We develop a reliable classification algorithm that solely uses RTT and CWND information pertaining to a single flow to classify the queuing scheme, Tail Drop or AQM, used by the bottleneck router. We evaluate our method and present results that demonstrate our algorithm's highly accurate classification ability across a wide array of complex network topologies and configurations.
Consensus is an important capability at the heart of many multi-agent systems. Unfortunately the ability to reach consensus can be easily disrupted by the presence of an adversarial agent that spawns or spoofs malicious nodes in the network in order to gain a disproportionate influence on the converged value of the system as a whole. In this letter, we present a light-weight approach for spoof-resiliency with provable guarantees that solely utilizes information from wireless signals. Unlike prior approaches, our method requires no additional protocol or data storage beyond signals that are already present in the network. We establish an analytical, probabilistic bound on the influence of spoofed nodes in the system on the converged consensus value. We present results of our Wi-Fi based resilient consensus algorithm and demonstrate its effectiveness for different consensus problems such as flocking and rendezvous.
Distilling knowledge from a large teacher model to a lightweight one is a widely successful approach for generating compact, powerful models in the semi-supervised learning setting where a limited amount of labeled data is available. In large-scale applications, however, the teacher tends to provide a large number of incorrect soft-labels that impairs student performance. The sheer size of the teacher additionally constrains the number of soft-labels that can be queried due to prohibitive computational and/or financial costs. The difficulty in achieving simultaneous \emph{efficiency} (i.e., minimizing soft-label queries) and \emph{robustness} (i.e., avoiding student inaccuracies due to incorrect labels) hurts the widespread application of knowledge distillation to many modern tasks. In this paper, we present a parameter-free approach with provable guarantees to query the soft-labels of points that are simultaneously informative and correctly labeled by the teacher. At the core of our work lies a game-theoretic formulation that explicitly considers the inherent trade-off between the informativeness and correctness of input instances. We establish bounds on the expected performance of our approach that hold even in worst-case distillation instances. We present empirical evaluations on popular benchmarks that demonstrate the improved distillation performance enabled by our work relative to that of state-of-the-art active learning and active distillation methods.
We present an efficient coreset construction algorithm for large-scale Support Vector Machine (SVM) training in Big Data and streaming applications. A coreset is a small, representative subset of the original data points such that a models trained on the coreset are provably competitive with those trained on the original data set. Since the size of the coreset is generally much smaller than the original set, our preprocess-then-train scheme has potential to lead to significant speedups when training SVM models. We prove lower and upper bounds on the size of the coreset required to obtain small data summaries for the SVM problem. As a corollary, we show that our algorithm can be used to extend the applicability of any off-the-shelf SVM solver to streaming, distributed, and dynamic data settings. We evaluate the performance of our algorithm on real-world and synthetic data sets. Our experimental results reaffirm the favorable theoretical properties of our algorithm and demonstrate its practical effectiveness in accelerating SVM training.
With the wide-spread availability of complex relational data, semi-supervised node classification in graphs has become a central machine learning problem. Graph neural networks are a recent class of easy-to-train and accurate methods for this problem that map the features in the neighborhood of a node to its label, but they ignore label correlation during inference and their predictions are difficult to interpret. On the other hand, collective classification is a traditional approach based on interpretable graphical models that explicitly model label correlations. Here, we introduce a model that combines the advantages of these two approaches, where we compute the marginal probabilities in a conditional random field, similar to collective classification, and the potentials in the random field are learned through end-to-end training, akin to graph neural networks. In our model, potentials on each node only depend on that node's features, and edge potentials are learned via a coupling matrix. This structure enables simple training with interpretable parameters, scales to large networks, naturally incorporates training labels at inference, and is often more accurate than related approaches. Our approach can be viewed as either an interpretable message-passing graph neural network or a collective classification method with higher capacity and modernized training.
We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an importance sampling scheme that judiciously defines a sampling distribution over the neural network parameters, and as a result, retains parameters of high importance while discarding redundant ones. We leverage a novel, empirical notion of sensitivity and extend traditional coreset constructions to the application of compressing parameters. Our theoretical analysis establishes guarantees on the size and accuracy of the resulting compressed network and gives rise to generalization bounds that may provide new insights into the generalization properties of neural networks. We demonstrate the practical effectiveness of our algorithm on a variety of neural network configurations and real-world data sets.
