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We introduce Tiered Sampling , a novel technique for estimating the count of sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size M , which can be magnitudes smaller than the number of edges. Our methods address the challenging task of counting sparse motifs—sub-graph patterns—that have a low probability of appearing in a sample of M edges in the graph, which is the maximum amount of data available to the algorithms in each step. To obtain an unbiased and low variance estimate of the count, we partition the available memory into tiers (layers) of reservoir samples. While the base layer is a standard reservoir sample of edges, other layers are reservoir samples of sub-structures of the desired motif. By storing more frequent sub-structures of the motif, we increase the probability of detecting an occurrence of the sparse motif we are counting, thus decreasing the variance and error of the estimate. While we focus on the designing and analysis of algorithms for counting 4-cliques, we present a method which allows generalizing Tiered Sampling to obtain high-quality estimates for the number of occurrence of any sub-graph of interest, while reducing the analysis effort due to specific properties of the pattern of interest. We present a complete analytical analysis and extensive experimental evaluation of our proposed method using both synthetic and real-world data. Our results demonstrate the advantage of our method in obtaining high-quality approximations for the number of 4 and 5-cliques for large graphs using a very limited amount of memory, significantly outperforming the single edge sample approach for counting sparse motifs in large scale graphs. 

We develop a rigorous approach for using a set of arbitrarily correlated weak supervision sources in order to solve a multiclass classification task when only a very small set of labeled data is available. Our learning algorithm provably converges to a model that has minimum empirical risk with respect to an adversarial choice over feasible labelings for a set of unlabeled data, where the feasibility of a labeling is computed through constraints defined by rigorously estimated statistics of the weak supervision sources. We show theoretical guarantees for this approach that depend on the information provided by the weak supervision sources. Notably, this method does not require the weak supervision sources to have the same labeling space as the multiclass classification task. We demonstrate the effectiveness of our approach with experiments on various image classification tasks. 

The topology of the hyperlink graph among pages expressing different opinions may influence the exposure of readers to diverse content. Structural bias may trap a reader in a 'polarized' bubble with no access to other opinions. We model readers' behavior as random walks. A node is in a 'polarized' bubble if the expected length of a random walk from it to a page of different opinion is large. The structural bias of a graph is the sum of the radii of highly-polarized bubbles. We study the problem of decreasing the structural bias through edge insertions. 'Healing' all nodes with high polarized bubble radius is hard to approximate within a logarithmic factor, so we focus on finding the best k edges to insert to maximally reduce the structural bias. We present RePBubLik, an algorithm that leverages a variant of the random walk closeness centrality to select the edges to insert. RePBubLik obtains, under mild conditions, a constant-factor approximation. It reduces the structural bias faster than existing edge-recommendation methods, including some designed to reduce the polarization of a graph. 

We develop a novel method that provides theoretical guarantees for learning from weak labelers without the (mostly unrealistic) assumption that the errors of the weak labelers are independent or come from a particular family of distributions. We show a rigorous technique for efficiently selecting small subsets of the labelers so that a majority vote from such subsets has a provably low error rate. We explore several extensions of this method and provide experimental results over a range of labeled data set sizes on 45 image classification tasks. Our performance-guaranteed methods consistently match the best performing alternative, which varies based on problem difficulty. On tasks with accurate weak labelers, our methods are on average 3 percentage points more accurate than the state-of-the-art adversarial method. On tasks with inaccurate weak labelers, our methods are on average 15 percentage points more accurate than the semi-supervised Dawid-Skene model (which assumes independence). 

We present an algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. In order to be efficient in terms of both time and space, our algorithm is based on a decomposition strategy which partitions the graph into disjoint clusters of bounded radius. Theoretically, our algorithm uses linear space and yields a polylogarithmic approximation guarantee; most importantly, for a large family of graphs, it features a round complexity asymptotically smaller than the one exhibited by a natural approximation algorithm based on the state-of-the-art Δ-stepping SSSP algorithm, which is its only practical, linear-space competitor in the distributed setting. We complement our theoretical findings with a proof-of-concept experimental analysis on large benchmark graphs, which suggests that our algorithm may attain substantial improvements in terms of running time compared to the aforementioned competitor, while featuring, in practice, a similar approximation ratio. 

We introduce Ordalia, a novel approach for speeding up deep learning hyperparameter optimization search through early-pruning of less promising configurations. Our method leverages empirical and theoretical results characterizing the shape of the generalization error curve for increasing training data size and number of epochs. We show that with relatively small computational resources one can estimate the dominant parameters of neural networks' learning curves to obtain consistently good evaluations of their learning process to reliably early-eliminate non-promising configurations. By iterating this process with increasing training resources Ordalia rapidly converges to a small candidate set that includes many of the most promising configurations. We compare the performance of Ordalia with Hyperband, the state-of-the-art model-free hyperparameter optimization algorithm, and show that Ordalia consistently outperforms it on a variety of deep learning tasks. Ordalia conservative use of computational resources and ability to evaluate neural networks learning progress leads to a much better exploration and coverage of the search space, which ultimately produces superior neural network configurations. 

Bias and polarization are not just about placing misinformation on the Web but also involve concerted efforts to change how we navigate it. One of the strongest points of Wikipedia is to allows readers to easily navigate a topic, through its hyperlinks structure. Thus, it is crucial to ensure a user to have the same probability of being exposed to knowledge that expresses different viewpoints concerning the given topic. In this work, we investigate whether the topology and polarization of a topic-induced-graph (e.g. U.S. Politics induced network) has an impact on users' navigation paths making them biased toward one of the possible topic perspectives. Modeling users behaviour and exploiting Wikipedia clickstreams, we analyze users exposure to different leaning during their sessions, thus the chance of being trapped within a knowledge bubble presenting a unique viewpoint about the topic, and differences among users that start their navigation from articles representing different perspectives. 

While standard statistical inference techniques and machine learning generalization bounds assume that tests are run on data selected independently of the hypotheses, practical data analysis and machine learning are usually iterative and adaptive processes where the same holdout data is often used for testing a sequence of hypotheses (or models), which may each depend on the outcome of the previous tests on the same data. In this work, we present RADABOUND a rigorous, efficient and practical procedure for controlling the generalization error when using a holdout sample for multiple adaptive testing. Our solution is based on a new application of the Rademacher Complexity generalization bounds, adapted to dependent tests. We demonstrate the statistical power and practicality of our method through extensive simulations and comparisons to alternative approaches. In particular, we show that our rigorous solution is a substantially more powerful and efficient than the differential privacy based approach proposed in Dwork et al. [1]-[3].