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We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex correlation structures which often arise in applications. We propose a novel family of approximate message passing (AMP) algorithms for signal estimation, and rigorously characterize their performance in the high-dimensional limit via a state evolution recursion. Our rotationally invariant AMP has complexity of the same order as the existing AMP derived under the restrictive assumption of a Gaussian design; our algorithm also recovers this existing AMP as a special case. Numerical results showcase a performance close to Vector AMP (which is conjectured to be Bayes-optimal in some settings), but obtained with a much lower complexity, as the proposed algorithm does not require a computationally expensive singular value decomposition.

Blockchain has recently attracted the attention of the industry due, in part, to its ability to automate asset transfers. It requires distributed participants to reach a consensus on a block despite the presence of malicious (a.k.a. Byzantine) participants. Malicious participants exploit regularly weaknesses of these blockchain consensus algorithms, with sometimes devastating consequences. In fact, these weaknesses are quite common and are well illustrated by the flaws in the hand-written proofs of existing blockchain consensus protocols [63]. Paradoxically, until now, no blockchain consensus has been holistically verified using model checking. In this paper, we remedy this paradox by model checking for the first time a blockchain consensus used in industry. We propose a holistic approach to verify the consensus algorithm of the Red Belly Blockchain [20], for any number $n$ of processes and any number $f<n/3$ of Byzantine processes. We decompose directly the algorithm pseudocode in two parts -- an inner broadcast algorithm and an outer decision algorithm -- each modelled as a threshold automaton [36], and we formalize their expected properties in linear-time temporal logic. We then automatically check the inner broadcasting algorithm, under a carefully identified fairness assumption. For the verification of the outer algorithm, we simplify the model of the inner algorithm by relying on its checked properties. Doing so, we formally verify not only the safety properties of the Red Belly Blockchain consensus but also its liveness in about 70 seconds.

In longitudinal study, it is common that response and covariate are not measured at the same time, which complicates the analysis to a large extent. In this paper, we take into account the estimation of generalized varying coefficient model with such asynchronous observations. A penalized kernel-weighted estimating equation is constructed through kernel technique in the framework of functional data analysis. Moreover, local sparsity is also considered in the estimating equation to improve the interpretability of the estimate. We extend the iteratively reweighted least squares (IRLS) algorithm in our computation. The theoretical properties are established in terms of both consistency and sparsistency, and the simulation studies further verify the satisfying performance of our method when compared with existing approaches. The method is applied to an AIDS study to reveal its practical merits.

Graph-based data structures have drawn great attention in recent years. The large and rapidly growing trend on developing graph processing systems focuses mostly on improving the performance by preprocessing the input graph and modifying its layout. These systems usually take several hours to days to complete processing a single graph on high-end machines, let alone the overhead of pre-processing which most of the time can be dominant. Yet for most graph applications the exact answer is not always crucial, and providing a rough estimate of the final result is adequate. Approximate computing is introduced to trade off accuracy of results for computation or energy savings that could not be achieved by conventional techniques alone. In this work, we design, implement and evaluate GraphGuess, inspired from the domain of approximate graph theory and extend it to a general, practical graph processing system. GraphGuess is essentially an approximate graph processing technique with adaptive correction, which can be implemented on top of any graph processing system. We build a vertex-centric processing system based on GraphGuess, where it allows the user to trade off accuracy for better performance. Our experimental studies show that using GraphGuess can significantly reduce the processing time for large scale graphs while maintaining high accuracy.

Performance assessment and optimization for networks jointly performing caching, computing, and communication (3C) has recently drawn significant attention because many emerging applications require 3C functionality. However, studies in the literature mostly focus on the particular algorithms and setups of such networks, while their theoretical understanding and characterization has been less explored. To fill this gap, this paper conducts the asymptotic (scaling-law) analysis for the delay-outage tradeoff of noise-limited wireless edge networks with joint 3C. In particular, assuming the user requests for different tasks following a Zipf distribution, we derive the analytical expression for the optimal caching policy. Based on this, we next derive the closed-form expression for the optimum outage probability as a function of delay and other network parameters for the case that the Zipf parameter is smaller than 1. Then, for the case that the Zipf parameter is larger than 1, we derive the closed-form expressions for upper and lower bounds of the optimum outage probability. We provide insights and interpretations based on the derived expressions. Computer simulations validate our analytical results and insights.

We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product, as well as ancillary workspace qubits as long as they start and end in states uncorrelated with the input, which rule out common "magic state injection" techniques that make Clifford circuits universal. We show that there are exactly 57 classes of Clifford unitaries and present a full classification characterizing the gate sets which generate them. This is the first attempt at a quantum extension of the classification of reversible classical gates introduced by Aaronson et al., another part of an ambitious program to classify all quantum gate sets. The classification uses, at its center, a reinterpretation of the tableau representation of Clifford gates to give circuit decompositions, from which elementary generators can easily be extracted. The 57 different classes are generated in this way, 30 of which arise from the single-qubit subgroups of the Clifford group. At a high level, the remaining classes are arranged according to the bases they preserve. For instance, the CNOT gate preserves the X and Z bases because it maps X-basis elements to X-basis elements and Z-basis elements to Z-basis elements. The remaining classes are characterized by more subtle tableau invariants; for instance, the T_4 and phase gate generate a proper subclass of Z-preserving gates.

Much of the literature on optimal design of bandit algorithms is based on minimization of expected regret. It is well known that designs that are optimal over certain exponential families can achieve expected regret that grows logarithmically in the number of arm plays, at a rate governed by the Lai-Robbins lower bound. In this paper, we show that when one uses such optimized designs, the regret distribution of the associated algorithms necessarily has a very heavy tail, specifically, that of a truncated Cauchy distribution. Furthermore, for $p>1$, the $p$'th moment of the regret distribution grows much faster than poly-logarithmically, in particular as a power of the total number of arm plays. We show that optimized UCB bandit designs are also fragile in an additional sense, namely when the problem is even slightly mis-specified, the regret can grow much faster than the conventional theory suggests. Our arguments are based on standard change-of-measure ideas, and indicate that the most likely way that regret becomes larger than expected is when the optimal arm returns below-average rewards in the first few arm plays, thereby causing the algorithm to believe that the arm is sub-optimal. To alleviate the fragility issues exposed, we show that UCB algorithms can be modified so as to ensure a desired degree of robustness to mis-specification. In doing so, we also provide a sharp trade-off between the amount of UCB exploration and the tail exponent of the resulting regret distribution.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.

We propose a novel method for automatic reasoning on knowledge graphs based on debate dynamics. The main idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to promote the fact being true (thesis) or the fact being false (antithesis), respectively. Based on these arguments, a binary classifier, called the judge, decides whether the fact is true or false. The two agents can be considered as sparse, adversarial feature generators that present interpretable evidence for either the thesis or the antithesis. In contrast to other black-box methods, the arguments allow users to get an understanding of the decision of the judge. Since the focus of this work is to create an explainable method that maintains a competitive predictive accuracy, we benchmark our method on the triple classification and link prediction task. Thereby, we find that our method outperforms several baselines on the benchmark datasets FB15k-237, WN18RR, and Hetionet. We also conduct a survey and find that the extracted arguments are informative for users.

Many tasks in natural language processing can be viewed as multi-label classification problems. However, most of the existing models are trained with the standard cross-entropy loss function and use a fixed prediction policy (e.g., a threshold of 0.5) for all the labels, which completely ignores the complexity and dependencies among different labels. In this paper, we propose a meta-learning method to capture these complex label dependencies. More specifically, our method utilizes a meta-learner to jointly learn the training policies and prediction policies for different labels. The training policies are then used to train the classifier with the cross-entropy loss function, and the prediction policies are further implemented for prediction. Experimental results on fine-grained entity typing and text classification demonstrate that our proposed method can obtain more accurate multi-label classification results.