We extract a core principle underlying seemingly different fundamental distributed settings, showing sparsity awareness may induce faster algorithms for problems in these settings. To leverage this, we establish a new framework by developing an intermediate auxiliary model weak enough to be simulated in the CONGEST model given low mixing time, as well as in the recently introduced HYBRID model. We prove that despite imposing harsh restrictions, this artificial model allows balancing massive data transfers with high bandwidth utilization. We exemplify the power of our methods, by deriving shortest-paths algorithms improving upon the state-of-the-art. Specifically, we show the following for graphs of $n$ nodes: A $(3+\epsilon)$ approximation for weighted APSP in $(n/\delta)\tau_{mix}\cdot 2^{O(\sqrt\log n)}$ rounds in the CONGEST model, where $\delta$ is the minimum degree of the graph and $\tau_{mix}$ is its mixing time. For graphs with $\delta=\tau_{mix}\cdot 2^{\omega(\sqrt\log n)}$, this takes $o(n)$ rounds, despite the $\Omega(n)$ lower bound for general graphs [Nanongkai, STOC'14]. An $(n^{7/6}/m^{1/2}+n^2/m)\cdot\tau_{mix}\cdot 2^{O(\sqrt\log n)}$-round exact SSSP algorithm in the CONGNEST model, for graphs with $m$ edges and a mixing time of $\tau_{mix}$. This improves upon the algorithm of [Chechik and Mukhtar, PODC'20] for significant ranges of values of $m$ and $ \tau_{mix}$. A CONGESTED CLIQUE simulation in the CONGEST model improving upon the state-of-the-art simulation of [Ghaffari, Kuhn, and SU, PODC'17] by a factor proportional to the average degree in the graph. An $\tilde O(n^{5/17}/\epsilon^9)$-round algorithm for a $(1+\epsilon)$ approximation for SSSP in the HYBRID model. The only previous $o(n^{1/3})$ round algorithm for distance approximations in this model is for a much larger factor [Augustine, Hinnenthal, Kuhn, Scheideler, Schneider, SODA'20].
相關內容
Protected attributes are often presented as categorical features that need to be encoded before feeding them into a machine learning algorithm. Encoding these attributes is paramount as they determine the way the algorithm will learn from the data. Categorical feature encoding has a direct impact on the model performance and fairness. In this work, we compare the accuracy and fairness implications of the two most well-known encoders: one-hot encoding and target encoding. We distinguish between two types of induced bias that can arise while using these encodings and can lead to unfair models. The first type, irreducible bias, is due to direct group category discrimination and a second type, reducible bias, is due to large variance in less statistically represented groups. We take a deeper look into how regularization methods for target encoding can improve the induced bias while encoding categorical features. Furthermore, we tackle the problem of intersectional fairness that arises when mixing two protected categorical features leading to higher cardinality. This practice is a powerful feature engineering technique used for boosting model performance. We study its implications on fairness as it can increase both types of induced bias
Iterative distributed optimization algorithms involve multiple agents that communicate with each other, over time, in order to minimize/maximize a global objective. In the presence of unreliable communication networks, the Age-of-Information (AoI), which measures the freshness of data received, may be large and hence hinder algorithmic convergence. In this paper, we study the convergence of general distributed gradient-based optimization algorithms in the presence of communication that neither happens periodically nor at stochastically independent points in time. We show that convergence is guaranteed provided the random variables associated with the AoI processes are stochastically dominated by a random variable with finite first moment. This improves on previous requirements of boundedness of more than the first moment. We then introduce stochastically strongly connected (SSC) networks, a new stochastic form of strong connectedness for time-varying networks. We show: If for any $p \ge0$ the processes that describe the success of communication between agents in a SSC network are $\alpha$-mixing with $n^{p-1}\alpha(n)$ summable, then the associated AoI processes are stochastically dominated by a random variable with finite $p$-th moment. In combination with our first contribution, this implies that distributed stochastic gradient descend converges in the presence of AoI, if $\alpha(n)$ is summable.
We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event requires only one evaluation of partial derivative of the potential, while its convergence rate is dimension independent. Using these properties, we prove that the zigzag sampling algorithm achieves $\varepsilon$ error in chi-square divergence with a computational cost equivalent to $O\bigl(\kappa^2 d^\frac{1}{2}(\log\frac{1}{\varepsilon})^{\frac{3}{2}}\bigr)$ gradient evaluations in the regime $\kappa \ll \frac{d}{\log d}$ under a warm start assumption, where $\kappa$ is the condition number and $d$ is the dimension.
Creativity, or the ability to produce new useful ideas, is commonly associated to the human being; but there are many other examples in nature where this phenomenon can be observed. Inspired by this fact, in engineering and particularly in computational sciences, many different models have been developed to tackle a number of problems. Composing music, a form of art broadly present along the human history, is the main topic addressed in this thesis. Taking advantage of the kind of ideas that bring diversity and creativity to nature and computation, we present Melomics: an algorithmic composition method based on evolutionary search. The solutions have a genetic encoding based on formal grammars and these are interpreted in a complex developmental process followed by a fitness assessment, to produce valid music compositions in standard formats. The system has exhibited a high creative power and versatility to produce music of different types and it has been tested, proving on many occasions the outcome to be indistinguishable from the music made by human composers. The system has also enabled the emergence of a set of completely novel applications: from effective tools to help anyone to easily obtain the precise music that they need, to radically new uses, such as adaptive music for therapy, exercise, amusement and many others. It seems clear that automated composition is an active research area and that countless new uses will be discovered.
We consider the scenario where important signals are not strong enough to be separable from a large amount of noise. Such weak signals commonly exist in large-scale data analysis and play vital roles in many biomedical applications. Existing methods however are mostly underpowered for such weak signals. We address the challenge from the perspective of false negative control and develop a new method to efficiently regulate false negative proportion at a user-specified level. The new method is developed in a realistic setting with arbitrary covariance dependence between variables. We calibrate the overall dependence through a parameter whose scale is compatible with the existing phase diagram in high-dimensional sparse inference. Utilizing the new calibration, we asymptotically explicate the joint effect of covariance dependence, signal sparsity, and signal intensity on the proposed method. We interpret the results using a new phase diagram, which shows that the proposed method can efficiently retain a high proportion of signals even when they cannot be well-separated from noise. Finite sample performance of the proposed method is compared to those of several existing methods in simulation studies. The proposed method outperforms the others in adapting to a user-specified false negative control level. We apply the new method to analyze an fMRI dataset to locate voxels that are functionally relevant to saccadic eye movements. The new method exhibits a nice balance in identifying functional relevant regions and avoiding excessive noise voxels.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Attributed graph clustering is challenging as it requires joint modelling of graph structures and node attributes. Recent progress on graph convolutional networks has proved that graph convolution is effective in combining structural and content information, and several recent methods based on it have achieved promising clustering performance on some real attributed networks. However, there is limited understanding of how graph convolution affects clustering performance and how to properly use it to optimize performance for different graphs. Existing methods essentially use graph convolution of a fixed and low order that only takes into account neighbours within a few hops of each node, which underutilizes node relations and ignores the diversity of graphs. In this paper, we propose an adaptive graph convolution method for attributed graph clustering that exploits high-order graph convolution to capture global cluster structure and adaptively selects the appropriate order for different graphs. We establish the validity of our method by theoretical analysis and extensive experiments on benchmark datasets. Empirical results show that our method compares favourably with state-of-the-art methods.
Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to bound the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.
Network embedding aims to learn a latent, low-dimensional vector representations of network nodes, effective in supporting various network analytic tasks. While prior arts on network embedding focus primarily on preserving network topology structure to learn node representations, recently proposed attributed network embedding algorithms attempt to integrate rich node content information with network topological structure for enhancing the quality of network embedding. In reality, networks often have sparse content, incomplete node attributes, as well as the discrepancy between node attribute feature space and network structure space, which severely deteriorates the performance of existing methods. In this paper, we propose a unified framework for attributed network embedding-attri2vec-that learns node embeddings by discovering a latent node attribute subspace via a network structure guided transformation performed on the original attribute space. The resultant latent subspace can respect network structure in a more consistent way towards learning high-quality node representations. We formulate an optimization problem which is solved by an efficient stochastic gradient descent algorithm, with linear time complexity to the number of nodes. We investigate a series of linear and non-linear transformations performed on node attributes and empirically validate their effectiveness on various types of networks. Another advantage of attri2vec is its ability to solve out-of-sample problems, where embeddings of new coming nodes can be inferred from their node attributes through the learned mapping function. Experiments on various types of networks confirm that attri2vec is superior to state-of-the-art baselines for node classification, node clustering, as well as out-of-sample link prediction tasks. The source code of this paper is available at //github.com/daokunzhang/attri2vec.
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191