pwc-archive/papers-with-abstracts huggingface dataset:
Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costs
Authors: Meyer Scetbon, Gabriel Peyré, Marco Cuturi
Date: 2021-06-02 00:00:00
Proceeding: NeurIPS 2021 12

The ability to align points across two related yet incomparable point clouds (e.g. living in different spaces) plays an important role in machine learning. The Gromov-Wasserstein (GW) framework provides an increasingly popular answer to such problems, by seeking a low-distortion, geometry-preserving assignment between these points. As a non-convex, quadratic generalization of optimal transport (OT), GW is NP-hard. While practitioners often resort to solving GW approximately as a nested sequence of entropy-regularized OT problems, the cubic complexity (in the number $n$ of samples) of that approach is a roadblock. We show in this work how a recent variant of the OT problem that restricts the set of admissible couplings to those having a low-rank factorization is remarkably well suited to the resolution of GW: when applied to GW, we show that this approach is not only able to compute a stationary point of the GW problem in time $O(n^2)$, but also uniquely positioned to benefit from the knowledge that the initial cost matrices are low-rank, to yield a linear time $O(n)$ GW approximation. Our approach yields similar results, yet orders of magnitude faster computation than the SoTA entropic GW approaches, on both simulated and real data.
Connections and Equivalences between the Nyström Method and Sparse Variational Gaussian Processes
Authors: Veit Wild, Motonobu Kanagawa, Dino Sejdinovic
Date: 2021-06-02 00:00:00
Tasks: Gaussian Processes

We investigate the connections between sparse approximation methods for making kernel methods and Gaussian processes (GPs) scalable to large-scale data, focusing on the Nystr\"om method and the Sparse Variational Gaussian Processes (SVGP). While sparse approximation methods for GPs and kernel methods share some algebraic similarities, the literature lacks a deep understanding of how and why they are related. This may pose an obstacle to the communications between the GP and kernel communities, making it difficult to transfer results from one side to the other. Our motivation is to remove this obstacle, by clarifying the connections between the sparse approximations for GPs and kernel methods. In this work, we study the two popular approaches, the Nystr\"om and SVGP approximations, in the context of a regression problem, and establish various connections and equivalences between them. In particular, we provide an RKHS interpretation of the SVGP approximation, and show that the Evidence Lower Bound of the SVGP contains the objective function of the Nystr\"om approximation, revealing the origin of the algebraic equivalence between the two approaches. We also study recently established convergence results for the SVGP and how they are related to the approximation quality of the Nystr\"om method.
Design and Comparison of Reward Functions in Reinforcement Learning for Energy Management of Sensor Nodes
Authors: Yohann Rioual, Yannick Le Moullec, Johann Laurent, Muhidul Islam Khan, Jean-Philippe Diguet
Date: 2021-06-02 00:00:00
Tasks: energy management, Management, Q-Learning, reinforcement-learning, Reinforcement Learning (RL)

Interest in remote monitoring has grown thanks to recent advancements in Internet-of-Things (IoT) paradigms. New applications have emerged, using small devices called sensor nodes capable of collecting data from the environment and processing it. However, more and more data are processed and transmitted with longer operational periods. At the same, the battery technologies have not improved fast enough to cope with these increasing needs. This makes the energy consumption issue increasingly challenging and thus, miniaturized energy harvesting devices have emerged to complement traditional energy sources. Nevertheless, the harvested energy fluctuates significantly during the node operation, increasing uncertainty in actually available energy resources. Recently, approaches in energy management have been developed, in particular using reinforcement learning approaches. However, in reinforcement learning, the algorithm's performance relies greatly on the reward function. In this paper, we present two contributions. First, we explore five different reward functions to identify the most suitable variables to use in such functions to obtain the desired behaviour. Experiments were conducted using the Q-learning algorithm to adjust the energy consumption depending on the energy harvested. Results with the five reward functions illustrate how the choice thereof impacts the energy consumption of the node. Secondly, we propose two additional reward functions able to find the compromise between energy consumption and a node performance using a non-fixed balancing parameter. Our simulation results show that the proposed reward functions adjust the node's performance depending on the battery level and reduce the learning time.
Improvement over Pinball Loss Support Vector Machine
Authors: Pritam Anand, Reshma Rastogi, Suresh Chandra
Date: 2021-06-02 00:00:00
Tasks: Binary Classification, valid

Recently, there have been several papers that discuss the extension of the Pinball loss Support Vector Machine (Pin-SVM) model, originally proposed by Huang et al.,[1][2]. Pin-SVM classifier deals with the pinball loss function, which has been defined in terms of the parameter $\tau$. The parameter $\tau$ can take values in $[ -1,1]$. The existing Pin-SVM model requires to solve the same optimization problem for all values of $\tau$ in $[ -1,1]$. In this paper, we improve the existing Pin-SVM model for the binary classification task. At first, we note that there is major difficulty in Pin-SVM model (Huang et al. [1]) for $ -1 \leq \tau < 0$. Specifically, we show that the Pin-SVM model requires the solution of different optimization problem for $ -1 \leq \tau < 0$. We further propose a unified model termed as Unified Pin-SVM which results in a QPP valid for all $-1\leq \tau \leq 1$ and hence more convenient to use. The proposed Unified Pin-SVM model can obtain a significant improvement in accuracy over the existing Pin-SVM model which has also been empirically justified by extensive numerical experiments with real-world datasets.
Learning a Single Neuron with Bias Using Gradient Descent
Authors: Gal Vardi, Gilad Yehudai, Ohad Shamir
Date: 2021-06-02 00:00:00
Proceeding: NeurIPS 2021 12

We theoretically study the fundamental problem of learning a single neuron with a bias term ($\mathbf{x} \mapsto \sigma(<\mathbf{w},\mathbf{x}> + b)$) in the realizable setting with the ReLU activation, using gradient descent. Perhaps surprisingly, we show that this is a significantly different and more challenging problem than the bias-less case (which was the focus of previous works on single neurons), both in terms of the optimization geometry as well as the ability of gradient methods to succeed in some scenarios. We provide a detailed study of this problem, characterizing the critical points of the objective, demonstrating failure cases, and providing positive convergence guarantees under different sets of assumptions. To prove our results, we develop some tools which may be of independent interest, and improve previous results on learning single neurons.
Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions
Authors: Leslie O'Bray, Max Horn, Bastian Rieck, Karsten Borgwardt
Date: 2021-06-02 00:00:00
Proceeding: ICLR 2022 4

Graph generative models are a highly active branch of machine learning. Given the steady development of new models of ever-increasing complexity, it is necessary to provide a principled way to evaluate and compare them. In this paper, we enumerate the desirable criteria for such a comparison metric and provide an overview of the status quo of graph generative model comparison in use today, which predominantly relies on the maximum mean discrepancy (MMD). We perform a systematic evaluation of MMD in the context of graph generative model comparison, highlighting some of the challenges and pitfalls researchers inadvertently may encounter. After conducting a thorough analysis of the behaviour of MMD on synthetically-generated perturbed graphs as well as on recently-proposed graph generative models, we are able to provide a suitable procedure to mitigate these challenges and pitfalls. We aggregate our findings into a list of practical recommendations for researchers to use when evaluating graph generative models.
Learning to Rehearse in Long Sequence Memorization
Authors: Zhu Zhang, Chang Zhou, Jianxin Ma, Zhijie Lin, Jingren Zhou, Hongxia Yang, Zhou Zhao
Date: 2021-06-02 00:00:00
Tasks: Memorization, Question Answering, Video Question Answering

Existing reasoning tasks often have an important assumption that the input contents can be always accessed while reasoning, requiring unlimited storage resources and suffering from severe time delay on long sequences. To achieve efficient reasoning on long sequences with limited storage resources, memory augmented neural networks introduce a human-like write-read memory to compress and memorize the long input sequence in one pass, trying to answer subsequent queries only based on the memory. But they have two serious drawbacks: 1) they continually update the memory from current information and inevitably forget the early contents; 2) they do not distinguish what information is important and treat all contents equally. In this paper, we propose the Rehearsal Memory (RM) to enhance long-sequence memorization by self-supervised rehearsal with a history sampler. To alleviate the gradual forgetting of early information, we design self-supervised rehearsal training with recollection and familiarity tasks. Further, we design a history sampler to select informative fragments for rehearsal training, making the memory focus on the crucial information. We evaluate the performance of our rehearsal memory by the synthetic bAbI task and several downstream tasks, including text/video question answering and recommendation on long sequences.
Statistical optimality conditions for compressive ensembles
Authors: Henry W. J. Reeve, Ata Kaban
Date: 2021-06-02 00:00:00
Tasks: regression

We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent upper-bound on the excess risk, framed in terms of a natural notion of compressibility. This bound is independent of the dimension of the original data representation, and explains the in-built regularisation effect of the compressive approach. We then instantiate this general bound to classification and regression tasks, considering Johnson-Lindenstrauss mappings as the compression scheme. For each of these tasks, our strategy is to develop a tight upper bound on the compressibility function, and by doing so we discover distributional conditions of geometric nature under which the compressive algorithm attains minimax-optimal rates up to at most poly-logarithmic factors. In the case of compressive classification, this is achieved with a mild geometric margin condition along with a flexible moment condition that is significantly more general than the assumption of bounded domain. In the case of regression with strongly convex smooth loss functions we find that compressive regression is capable of exploiting spectral decay with near-optimal guarantees. In addition, a key ingredient for our central upper bound is a high probability uniform upper bound on the integrated deviation of dependent empirical processes, which may be of independent interest.
Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations
Authors: Yingtao Luo, Qiang Liu, Yuntian Chen, WenBo Hu, Tian Tian, Jun Zhu
Date: 2021-06-02 00:00:00
Tasks: Density Estimation, Model Optimization

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from scientific data thrives as a new attempt to model complex phenomena in nature, but the effectiveness of current practice is typically limited by the scarcity of data and the complexity of phenomena. Especially, the discovery of PDEs with highly nonlinear coefficients from low-quality data remains largely under-addressed. To deal with this challenge, we propose a novel physics-guided learning method, which can not only encode observation knowledge such as initial and boundary conditions but also incorporate the basic physical principles and laws to guide the model optimization. We theoretically show that our proposed method strictly reduces the coefficient estimation error of existing baselines, and is also robust against noise. Extensive experiments show that the proposed method is more robust against data noise, and can reduce the estimation error by a large margin. Moreover, all the PDEs in the experiments are correctly discovered, and for the first time we are able to discover three-dimensional PDEs with highly nonlinear coefficients.
Testing Group Fairness via Optimal Transport Projections
Authors: Nian Si, Karthyek Murthy, Jose Blanchet, Viet Anh Nguyen
Date: 2021-06-02 00:00:00
Tasks: Fairness

We present a statistical testing framework to detect if a given machine learning classifier fails to satisfy a wide range of group fairness notions. The proposed test is a flexible, interpretable, and statistically rigorous tool for auditing whether exhibited biases are intrinsic to the algorithm or due to the randomness in the data. The statistical challenges, which may arise from multiple impact criteria that define group fairness and which are discontinuous on model parameters, are conveniently tackled by projecting the empirical measure onto the set of group-fair probability models using optimal transport. This statistic is efficiently computed using linear programming and its asymptotic distribution is explicitly obtained. The proposed framework can also be used to test for testing composite fairness hypotheses and fairness with multiple sensitive attributes. The optimal transport testing formulation improves interpretability by characterizing the minimal covariate perturbations that eliminate the bias observed in the audit.
Decision-making Oriented Clustering: Application to Pricing and Power Consumption Scheduling
Authors: Chao Zhang, Samson Lasaulce, Martin Hennebel, Lucas Saludjian, Patrick Panciatici, H. Vincent Poor
Date: 2021-06-02 00:00:00
Tasks: Clustering, Decision Making, Management, Scheduling

Data clustering is an instrumental tool in the area of energy resource management. One problem with conventional clustering is that it does not take the final use of the clustered data into account, which may lead to a very suboptimal use of energy or computational resources. When clustered data are used by a decision-making entity, it turns out that significant gains can be obtained by tailoring the clustering scheme to the final task performed by the decision-making entity. The key to having good final performance is to automatically extract the important attributes of the data space that are inherently relevant to the subsequent decision-making entity, and partition the data space based on these attributes instead of partitioning the data space based on predefined conventional metrics. For this purpose, we formulate the framework of decision-making oriented clustering and propose an algorithm providing a decision-based partition of the data space and good representative decisions. By applying this novel framework and algorithm to a typical problem of real-time pricing and that of power consumption scheduling, we obtain several insightful analytical results such as the expression of the best representative price profiles for real-time pricing and a very significant reduction in terms of required clusters to perform power consumption scheduling as shown by our simulations.
Deep Reinforcement Learning-based UAV Navigation and Control: A Soft Actor-Critic with Hindsight Experience Replay Approach
Authors: Myoung Hoon Lee, Jun Moon
Date: 2021-06-02 00:00:00
Tasks: Deep Reinforcement Learning

In this paper, we propose SACHER (soft actor-critic (SAC) with hindsight experience replay (HER)), which constitutes a class of deep reinforcement learning (DRL) algorithms. SAC is known as an off-policy model-free DRL algorithm based on the maximum entropy framework, which outperforms earlier DRL algorithms in terms of exploration, robustness and learning performance. However, in SAC, maximizing the entropy-augmented objective may degrade the optimality of learning outcomes. HER is known as a sample-efficient replay method that enhances the performance of off-policy DRL algorithms by allowing the agent to learn from both failures and successes. We apply HER to SAC and propose SACHER to improve the learning performance of SAC. More precisely, SACHER achieves the desired optimal outcomes faster and more accurately than SAC, since HER improves the sample efficiency of SAC. We apply SACHER to the navigation and control problem of unmanned aerial vehicles (UAVs), where SACHER generates the optimal navigation path of the UAV under various obstacles in operation. Specifically, we show the effectiveness of SACHER in terms of the tracking error and cumulative reward in UAV operation by comparing them with those of state-of-the-art DRL algorithms, SAC and DDPG. Note that SACHER in UAV navigation and control problems can be applied to arbitrary models of UAVs.
Warming up recurrent neural networks to maximise reachable multistability greatly improves learning
Authors: Gaspard Lambrechts, Florent De Geeter, Nicolas Vecoven, Damien Ernst, Guillaume Drion
Date: 2021-06-02 00:00:00
Tasks: Time Series Analysis

Training recurrent neural networks is known to be difficult when time dependencies become long. In this work, we show that most standard cells only have one stable equilibrium at initialisation, and that learning on tasks with long time dependencies generally occurs once the number of network stable equilibria increases; a property known as multistability. Multistability is often not easily attained by initially monostable networks, making learning of long time dependencies between inputs and outputs difficult. This insight leads to the design of a novel way to initialise any recurrent cell connectivity through a procedure called "warmup" to improve its capability to learn arbitrarily long time dependencies. This initialisation procedure is designed to maximise network reachable multistability, i.e., the number of equilibria within the network that can be reached through relevant input trajectories, in few gradient steps. We show on several information restitution, sequence classification, and reinforcement learning benchmarks that warming up greatly improves learning speed and performance, for multiple recurrent cells, but sometimes impedes precision. We therefore introduce a double-layer architecture initialised with a partial warmup that is shown to greatly improve learning of long time dependencies while maintaining high levels of precision. This approach provides a general framework for improving learning abilities of any recurrent cell when long time dependencies are present. We also show empirically that other initialisation and pretraining procedures from the literature implicitly foster reachable multistability of recurrent cells.
Communication-Efficient Split Learning Based on Analog Communication and Over the Air Aggregation
Authors: Mounssif Krouka, Anis Elgabli, Chaouki Ben Issaid, Mehdi Bennis
Date: 2021-06-02 00:00:00
Tasks: Collaborative Inference, Privacy Preserving

Split-learning (SL) has recently gained popularity due to its inherent privacy-preserving capabilities and ability to enable collaborative inference for devices with limited computational power. Standard SL algorithms assume an ideal underlying digital communication system and ignore the problem of scarce communication bandwidth. However, for a large number of agents, limited bandwidth resources, and time-varying communication channels, the communication bandwidth can become the bottleneck. To address this challenge, in this work, we propose a novel SL framework to solve the remote inference problem that introduces an additional layer at the agent side and constrains the choices of the weights and the biases to ensure over the air aggregation. Hence, the proposed approach maintains constant communication cost with respect to the number of agents enabling remote inference under limited bandwidth. Numerical results show that our proposed algorithm significantly outperforms the digital implementation in terms of communication-efficiency, especially as the number of agents grows large.
Energy-Efficient Model Compression and Splitting for Collaborative Inference Over Time-Varying Channels
Authors: Mounssif Krouka, Anis Elgabli, Chaouki Ben Issaid, Mehdi Bennis
Date: 2021-06-02 00:00:00
Tasks: Collaborative Inference, image-classification, Image Classification, Model Compression

Today's intelligent applications can achieve high performance accuracy using machine learning (ML) techniques, such as deep neural networks (DNNs). Traditionally, in a remote DNN inference problem, an edge device transmits raw data to a remote node that performs the inference task. However, this may incur high transmission energy costs and puts data privacy at risk. In this paper, we propose a technique to reduce the total energy bill at the edge device by utilizing model compression and time-varying model split between the edge and remote nodes. The time-varying representation accounts for time-varying channels and can significantly reduce the total energy at the edge device while maintaining high accuracy (low loss). We implement our approach in an image classification task using the MNIST dataset, and the system environment is simulated as a trajectory navigation scenario to emulate different channel conditions. Numerical simulations show that our proposed solution results in minimal energy consumption and $CO_2$ emission compared to the considered baselines while exhibiting robust performance across different channel conditions and bandwidth regime choices.
Multiresolution Equivariant Graph Variational Autoencoder
Authors: Truong Son Hy, Risi Kondor
Date: 2021-06-02 00:00:00
Tasks: Graph Generation, Image Generation, Link Prediction, molecular representation, Representation Learning

In this paper, we propose Multiresolution Equivariant Graph Variational Autoencoders (MGVAE), the first hierarchical generative model to learn and generate graphs in a multiresolution and equivariant manner. At each resolution level, MGVAE employs higher order message passing to encode the graph while learning to partition it into mutually exclusive clusters and coarsening into a lower resolution that eventually creates a hierarchy of latent distributions. MGVAE then constructs a hierarchical generative model to variationally decode into a hierarchy of coarsened graphs. Importantly, our proposed framework is end-to-end permutation equivariant with respect to node ordering. MGVAE achieves competitive results with several generative tasks including general graph generation, molecular generation, unsupervised molecular representation learning to predict molecular properties, link prediction on citation graphs, and graph-based image generation.