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Clustering with outliers is one of the most fundamental problems in Computer Science.  Given a set $X$ of $n$ points and two numbers $k,m$, the clustering with outliers aims to exclude $m$ points from $X$ and partition the remaining points into $k$ clusters that minimizes a certain cost function. In this paper, we give a general approach for solving clustering with outliers, which results in a fixed-parameter tractable (FPT) algorithm in $k$ and $m$, that almost matches the approximation ratio for its outlier-free counterpart. As a corollary, we obtain FPT approximation algorithms with optimal approximation ratios for $k$-\textsc{Median} and $k$-\textsc{Means} with outliers in general and Euclidean metrics. We also exhibit more applications of our approach to other variants of the problem that impose additional constraints on the clustering, such as fairness or matroid constraints. 

AAAI 2023

Clustering What Matters: Optimal Approximation for Clustering with Outliers

approximation algorithms

outliers

clustering

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
AAAI is providing you with a conference planner, which you can use to help organize your itinerary of activities. This includes talks to attend in person, talks to attend remotely, breaks with colleagues and your site seeing activities. To access this conference planner, please go to [https://aaai-2023.takemobi.io](https://aaai-2023.takemobi.io).

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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

poster

In modern electronic manufacturing processes, multi-layer Printed Circuit Board (PCB) routing requires connecting more than hundreds of nets with perplexing topology under complex routing constraints and highly limited resources, so that takes intense effort and time of human engineers. PCB fanout as a pre-design of PCB routing has been proved to be an ideal technique to reduce the complexity of PCB routing by pre-allocating resources and pre-routing. However, current PCB fanout design heavily relies on the experience of human engineers, and there is no existing solution for PCB fanout automation in industry, which limits the quality of PCB routing automation. To address the problem, we propose a neuralized PCB fanout method by deep reinforcement learning. To the best of our knowledge, we are the first in the literature to propose the automation method for PCB fanout. We combine with Convolution Neural Network (CNN) and attention-based network to train our fanout policy model and value model. The models learn representations of PCB layout and netlist to make decisions and evaluations in place of human engineers. We employ Proximal Policy Optimization (PPO) to update the parameters of the models. In addition, we apply our PCB fanout method to a PCB router to improve the quality of PCB routing. Extensive experimental results on real-world industrial PCB benchmarks demonstrate that our approach achieves 100% routability in all industrial cases and improves wire length by an average of 6.8%, which makes a significant improvement compared with the state-of-the-art methods.

FanoutNet: A Neuralized PCB Fanout Automation Method Using Deep Reinforcement Learning

Role-based learning is a promising approach to improving the performance of Multi-Agent Reinforcement Learning (MARL). Nevertheless, without manual assistance, current role-based methods cannot guarantee stably discovering a set of roles to effectively decompose a complex task, as they assume either a predefined role structure or practical experience for selecting hyperparameters. In this article, we propose a mathematical Structural Information principles-based Role Discovery method, namely SIRD, and then present a SIRD optimizing MARL framework, namely SR-MARL, for multi-agent collaboration. The SIRD transforms role discovery into a hierarchical action space clustering. Specifically, the SIRD consists of structuralization, sparsification, and optimization modules, where an optimal encoding tree is generated to perform abstracting to discover roles. The SIRD is agnostic to specific MARL algorithms and flexibly integrated with various value function factorization approaches. Empirical evaluations on the StarCraft II micromanagement benchmark demonstrate that, compared with state-of-the-art MARL algorithms, the SR-MARL framework improves the average test win rate by 0.17%, 6.08%, and 3.24%, and reduces the deviation by 16.67%, 30.80%, and 66.30%, under easy, hard, and super hard scenarios. 

Effective and Stable Role-based Multi-Agent Collaboration by Structural Information Principles

Many challenges from natural world can be formulated as a graph matching problem. Previous deep learning-based methods mainly consider a full two-graph matching setting. In this work, we study the more general partial matching problem with multi-graph cycle consistency guarantees. Building on a recent progress in deep learning on graphs, we propose a novel data-driven method (URL) for partial multi-graph matching, which uses an object-to-universe formulation and learns latent representations of abstract universe points. The proposed approach advances the state of the art in semantic keypoint matching problem, evaluated on Pascal VOC, CUB, and Willow datasets. Moreover, the set of controlled experiments on a synthetic graph matching dataset demonstrates the scalability of our method to graphs with large number of nodes and its robustness to high partiality. 

Universe Points Representation Learning for Partial Multi-Graph Matching

This paper presents an inverse kinematic optimization layer (IKOL) for 3D human pose and shape estimation that leverages the strength of both optimization- and regression-based methods within an end-to-end framework. IKOL involves a nonconvex optimization that establishes an implicit mapping from an image’s 3D keypoints and body shapes to the relative body-part rotations. The 3D keypoints and the body shapes are the inputs and the relative body-part rotations are the solutions. However, this procedure is implicit and hard to make differentiable. So, to overcome this issue, we designed a Gauss-Newton differentiation (GN-Diff) procedure to differentiate IKOL. GN-Diff iteratively linearizes the nonconvex objective function to obtain Gauss-Newton directions with closed form solutions. Then, an automatic differentiation procedure is directly applied to generate a Jacobian matrix for end-to-end training. Notably, the GN-Diff procedure works fast because it does not rely on a time-consuming implicit differentiation procedure. The twist rotation and shape parameters are learned from the neural networks and, as a result, IKOL has a much lower computational overhead than most existing optimization-based methods. Additionally, compared to existing regression-based methods, IKOL provides a more accurate mesh-image correspondence. This is because it iteratively reduces the distance between the keypoints and also enhances the reliability of the pose structures. Extensive experiments demonstrate the superiority of our proposed framework over a wide range of 3D human pose and shape estimation methods. 

IKOL: Inverse kinematics optimization layer for 3D human pose and shape estimation via Gauss-Newton differentiation

Adversarial training is an effective learning technique to improve the robustness of deep neural networks. In this study, the influence of adversarial training on deep learning models in terms of fairness, robustness, and generalization is theoretically investigated under more general perturbation scope that different samples can have different perturbation directions (the adversarial and anti-adversarial directions) and varied perturbation bounds. Our theoretical explorations suggest that the combination of adversaries and anti-adversaries (samples with anti-adversarial perturbations) in training can be more effective in achieving better fairness between classes and a better tradeoff between robustness and generalization in some typical learning scenarios (e.g., noisy label learning and imbalance learning) compared with standard adversarial training. On the basis of our theoretical findings, a more general learning objective that combines adversaries and anti-adversaries with varied bounds on each training sample is presented. Meta learning is utilized to optimize the combination weights. Experiments on benchmark datasets under different learning scenarios verify our theoretical findings and the effectiveness of the proposed methodology.

Combining Adversaries with Anti-adversaries in Training

Goal-conditioned reinforcement learning (GCRL) has a wide range of potential real-world applications, including manipulation and navigation problems in robotics. Especially in such robotics tasks, sample efficiency is of the utmost importance for GCRL since, by default, the agent is only rewarded when it reaches its goal. While several methods have been proposed to improve the sample efficiency of GCRL, one relatively under-studied approach is the design of neural architectures to support sample efficiency.
In this work, we introduce a novel neural architecture for GCRL that achieves significantly better sample efficiency than the commonly-used monolithic network architecture. 
The key insight is that the 
optimal action-value function $Q^*(s, a, g)$ must satisfy the triangle inequality in a specific sense.
Furthermore, we introduce the \emph{metric residual network} (MRN)  that deliberately decomposes the action-value function $Q(s,a,g)$ into the negated summation of a metric plus a residual asymmetric component. MRN provably approximates any optimal action-value function $Q^*(s,a,g)$, thus making it a fitting neural architecture for GCRL.
We conduct comprehensive experiments across 12 standard benchmark environments in GCRL. The empirical results demonstrate that MRN uniformly outperforms other state-of-the-art GCRL neural architectures in terms of sample efficiency. The code is publicly available at \url{https://github.com/Cranial-XIX/metric-residual-network}.

Metric Residual Network for Sample Efficient Goal-conditioned Reinforcement Learning

Most entropy measures depend on the spread of the probability distribution over the sample space X, and the maximum entropy achievable scales proportionately with the sample space cardinality |X|. For a finite |X|, this yields robust entropy measures which satisfy many important properties, such as invariance to bijections, while the same is not true for continuous spaces (where |X|=infinity).
Furthermore, since R and R^d (d in Z+) have the same cardinality (from Cantor's correspondence argument), cardinality-dependent entropy measures cannot encode the data dimensionality. In this work, we question the role of cardinality and distribution spread in defining entropy measures for continuous spaces, which can undergo multiple rounds of transformations and distortions, e.g., in neural networks. We find that the average value of the local intrinsic dimension of a distribution, denoted as ID-Entropy, can serve as a robust entropy measure for continuous spaces, while capturing the data dimensionality. We find that ID-Entropy satisfies many desirable properties and can be extended to conditional entropy, joint entropy and mutual-information variants. ID-Entropy also yields new information bottleneck principles and also links to causality. In the context of deep learning, for feedforward architectures, we show, theoretically and empirically, that the ID-Entropy of a hidden layer directly controls the generalization gap for both supervised and unsupervised scenarios, when the target function is Lipschitz continuous. Our work primarily shows that, for continuous spaces, taking a structural rather than a statistical approach yields entropy measures which preserve intrinsic data dimensionality, while being relevant for studying supervised and unsupervised architectures.

Local Intrinsic Dimensional Entropy

Real-time Detection Of Robotic Traffic in Online Advertising

Robots will play a crucial role in the future and need to work as a team in increasingly more complex applications. Advances in robotics have laid the hardware foundations for building large-scale multi-robot systems, such as for mobile robots and drones. But how to coordinate robots intelligently is a difficult problem. In this talk, I will introduce intelligent planning algorithms for solving this challenge with a focus on one fundamental problem: letting a large team of agents navigate without collisions in congested environments while minimizing their travel times. I will present principled planning algorithms that can efficiently coordinate hundreds of agents while providing rigorous guarantees on completeness and even optimality. I will also present techniques to apply these algorithms to real-world problems with robustness guarantees, such as warehouse robot coordination, railway planning, and multi-arm assembly.

Intelligent Planning for Large-Scale Multi-Robot Coordination

The use of voice-over-IP technology has rapidly expanded over the past several years, and has thus become a significant portion of traffic in the real, complex network environment. Deep packet inspection and middlebox technologies need to analyze call flows in order to perform network management, load-balancing, content monitoring, forensic analysis, and intelligence gathering. Because the session setup and management data can be sent on different ports or out of sync with VoIP call data over the Real-time Transport Protocol (RTP) with low latency, inspection software may miss calls or parts of calls. To solve this problem, we engineered two different deep learning models based on hidden representation learning. MAPLE, a matrix-based encoder which transforms packets into an image representation, uses convolutional neural networks to determine RTP packets from data flow. DATE is a density-analysis based tensor encoder which transforms packet data into a three-dimensional point cloud representation. We then perform density-based clustering over the point clouds as latent representations of the data, and classify packets as RTP or non-RTP based on their statistical clustering features. In this research, we show that these tools may allow a data collection and analysis pipeline to begin detecting and buffering RTP streams for later session association, solving the initial drop problem. MAPLE achieves over ninety-nine percent accuracy in RTP/non-RTP detection. The results of our experiments show that both models can not only classify RTP versus non-RTP packet streams, but could extend to other network traffic classification problems in real deployments of network analysis pipelines.

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Clustering What Matters: Optimal Approximation for Clustering with Outliers

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