United States

We introduce the triangle-densest-K-subgraph problem (TDKS) for undirected graphs: given a size parameter K, compute a subset of K vertices that maximizes the number of induced triangles. The problem corresponds to the simplest generalization of the edge based densest-K-subgraph problem (DKS) to the case of higher-order network motifs. We prove that TDKS is NP-hard and is not amenable to efficient approximation, in the worst-case. By judiciously exploiting the structure of the problem, we propose a relaxation algorithm for the purpose of obtaining high-quality, sub-optimal solutions. Our approach utilizes the fact that the cost function of TDKS is submodular to construct a convex relaxation for the problem based on the LovÃ¡sz extension for submodular functions. We demonstrate that our approaches attain state-of-the-art performance on real-world graphs and can offer substantially improved exploration of the optimal density-size curve compared to sophisticated approximation baselines for DKS. We use document summarization to showcase why TDKS is a useful generalization of DKS.

AAAI 2022

The Triangle-Densest-k-Subgraph Problem: Hardness, Lovász Extension, and Application to Document Summarization

technical paper

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

Active learning attempts to maximize a task model's performance gain by obtaining a set of informative samples from an unlabeled data pool. Previous active learning methods usually rely on specific network architectures or task-dependent sample acquisition algorithms. Moreover, when selecting a batch sample, previous works suffer from insufficient diversity of batch samples because they only consider the informativeness of each sample. This paper proposes a task-independent batch acquisition method using triplet loss to distinguish hard samples in an unlabeled data pool with similar features but difficult to identify labels. To assess the effectiveness of the proposed method, we compare the proposed method with state-of-the-art active learning methods on two tasks, relation extraction and sentence classification. Experimental results show that our method outperforms baselines on the benchmark datasets.

Active Learning on Pre-Trained Language Model with Task-Independent Triplet Loss

In recent years, machine learning (ML) algorithms have been deployed in safety-critical and high-stake decision-making, where the fairness of algorithms is of paramount importance. Fairness in ML centers on detecting bias towards certain demographic populations induced by an ML classifier and proposes algorithmic solutions to mitigate the bias with respect to different fairness definitions. To this end, several fairness verifiers have been proposed that compute the bias in the prediction of an ML classifierâ€”essentially beyond a finite datasetâ€”given the probability distribution of input features. In the context of verifying linear classifiers, existing fairness verifiers are limited by accuracy due to imprecise modeling of correlations among features and scalability due to restrictive formulations of the classifiers as SSAT/SMT formulas or by sampling.


In this paper, we propose an efficient fairness verifier, called FVGM, that encodes the correlations among features as a Bayesian network. In contrast to existing verifiers, FVGM proposes a stochastic subset-sum based approach for verifying linear classifiers. Experimentally, we show that FVGM leads to an accurate and scalable assessment for more diverse families of fairness-enhancing algorithms, fairness attacks, and group/causal fairness metrics than the state-of-the-art fairness verifiers. We also demonstrate that FVGM facilitates the computation of fairness influence functions as a stepping stone to detect the source of bias induced by subsets of features.

Algorithmic Fairness Verification with Graphical Models

The non-dominated sorting genetic algorithm II (NSGA-II) is the most intensively used multi-objective evolutionary algorithm (MOEA) in real-world applications. However, in contrast to several simple MOEAs analyzed also via mathematical means, no such study exists for the NSGA-II so far. In this work, we show that mathematical runtime analyses are feasible also for the NSGA-II. As particular results, we prove that with a population size larger than the Pareto front size by a constant factor, the NSGA-II with two classic mutation operators and three different ways to select the parents satisfies the same asymptotic runtime guarantees as the SEMO and GSEMO algorithms on the basic OneMinMax and LOTZ benchmark functions. However, if the population size is only equal to the size of the Pareto front, then the NSGA-II cannot efficiently compute the full Pareto front (for an exponential number of iterations, the population will always miss a constant fraction of the Pareto front). Our experiments confirm the above findings.

A First Mathematical Runtime Analysis of the Non-Dominated Sorting Genetic Algorithm II (NSGA-II)

In this paper we show that behavioral cloning can be used to learn effective sketches of programmatic strategies. We show that even the sketches learned by cloning the behavior of weak players can help the synthesis of programmatic strategies. This is because even weak players can provide helpful information, e.g., that a player must choose an action in their turn of the game. If behavioral cloning is not employed, the synthesizer needs to learn even the most basic information by playing the game, which can be computationally expensive. We demonstrate empirically the advantages of our sketch-learning approach with simulated annealing and UCT synthesizers. We evaluate our synthesizers in the games of Can't Stop and MicroRTS. The sketch-based synthesizers are able to learn stronger programmatic strategies than their original counterparts. Our synthesizers generate strategies of Can't Stop that defeat a traditional programmatic strategy for the game. They also synthesize strategies that defeat the best performing method from the latest MicroRTS competition.

What Can We Learn Even from the Weakest? Learning Sketches for Programmatic Strategies

We study identifiability of linear Andersson-Madigan-Perlman (AMP) chain graph models, which are a common generalization of linear structural equation models and Gaussian graphical models. AMP models are described by DAGs on chain components which themselves are undirected graphs.
For a known chain component decomposition, we show that the DAG on the chain components is identifiable if the determinants of the residual covariance matrices of the chain components are equal (or more generally, monotone non-decreasing in topological order). This condition extends the equal variance identifiability criterion for Bayes nets, and it can be generalized from determinants to any super-additive function on positive semidefinite matrices. When the component decomposition is unknown, we describe conditions that allow recovery of the full structure using a polynomial time algorithm based on submodular function minimization. We also conduct experiments comparing our algorithm's performance against existing baselines.

Identifiability of Linear AMP Chain Graph Models

Traditional subspace clustering aims to cluster data lying in a union of linear subspaces. The vectorization of high-dimensional data to 1-D vectors to perform clustering ignores much of the structure intrinsic to such data. To preserve said structure, in this work we exploit clustering in a high-order tensor space rather than a vector space. We develop a novel low-tensor-rank representation (LTRR) for unfolded matrices of tensor data lying in a low-rank tensor space. The representation coefficient matrix of an unfolding matrix is tensorized to a 3-order tensor, and the low-tensor-rank constraint is imposed on the transformed coefficient tensor to exploit the self-expressiveness property. Then, inspired by the multi-view clustering framework, we develop a multi-mode tensor space clustering algorithm (MMTSC) that can deal with tensor space clustering with or without missing entries. The tensor is unfolded along each mode, and the coefficient matrices are obtained for each unfolded matrix. The low tensor rank constraint is imposed on a tensor combined from transformed coefficient tensors of each mode, such that the proposed method can simultaneously capture the low rank property for the data within each tensor space and maintain cluster consistency across different modes. Experimental results demonstrate that the proposed MMTSC algorithm can outperform existing clustering algorithms in many cases.

Multi-Mode Tensor Space Clustering Based on Low-Tensor-Rank Representation

Unsupervised point cloud registration algorithm usually suffers from the unsatisfied registration precision in the partially overlapping problem due to the lack of effective inlier evaluation. In this paper, we propose a neighborhood consensus based reliable inlier evaluation method for robust unsupervised point cloud registration. It is expected to capture the discriminative geometric difference between the source neighborhood and the corresponding pseudo target neighborhood for effective inlier distinction. Specifically, our model consists of a matching map refinement module and an inlier evaluation module. In our matching map refinement module, we improve the point-wise matching map estimation by integrating the matching scores of neighbors into it. The aggregated neighborhood information potentially facilitates the discriminative map construction so that high-quality correspondences can be provided for generating the pseudo target point cloud. Based on the observation that the outlier has the significant structure-wise difference between its source neighborhood and corresponding pseudo target neighborhood while this difference for inlier is small, the inlier evaluation module exploits this difference to score the inlier confidence for each estimated correspondence. In particular, we construct an effective graph representation for capturing this geometric difference between the neighborhoods. Finally, with the learned correspondences and the corresponding inlier confidence, we use the weighted SVD algorithm for transformation estimation.Under the unsupervised setting, we exploit the Huber function based global alignment loss, the local neighborhood consensus loss and spatial consistency loss for model optimization. The experimental results on extensive datasets demonstrate that our unsupervised point cloud registration method can yield comparable performance.

Reliable Inlier Evaluation for Unsupervised Point Cloud Registration

Unsupervised reinforcement learning aims to train agents to learn a handful of policies or skills in environments without external reward. These pre-trained policies can accelerate learning when endowed with external reward, and can also be used as primitive options in hierarchical reinforcement learning. Conventional approaches of unsupervised skill discovery feed a latent variable to the agent and shed its empowerment on agent's behavior by mutual information (MI) maximization. However, the policies learned by MI-based methods cannot sufficiently explore the state space, despite they can be successfully identified from each other. Therefore we propose a new framework Wasserstein unsupervised reinforcement learning (WURL) where we directly maximize the distance of state distributions induced by different policies. Additionally, we overcome difficulties in simultaneously training N(N>2) policies, and amortizing the overall reward to each step. Experiments show policies learned by our approach outperform MI-based methods on the metric of Wasserstein distance while keeping high discriminability. Furthermore, the agents trained by WURL can sufficiently explore the state space in mazes and MuJoCo tasks and the pre-trained policies can be applied to downstream tasks by hierarchical learning.

Wasserstein Unsupervised Reinforcement Learning

Keypoint detection and description play a central role in computer vision. Most existing methods are in the form of scene-level prediction, without returning the object classes of different keypoints. In this paper, we propose the object-centric formulation, which, beyond the conventional setting, requires further identifying which object each interest point belongs to. With such fine-grained information, our framework enables more downstream potentials, such as object-level matching and pose estimation in a clustered environment. To get around the difficulty of label collection in the real world, we develop a sim2real contrastive learning mechanism that can generalize the model trained in simulation to real-world applications. The novelties of our training method are three-fold: (i) we integrate the uncertainty into the learning framework to improve feature description of hard cases, e.g., less-textured or symmetric patches; (ii) we decouple the object descriptor into two independent branches, intra-object salience and inter-object distinctness, resulting in a better pixel-wise description; (iii) we enforce cross-view semantic consistency for enhanced robustness in representation learning. Comprehensive experiments on image matching and 6D pose estimation verify the encouraging generalization ability of our method. Particularly for 6D pose estimation, our method significantly outperforms typical unsupervised/sim2real methods, achieving a closer gap with the fully supervised counterpart.

Sim2Real Object-Centric Keypoint Detection and Description

In recent years, optical flow methods develop rapidly, achieving unprecedented high performance. Most of the methods only consider single-modal optical flow under the well-known brightness-constancy assumption. However, in many application systems, images of different modalities need to be aligned, which demands to estimate cross-modal flow between the cross-modal image pairs. A lot of cross-modal matching methods are designed for some specific cross-modal scenarios. We argue that the prior knowledge of the advanced optical flow models can be transferred to the cross-modal flow estimation, which may be a simple but unified solution for diverse cross-modal matching tasks. To verify our hypothesis, we design a self-supervised framework to promote the single-modal optical flow networks for diverse corss-modal flow estimation. Moreover, we add a Cross-Modal-Adapter block as a plugin to  the state-of-the-art optical flow model RAFT for better performance in cross-modal scenarios. Our proposed Modality Promotion Framework and Cross-Modal Adapter have multiple advantages compared to the existing methods. The experiments demonstrate that our method is effective on multiple datasets of different cross-modal scenarios.

The Triangle-Densest-k-Subgraph Problem: Hardness, Lovász Extension, and Application to Document Summarization

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Active Learning on Pre-Trained Language Model with Task-Independent Triplet Loss

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The Triangle-Densest-k-Subgraph Problem: Hardness, Lovász Extension, and Application to Document Summarization

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Active Learning on Pre-Trained Language Model with Task-Independent Triplet Loss

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