Coresets for k-means and k-median problems yield a small summary of the data, which preserves the clustering cost with respect to any set of k centers. Recently coresets have also been constructed for constrained k-means and k-median problems. However, the notion of coresets has the drawback that (i) they can only be applied in settings where the input points are allowed to have weights, and (ii) in general metric spaces, the size of the coresets can depend logarithmically on the number of points. The notion of weak coresets, which has less stringent requirements than coresets, has been studied in the context of classical k-means and k-median problems. A weak coreset is a pair (J,S) of subsets of points, where S acts as a summary of the point set and J as a set of potential centers. This pair satisfies the properties that (i) S is a good summary of the data as long as the k centers are chosen from J only, and (ii) there is a good choice of k centers in J with a cost close to the optimal cost. We develop this framework, which we call universal weak coresets, for constrained clustering settings. In conjunction with recent coreset constructions for constrained settings, our designs give greater data compression, are conceptually simpler, and apply to a wide range of constrained k-median and k-means problems.
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Slow concept drift is a ubiquitous, yet under-studied problem in practical machine learning systems. In such settings, although recent data is more indicative of future data, naively prioritizing recent instances runs the risk of losing valuable information from the past. We propose an optimization-driven approach towards balancing instance importance over large training windows. First, we model instance relevance using a mixture of multiple timescales of decay, allowing us to capture rich temporal trends. Second, we learn an auxiliary scorer model that recovers the appropriate mixture of timescales as a function of the instance itself. Finally, we propose a nested optimization objective for learning the scorer, by which it maximizes forward transfer for the learned model. Experiments on a large real-world dataset of 39M photos over a 9 year period show upto 15% relative gains in accuracy compared to other robust learning baselines. We replicate our gains on two collections of real-world datasets for non-stationary learning, and extend our work to continual learning settings where, too, we beat SOTA methods by large margins.
GO-DICE: Goal-Conditioned Option-Aware Offline Imitation Learning via Stationary Distribution Correction Estimation
PDF ↗Offline imitation learning (IL) refers to learning expert behavior solely from demonstrations, without any additional interaction with the environment. Despite significant advances in offline IL, existing techniques find it challenging to learn policies for long-horizon tasks and require significant re-training when task specifications change. Towards addressing these limitations, we present GO-DICE an offline IL technique for goal-conditioned long-horizon sequential tasks. GO-DICE discerns a hierarchy of sub-tasks from demonstrations and uses these to learn separate policies for sub-task transitions and action execution, respectively; this hierarchical policy learning facilitates long-horizon reasoning.Inspired by the expansive DICE-family of techniques, policy learning at both the levels transpires within the space of stationary distributions. Further, both policies are learnt with goal conditioning to minimize need for retraining when task goals change. Experimental results substantiate that GO-DICE outperforms recent baselines, as evidenced by a marked improvement in the completion rate of increasingly challenging pick-and-place Mujoco robotic tasks. GO-DICE is also capable of leveraging imperfect demonstration and partial task segmentation when available, both of which boost task performance relative to learning from expert demonstrations alone.
Unified Framework for Diffusion Generative Models in SO(3): Applications in Computer Vision and Astrophysics
PDF ↗Diffusion-based generative models represent the current state-of-the-art for image generation. However, standard diffusion models are based on Euclidean geometry and do not translate directly to manifold-valued data. In this work, we develop extensions of both score-based generative models (SGMs) and Denoising Diffusion Probabilistic Models (DDPMs) to the Lie group of 3D rotations, SO(3). SO(3) is of particular interest in many disciplines such as robotics, biochemistry and astronomy/cosmology science. Contrary to more general Riemannian manifolds, SO(3) admits a tractable solution to heat diffusion, and allows us to implement efficient training of diffusion models. We apply both SO(3) DDPMs and SGMs to synthetic densities on SO(3) and demonstrate state-of-the-art results. Additionally, we demonstrate the practicality of our model on pose estimation tasks and in predicting correlated galaxy orientations for astrophysics/cosmology.
In the quest for Explainable Artificial Intelligence (XAI) one of the questions that frequently arises given a decision made by an AI system is, ``why was the decision made in this way?'' Formal approaches to explainability build a formal model of the AI system and use this to reason about the properties of the system. Given a set of feature values for an instance to be explained, and a resulting decision, a formal abductive explanation is a set of features, such that if they take the given value will always lead to the same decision. This explanation is useful, it shows that only some features were used in making the final decision. But it is narrow, it only shows that if the selected features take their given values the decision is unchanged. It is possible that some features may change values and still lead to the same decision. In this paper we formally define inflated explanations which is a set of features, and for each feature a set of values (always including the value of the instance being explained), such that the decision will remain unchanged, for any of the values allowed for any of the features in the (inflated) abductive explanation. Inflated formal explanations are more informative than common abductive explanations since e.g. they allow us to see if the exact value of a feature is important, or it could be any nearby value. Overall they allow us to better understand the role of each feature in the decision. We show that we can compute inflated explanations for not that much greater cost than abductive explanations, and that we can extend duality results for abductive explanations also to inflated explanations.
Personalization in machine learning (ML) tailors models' decisions to the individual characteristics of users. While this approach has seen success in areas like recommender systems, its expansion into high-stakes fields such as healthcare and autonomous driving is hindered by the extensive regulatory approval processes involved. To address this challenge, we propose a novel framework termed represented Markov Decision Processes (r-MDPs) that is designed to balance the need for personalization with the regulatory constraints. In an r-MDP, we cater to a diverse user population, each with unique preferences, through interaction with a small set of representative policies. Our objective is twofold: efficiently match each user to an appropriate representative policy and simultaneously optimize these policies to maximize overall social welfare. We develop two deep reinforcement learning algorithms that efficiently solve r-MDPs. These algorithms draw inspiration from the principles of classic K-means clustering and are underpinned by robust theoretical foundations. Our empirical investigations, conducted across a variety of simulated environments, showcase the algorithms' ability to facilitate meaningful personalization even under constrained policy budgets. Furthermore, they demonstrate scalability, efficiently adapting to larger policy budgets.
The paper presents Taylor Map Polynomial Neural Network (TMPNN), a novel form of very high-order polynomial regression, in which the same coefficients for a lower-to-moderate-order polynomial regression are iteratively reapplied so as to achieve a higher-order model without the number of coefficients to be fit exploding in the usual curse-of-dimensionality way. This method naturally implements multi-target regression and can capture internal relationships between targets. We also introduce an approach for model interpretation in the form of systems of differential equations. By benchmarking on Feynman regression, UCI, Friedman-1, and real-life industrial datasets, we demonstrate that the proposed method performs comparably to the state-of-the-art regression methods and outperforms them on specific tasks.
Ensuring fairness in machine learning (ML) is crucial, particularly in applications that impact diverse populations. The majority of existing works heavily rely on the availability of protected features like race and gender. However, practical challenges such as privacy concerns and regulatory restrictions often prohibit the use of this data, limiting the scope of traditional fairness research. To address this, we introduce a Shared Latent Space-based Debiasing (SLSD) method that transforms data from both the target domain, which lacks protected features, and a separate source domain, which contains these features, into correlated latent representations. This allows for joint training of a cross-domain protected group estimator on the representations. We then debias the downstream ML model with an adversarial learning technique that leverages the group estimator. We also present a relaxed variant of SLSD, the R-SLSD, that occasionally accesses a small subset of protected features from the target domain during its training phase. Our extensive experiments on benchmark datasets demonstrate that our methods consistently outperform existing state-of-the-art models in standard group fairness metrics.
New Classes of the Greedy-Applicable Arm Feature Distributions in the Sparse Linear Bandit Problem
PDF ↗We consider the sparse contextual bandit problem where arm feature affects reward through the inner product of sparse parameters. Recent studies have developed sparsity-agnostic algorithms based on the greedy arm selection policy. However, the analysis of these algorithms requires strong assumptions on the arm feature distribution to ensure that the greedily selected samples are sufficiently diverse; One of the most common assumptions, relaxed symmetry, imposes approximate origin-symmetry on the distribution, which cannot allow distributions that has origin-asymmetric support. In this paper, we show that the greedy algorithm is applicable to a wider range of the arm feature distributions from two aspects. Firstly, we show that a mixture distribution that has a greedy-applicable component is also greedy-applicable. Second, we propose new distribution classes, related to Gaussian mixture, discrete, and radial distribution, for which the sample diversity is guaranteed. The proposed classes can describe distributions with origin-asymmetric support and, in conjunction with the first claim, provide theoretical guarantees of the greedy policy for a very wide range of the arm feature distributions.
Non-exemplar Online Class-Incremental Continual Learning via Dual-Prototype Self-Augment and Refinement
PDF ↗This paper investigates a new, practical, but challenging problem named Non-exemplar Online Class-incremental continual Learning (NO-CL), which aims to preserve the discernibility of base classes without buffering data examples and efficiently learn novel classes continuously in a single-pass (i.e., online) data stream. The challenges of this task are mainly two-fold: (1) Both base and novel classes suffer from severe catastrophic forgetting as no previous samples are available for replay. (2) As the online data can only be observed once, there is no way to fully re-train the whole model, e.g., re-calibrate the decision boundaries via prototype alignment or feature distillation. In this paper, we propose a novel Dual-prototype Self-augment and Refinement method (DSR) for NO-CL problem, which consists of two strategies: 1) Dual class prototypes: vanilla and high-dimensional prototypes are exploited to utilize the pre-trained information and obtain robust quasi-orthogonal representations rather than example buffers for both privacy preservation and memory reduction. 2) Self-augment and refinement: Instead of updating the whole network, we optimize high-dimensional prototypes alternatively with the extra projection module based on self-augment vanilla prototypes, through a bi-level optimization problem. Extensive experiments demonstrate the effectiveness and superiority of the proposed DSR in NO-CL.
ProCC: Progressive Cross-Primitive Compatibility for Open-World Compositional Zero-Shot Learning
PDF ↗Open-World Compositional Zero-shot Learning (OW-CZSL) aims to recognize novel compositions of state and object primitives in images with no priors on the compositional space, which induces a tremendously large output space containing all possible state-object compositions. Existing works either learn the joint compositional state-object embedding or predict simple primitives with separate classifiers. However, the former method heavily relies on external word embedding methods, and the latter ignores the interactions of interdependent primitives, respectively. In this paper, we revisit the primitive prediction approach and propose a novel method, termed Progressive Cross-primitive Compatibility (ProCC), to mimic the human learning process for OW-CZSL tasks. Specifically, the cross-primitive compatibility module explicitly learns to model the interactions of state and object features with the trainable memory units, which efficiently acquires cross-primitive visual attention to reason high-feasibility compositions, without the aid of external knowledge. Moreover, to alleviate the invalid cross-primitive interactions, especially for partial-supervision conditions (pCZSL), we design a progressive training paradigm to optimize the primitive classifiers conditioned on pre-trained features in an easy-to-hard manner. Extensive experiments on three widely used benchmark datasets demonstrate that our method outperforms other representative methods on both OW-CZSL and pCZSL settings by large margins.
Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear relations in a compact human comprehensible model, by recursively splitting the population and predicting a distinct survival distribution in each leaf node. We use dynamic programming to provide the first survival tree method with optimality guarantees, enabling the assessment of the optimality gap of heuristics. We improve the scalability of our method through a special algorithm for computing trees up to depth two. The experiments show that our method's run time even outperforms some heuristics for realistic cases while obtaining similar out-of-sample performance with the state-of-the-art.
Structure-based drug design (SBDD) aims to generate 3D ligand molecules that bind to specific protein targets. Existing 3D deep generative models including diffusion models have shown great promise for SBDD. However, it is complex to capture the essential protein-ligand interactions exactly in 3D space for molecular generation. To address this problem, we propose a novel framework, namely Binding-Adaptive Diffusion Models (BindDM). In BindDM, we adaptively extract subcomplex, the essential part of binding sites responsible for protein-ligand interactions. Then the selected protein-ligand subcomplex is processed with SE(3)-equivariant neural networks, and transmitted back to each atom of the complex for augmenting the target-aware 3D molecule diffusion generation with binding interaction information. We iterate this hierarchical complex-subcomplex process with cross-hierarchy interaction node for adequately fusing global binding context between the complex and its corresponding subcomplex. Empirical studies on the CrossDocked2020 dataset show BindDM can generate molecules with more realistic 3D structures and higher binding affinities towards the protein targets, with up to -5.92 Avg. Vina Score, while maintaining proper molecular properties. Our code is available at https://github.com/YangLing0818/BindDM
Protein structure-based property prediction has emerged as a promising approach for various biological tasks, such as protein function prediction and sub-cellular location estimation. The existing methods highly rely on experimental protein structure data and fail in scenarios where these data are unavailable. Predicted protein structures from AI tools (e.g., AlphaFold2) were utilized as alternatives. However, we observed that current practices, which simply employ accurately predicted structures during inference, suffer from notable degradation in prediction accuracy. While similar phenomena have been extensively studied in general fields (e.g., Computer Vision) as model robustness, their impact on protein property prediction remains unexplored. In this paper, we first investigate the reason behind the performance decrease when utilizing predicted structures, attributing it to the structure embedding bias from the perspective of structure representation learning. To study this problem, we identify a Protein 3D Graph Structure Learning Problem for Robust Protein Property Prediction (PGSL-RP3), collect benchmark datasets, and present a protein Structure embedding Alignment Optimization framework (SAO) to mitigate the problem of structure embedding bias between the predicted and experimental protein structures. Extensive experiments have shown that our framework is model-agnostic and effective in improving the property prediction of both predicted structures and experimental structures.
Higher-Order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes
PDF ↗Despite the recent successes of vanilla Graph Neural Networks (GNNs) on various tasks, their foundation on pairwise networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs. Codes and datasets are available at https://github.com/Yiminghh/HiGCN.
Visual fine-tuning has garnered significant attention with the rise of pre-trained vision models. The current prevailing method, full fine-tuning, suffers from the issue of knowledge forgetting as it focuses solely on fitting the downstream training set. In this paper, we propose a novel weight rollback-based fine-tuning method called OLOR (One step Learning, One step Review). OLOR combines fine-tuning with optimizers, incorporating a weight rollback term into the weight update term at each step. This ensures consistency in the weight range of upstream and downstream models, effectively mitigating knowledge forgetting and enhancing fine-tuning performance. In addition, a layer-wise penalty is presented to employ penalty decay and the diversified decay rate to adjust the weight rollback levels of layers for adapting varying downstream tasks. Through extensive experiments on various tasks such as image classification, object detection, semantic segmentation, and instance segmentation, we demonstrate the general applicability and state-of-the-art performance of our proposed OLOR. Code is available at https://github.com/rainbow-xiao/OLOR-AAAI-2024.
Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation
PDF ↗Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by context variable in the environment, which is uncontrollable by decision makers. In this paper, we focus on the optimization of functions' expectations over continuous context variable, subject to an unknown distribution. To address this problem, we propose two algorithms that employ kernel density estimation to learn the probability density function (PDF) of continuous context variable online. The first algorithm is simpler, which directly optimizes the expectation under the estimated PDF. Considering that the estimated PDF may have high estimation error when the true distribution is complicated, we further propose the second algorithm that optimizes the distributionally robust objective. Theoretical results demonstrate that both algorithms have sub-linear Bayesian cumulative regret on the expectation objective. Furthermore, we conduct numerical experiments to empirically demonstrate the effectiveness of our algorithms.
Graph Neural Networks (GNNs) have received increasing attention due to their ability to learn from graph-structured data. To open the black-box of these deep learning models, post-hoc instance-level explanation methods have been proposed to understand GNN predictions. These methods seek to discover substructures that explain the prediction behavior of a trained GNN. In this paper, we show analytically that for a large class of explanation tasks, conventional approaches, which are based on the principle of graph information bottleneck (GIB), admit trivial solutions that do not align with the notion of explainability. Instead, we argue that a modified GIB principle may be used to avoid the aforementioned trivial solutions. We further introduce a novel factorized explanation model with theoretical performance guarantees. The modified GIB is used to analyze the structural properties of the proposed factorized explainer. We conduct extensive experiments on both synthetic and real-world datasets to validate the effectiveness of our proposed factorized explainer.
The paradigm of pre-training and fine-tuning graph neural networks has attracted wide research attention. In previous studies, the pre-trained models are viewed as universally versatile, and applied for a diverse range of downstream tasks. In many situations, however, this practice results in limited or even negative transfer. This paper, for the first time, emphasizes the specific application scope of graph pre-trained models: not all downstream tasks can effectively benefit from a graph pre-trained model. In light of this, we introduce the measure task consistency to quantify the similarity between graph pre-training and downstream tasks. This measure assesses the extent to which downstream tasks can benefit from specific pre-training tasks. Moreover, a novel fine-tuning strategy, Bridge-Tune, is proposed to further diminish the impact of the difference between pre-training and downstream tasks. The key innovation in Bridge-Tune is an intermediate step that bridges pre-training and downstream tasks. This step takes into account the task differences and further refines the pre-trained model. The superiority of the presented fine-tuning strategy is validated via numerous experiments with different pre-trained models and downstream tasks.
HDMixer: Hierarchical Dependency with Extendable Patch for Multivariate Time Series Forecasting
PDF ↗Multivariate time series (MTS) prediction has been widely adopted in various scenarios. Recently, some methods have employed patching to enhance local semantics and improve model performance. However, length-fixed patch are prone to losing temporal boundary information, such as complete peaks and periods. Moreover, existing methods mainly focus on modeling long-term dependencies across patches, while paying little attention to other dimensions (e.g., short-term dependencies within patches and complex interactions among cross-variavle patches). To address these challenges, we propose a pure MLP-based HDMixer, aiming to acquire patches with richer semantic information and efficiently modeling hierarchical interactions. Specifically, we design a Length-Extendable Patcher (LEP) tailored to MTS, which enriches the boundary information of patches and alleviates semantic incoherence in series. Subsequently, we devise a Hierarchical Dependency Explorer (HDE) based on pure MLPs. This explorer effectively models short-term dependencies within patches, long-term dependencies across patches, and complex interactions among variables. Extensive experiments on 9 real-world datasets demonstrate the superiority of our approach. The code is available at https://github.com/hqh0728/HDMixer.