Designing small-sized \emph{coresets}, which approximately preserve the costs of the solutions for large datasets, has been an important research direction for the past decade. We consider coreset construction for a variety of general constrained clustering problems. We introduce a general class of assignment constraints, including capacity constraints on cluster centers, and assignment structure constraints for data points (modeled by a convex body $\mathcal{B}$). We give coresets for constrained clustering problems with such general assignment constraints, significantly generalizing known coreset results for constrained clustering. Notable implications of our general theorem include the first $\epsilon$-coreset for capacitated and fair $k$-Median with $m$ outliers in Euclidean spaces whose size is $\tilde{O}(m + k^2 \epsilon^{-4})$, generalizing and improving upon the prior bounds in [Braverman et al., FOCS'22; Huang et al., ICLR'23] (for capacitated $k$-Median, the coreset size bound obtained in [Braverman et al., FOCS'22] is $\tilde{O}(k^3 \epsilon^{-6})$, and for $k$-Median with $m$ outliers, the coreset size bound obtained in [Huang et al., ICLR'23] is $\tilde{O}(m + k^3 \epsilon^{-5})$), and the first $\epsilon$-coreset of size $\mathrm{poly}(k \epsilon^{-1})$ for fault-tolerant clustering for metric spaces with bounded covering exponent.
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Recent work demonstrated the existence of Boolean functions for which Shapley values provide misleading information about the relative importance of features in rule-based explanations. Such misleading information was broadly categorized into a number of possible issues. Each of those issues relates with features being relevant or irrelevant for a prediction, and all are significant regarding the inadequacy of Shapley values for rule-based explainability. This earlier work devised a brute-force approach to identify Boolean functions, defined on small numbers of features, and also associated instances, which displayed such inadequacy-revealing issues, and so served as evidence to the inadequacy of Shapley values for rule-based explainability. However, an outstanding question is how frequently such inadequacy-revealing issues can occur for Boolean functions with arbitrary large numbers of features. It is plain that a brute-force approach would be unlikely to provide insights on how to tackle this question. This paper answers the above question by proving that, for any number of features, there exist Boolean functions that exhibit one or more inadequacy-revealing issues, thereby contributing decisive arguments against the use of Shapley values as the theoretical underpinning of feature-attribution methods in explainability.
We consider the problem of optimising an expensive-to-evaluate grey-box objective function, within a finite budget, where known side-information exists in the form of the causal structure between the design variables. Standard black-box optimisation ignores the causal structure, often making it inefficient and expensive. The few existing methods that consider the causal structure are myopic and do not fully accommodate the observation-intervention trade-off that emerges when estimating causal effects. In this paper, we show that the observation-intervention trade-off can be formulated as a non-myopic optimal stopping problem which permits an efficient solution. We give theoretical results detailing the structure of the optimal stopping times and demonstrate the generality of our approach by showing that it can be integrated with existing causal Bayesian optimisation algorithms. Experimental results show that our formulation can enhance existing algorithms on real and synthetic benchmarks.
In many learning applications, data are collected from multiple sources, each providing a \emph{batch} of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one of several unknown subgroups, each with an unknown input distribution and input-output relationship. We consider one of this setup's most fundamental and important manifestations where the output is a noisy linear combination of the inputs, and there are $k$ subgroups, each with its own regression vector. Prior work~\cite{kong2020meta} showed that with abundant small-batches, the regression vectors can be learned with only few, $\tilde\Omega( k^{3/2})$, batches of medium-size with $\tilde\Omega(\sqrt k)$ samples each. However, the paper requires that the input distribution for all $k$ subgroups be isotropic Gaussian, and states that removing this assumption is an ``interesting and challenging problem". We propose a novel gradient-based algorithm that improves on the existing results in several ways. It extends the applicability of the algorithm by: (1) allowing the subgroups' underlying input distributions to be different, unknown, and heavy-tailed; (2) recovering all subgroups followed by a significant proportion of batches even for infinite $k$; (3) removing the separation requirement between the regression vectors; (4) reducing the number of batches and allowing smaller batch sizes.
The distributed data analytic system -- Spark is a common choice for processing massive volumes of heterogeneous data, while it is challenging to tune its parameters to achieve high performance. Recent studies try to employ auto-tuning techniques to solve this problem but suffer from three issues: limited functionality, high overhead, and inefficient search. In this paper, we present a general and efficient Spark tuning framework that can deal with the three issues simultaneously. First, we introduce a generalized tuning formulation, which can support multiple tuning goals and constraints conveniently, and a Bayesian optimization (BO) based solution to solve this generalized optimization problem. Second, to avoid high overhead from additional offline evaluations in existing methods, we propose to tune parameters along with the actual periodic executions of each job (i.e., online evaluations). To ensure safety during online job executions, we design a safe configuration acquisition method that models the safe region. Finally, three innovative techniques are leveraged to further accelerate the search process: adaptive sub-space generation, approximate gradient descent, and meta-learning method. We have implemented this framework as an independent cloud service, and applied it to the data platform in Tencent. The empirical results on both public benchmarks and large-scale production tasks demonstrate its superiority in terms of practicality, generality, and efficiency. Notably, this service saves an average of 57.00% memory cost and 34.93% CPU cost on 25K in-production tasks within 20 iterations, respectively.
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on heuristics, e.g., the solution operators of partial differential equations (PDE), such as the Laplace or biharmonic equation. Especially the latter, which shows good numerical performance for large displacements, is expensive. Moreover, from a continuous perspective, choosing the mesh motion technique is to a certain extent arbitrary and has no influence on the physically relevant quantities. Therefore, we consider approaches inspired by machine learning. We present a hybrid PDE-NN approach, where the neural network (NN) serves as parameterization of a coefficient in a second order nonlinear PDE. We ensure existence of solutions for the nonlinear PDE by the choice of the neural network architecture. Moreover, we present an approach where a neural network corrects the harmonic extension such that the boundary displacement is not changed. In order to avoid technical difficulties in coupling finite element and machine learning software, we work with a splitting of the monolithic FSI system into three smaller subsystems. This allows to solve the mesh motion equation in a separate step. We assess the quality of the learned mesh motion technique by applying it to a FSI benchmark problem.
We derive large-sample and other limiting distributions of the ``frequency of frequencies'' vector, ${\bf M_n}$, together with the number of species, $K_n$, in a Poisson-Dirichlet or generalised Poisson-Dirichlet gene or species sampling model. Models analysed include those constructed from gamma and $\alpha$-stable subordinators by Kingman, the two-parameter extension by Pitman and Yor, and another two-parameter version constructed by omitting large jumps from an $\alpha$-stable subordinator. In the Poisson-Dirichlet case ${\bf M_n}$ and $K_n$ turn out to be asymptotically independent, and notable, especially for statistical applications, is that in other cases the conditional limiting distribution of ${\bf M_n}$, given $K_n$, is normal, after certain centering and norming.
Collective perception is a foundational problem in swarm robotics, in which the swarm must reach consensus on a coherent representation of the environment. An important variant of collective perception casts it as a best-of-$n$ decision-making process, in which the swarm must identify the most likely representation out of a set of alternatives. Past work on this variant primarily focused on characterizing how different algorithms navigate the speed-vs-accuracy tradeoff in a scenario where the swarm must decide on the most frequent environmental feature. Crucially, past work on best-of-$n$ decision-making assumes the robot sensors to be perfect (noise- and fault-less), limiting the real-world applicability of these algorithms. In this paper, we derive from first principles an optimal, probabilistic framework for minimalistic swarm robots equipped with flawed sensors. Then, we validate our approach in a scenario where the swarm collectively decides the frequency of a certain environmental feature. We study the speed and accuracy of the decision-making process with respect to several parameters of interest. Our approach can provide timely and accurate frequency estimates even in presence of severe sensory noise.
In multi-turn dialog, utterances do not always take the full form of sentences \cite{Carbonell1983DiscoursePA}, which naturally makes understanding the dialog context more difficult. However, it is essential to fully grasp the dialog context to generate a reasonable response. Hence, in this paper, we propose to improve the response generation performance by examining the model's ability to answer a reading comprehension question, where the question is focused on the omitted information in the dialog. Enlightened by the multi-task learning scheme, we propose a joint framework that unifies these two tasks, sharing the same encoder to extract the common and task-invariant features with different decoders to learn task-specific features. To better fusing information from the question and the dialog history in the encoding part, we propose to augment the Transformer architecture with a memory updater, which is designed to selectively store and update the history dialog information so as to support downstream tasks. For the experiment, we employ human annotators to write and examine a large-scale dialog reading comprehension dataset. Extensive experiments are conducted on this dataset, and the results show that the proposed model brings substantial improvements over several strong baselines on both tasks. In this way, we demonstrate that reasoning can indeed help better response generation and vice versa. We release our large-scale dataset for further research.
While existing work in robust deep learning has focused on small pixel-level $\ell_p$ norm-based perturbations, this may not account for perturbations encountered in several real world settings. In many such cases although test data might not be available, broad specifications about the types of perturbations (such as an unknown degree of rotation) may be known. We consider a setup where robustness is expected over an unseen test domain that is not i.i.d. but deviates from the training domain. While this deviation may not be exactly known, its broad characterization is specified a priori, in terms of attributes. We propose an adversarial training approach which learns to generate new samples so as to maximize exposure of the classifier to the attributes-space, without having access to the data from the test domain. Our adversarial training solves a min-max optimization problem, with the inner maximization generating adversarial perturbations, and the outer minimization finding model parameters by optimizing the loss on adversarial perturbations generated from the inner maximization. We demonstrate the applicability of our approach on three types of naturally occurring perturbations -- object-related shifts, geometric transformations, and common image corruptions. Our approach enables deep neural networks to be robust against a wide range of naturally occurring perturbations. We demonstrate the usefulness of the proposed approach by showing the robustness gains of deep neural networks trained using our adversarial training on MNIST, CIFAR-10, and a new variant of the CLEVR dataset.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.
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