The growing demand for data and AI-generated digital goods, such as personalized written content and artwork, necessitates effective pricing and feedback mechanisms that account for uncertain utility and costly production. Motivated by these developments, this study presents a novel mechanism design addressing a general repeated-auction setting where the utility derived from a sold good is revealed post-sale. The mechanism's novelty lies in using pairwise comparisons for eliciting information from the bidder, arguably easier for humans than assigning a numerical value. Our mechanism chooses allocations using an epsilon-greedy strategy and relies on pairwise comparisons between realized utility from allocated goods and an arbitrary value, avoiding the learning-to-bid problem explored in previous work. We prove this mechanism to be asymptotically truthful, individually rational, and welfare and revenue maximizing. The mechanism's relevance is broad, applying to any setting with made-to-order goods of variable quality. Experimental results on multi-label toxicity annotation data, an example of negative utilities, highlight how our proposed mechanism could enhance social welfare in data auctions. Overall, our focus on human factors contributes to the development of more human-aware and efficient mechanism design.
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Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning objectives beyond this. This work proposes algorithms for a general model of hypergraph partitioning that unifies both undirected and directed versions of many well-studied partitioning objectives. The first contribution of this paper introduces polymatroidal cut functions, a large class of cut functions amenable to approximation algorithms via metric embeddings and routing multicommodity flows. We demonstrate an $O(\sqrt{\log n})$-approximation, where $n$ is the number of vertices in the hypergraph, for these problems by rounding relaxations to metrics of negative-type. The second contribution of this paper generalizes the cut-matching game framework of Khandekar et. al. to tackle polymatroidal cut functions. This yields the first almost-linear time $O(\log n)$-approximation algorithm for standard versions of undirected and directed hypergraph partitioning. A technical consequence of our construction is that a cut-matching game which greatly relaxes the set of allowed actions for both players can be used to partition hypergraphs with negligible impact on the approximation ratio. We believe this to be of independent interest.
The precision of unsupervised point cloud registration methods is typically limited by the lack of reliable inlier estimation and self-supervised signal, especially in partially overlapping scenarios. In this paper, we propose an effective inlier estimation method for unsupervised point cloud registration by capturing geometric structure consistency between the source point cloud and its corresponding reference point cloud copy. Specifically, to obtain a high quality reference point cloud copy, an One-Nearest Neighborhood (1-NN) point cloud is generated by input point cloud. This facilitates matching map construction and allows for integrating dual neighborhood matching scores of 1-NN point cloud and input point cloud to improve matching confidence. Benefiting from the high quality reference copy, we argue that the neighborhood graph formed by inlier and its neighborhood should have consistency between source point cloud and its corresponding reference copy. Based on this observation, we construct transformation-invariant geometric structure representations and capture geometric structure consistency to score the inlier confidence for estimated correspondences between source point cloud and its reference copy. This strategy can simultaneously provide the reliable self-supervised signal for model optimization. Finally, we further calculate transformation estimation by the weighted SVD algorithm with the estimated correspondences and corresponding inlier confidence. We train the proposed model in an unsupervised manner, and extensive experiments on synthetic and real-world datasets illustrate the effectiveness of the proposed method.
User-generated content from social media is produced in many languages, making it technically challenging to compare the discussed themes from one domain across different cultures and regions. It is relevant for domains in a globalized world, such as market research, where people from two nations and markets might have different requirements for a product. We propose a simple, modern, and effective method for building a single topic model with sentiment analysis capable of covering multiple languages simultanteously, based on a pre-trained state-of-the-art deep neural network for natural language understanding. To demonstrate its feasibility, we apply the model to newspaper articles and user comments of a specific domain, i.e., organic food products and related consumption behavior. The themes match across languages. Additionally, we obtain an high proportion of stable and domain-relevant topics, a meaningful relation between topics and their respective textual contents, and an interpretable representation for social media documents. Marketing can potentially benefit from our method, since it provides an easy-to-use means of addressing specific customer interests from different market regions around the globe. For reproducibility, we provide the code, data, and results of our study.
The Graphical House Allocation (GHA) problem asks: how can $n$ houses (each with a fixed non-negative value) be assigned to the vertices of an undirected graph $G$, so as to minimize the sum of absolute differences along the edges of $G$? This problem generalizes the classical Minimum Linear Arrangement problem, as well as the well-known House Allocation Problem from Economics. Recent work has studied the computational aspects of GHA and observed that the problem is NP-hard and inapproximable even on particularly simple classes of graphs, such as vertex disjoint unions of paths. However, the dependence of any approximations on the structural properties of the underlying graph had not been studied. In this work, we give a nearly complete characterization of the approximability of GHA. We present algorithms to approximate the optimal envy on general graphs, trees, planar graphs, bounded-degree graphs, and bounded-degree planar graphs. For each of these graph classes, we then prove matching lower bounds, showing that in each case, no significant improvement can be attained unless P = NP. We also present general approximation ratios as a function of structural parameters of the underlying graph, such as treewidth; these match the tight upper bounds in general, and are significantly better approximations for many natural subclasses of graphs. Finally, we investigate the special case of bounded-degree trees in some detail. We first refute a conjecture by Hosseini et al. [2023] about the structural properties of exact optimal allocations on binary trees by means of a counterexample on a depth-$3$ complete binary tree. This refutation, together with our hardness results on trees, might suggest that approximating the optimal envy even on complete binary trees is infeasible. Nevertheless, we present a linear-time algorithm that attains a $3$-approximation on complete binary trees.
The Population Stability Index (PSI) is a widely used measure in credit risk modeling and monitoring within the banking industry. Its purpose is to monitor for changes in the population underlying a model, such as a scorecard, to ensure that the current population closely resembles the one used during model development. If substantial differences between populations are detected, model reconstruction may be necessary. Despite its widespread use, the origins and properties of the PSI are not well documented. Previous literature has suggested using arbitrary constants as a rule-of-thumb to assess stability, regardless of sample size. However, this approach too often calls for model reconstruction in small sample sizes while not detecting the need often enough in large sample sizes. This paper introduces an alternative discrepancy measure called the Population Resemblance statistic (PRS). It is based on the Pearson chi-square statistic. Properties of the PRS follow from the non-central chi-square distribution. Notably, the PRS accommodates sample-size dependent critical values and enables the specification of risk tolerances. Its efficacy is demonstrated in a simulation study and with real-world examples.
Hate speech moderation remains a challenging task for social media platforms. Human-AI collaborative systems offer the potential to combine the strengths of humans' reliability and the scalability of machine learning to tackle this issue effectively. While methods for task handover in human-AI collaboration exist that consider the costs of incorrect predictions, insufficient attention has been paid to accurately estimating these costs. In this work, we propose a value-sensitive rejection mechanism that automatically rejects machine decisions for human moderation based on users' value perceptions regarding machine decisions. We conduct a crowdsourced survey study with 160 participants to evaluate their perception of correct and incorrect machine decisions in the domain of hate speech detection, as well as occurrences where the system rejects making a prediction. Here, we introduce Magnitude Estimation, an unbounded scale, as the preferred method for measuring user (dis)agreement with machine decisions. Our results show that Magnitude Estimation can provide a reliable measurement of participants' perception of machine decisions. By integrating user-perceived value into human-AI collaboration, we further show that it can guide us in 1) determining when to accept or reject machine decisions to obtain the optimal total value a model can deliver and 2) selecting better classification models as compared to the more widely used target of model accuracy.
The number of modes in a probability density function is representative of the model's complexity and can also be viewed as the number of existing subpopulations. Despite its relevance, little research has been devoted to its estimation. Focusing on the univariate setting, we propose a novel approach targeting prediction accuracy inspired by some overlooked aspects of the problem. We argue for the need for structure in the solutions, the subjective and uncertain nature of modes, and the convenience of a holistic view blending global and local density properties. Our method builds upon a combination of flexible kernel estimators and parsimonious compositional splines. Feature exploration, model selection and mode testing are implemented in the Bayesian inference paradigm, providing soft solutions and allowing to incorporate expert judgement in the process. The usefulness of our proposal is illustrated through a case study in sports analytics, showcasing multiple companion visualisation tools. A thorough simulation study demonstrates that traditional modality-driven approaches paradoxically struggle to provide accurate results. In this context, our method emerges as a top-tier alternative offering innovative solutions for analysts.
Adam is a commonly used stochastic optimization algorithm in machine learning. However, its convergence is still not fully understood, especially in the non-convex setting. This paper focuses on exploring hyperparameter settings for the convergence of vanilla Adam and tackling the challenges of non-ergodic convergence related to practical application. The primary contributions are summarized as follows: firstly, we introduce precise definitions of ergodic and non-ergodic convergence, which cover nearly all forms of convergence for stochastic optimization algorithms. Meanwhile, we emphasize the superiority of non-ergodic convergence over ergodic convergence. Secondly, we establish a weaker sufficient condition for the ergodic convergence guarantee of Adam, allowing a more relaxed choice of hyperparameters. On this basis, we achieve the almost sure ergodic convergence rate of Adam, which is arbitrarily close to $o(1/\sqrt{K})$. More importantly, we prove, for the first time, that the last iterate of Adam converges to a stationary point for non-convex objectives. Finally, we obtain the non-ergodic convergence rate of $O(1/K)$ for function values under the Polyak-Lojasiewicz (PL) condition. These findings build a solid theoretical foundation for Adam to solve non-convex stochastic optimization problems.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
In recent years, DBpedia, Freebase, OpenCyc, Wikidata, and YAGO have been published as noteworthy large, cross-domain, and freely available knowledge graphs. Although extensively in use, these knowledge graphs are hard to compare against each other in a given setting. Thus, it is a challenge for researchers and developers to pick the best knowledge graph for their individual needs. In our recent survey, we devised and applied data quality criteria to the above-mentioned knowledge graphs. Furthermore, we proposed a framework for finding the most suitable knowledge graph for a given setting. With this paper we intend to ease the access to our in-depth survey by presenting simplified rules that map individual data quality requirements to specific knowledge graphs. However, this paper does not intend to replace our previously introduced decision-support framework. For an informed decision on which KG is best for you we still refer to our in-depth survey.
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