IRJun 2, 2023
Prompt Tuning Large Language Models on Personalized Aspect Extraction for RecommendationsPan Li, Yuyan Wang, Ed H. Chi et al.
Existing aspect extraction methods mostly rely on explicit or ground truth aspect information, or using data mining or machine learning approaches to extract aspects from implicit user feedback such as user reviews. It however remains under-explored how the extracted aspects can help generate more meaningful recommendations to the users. Meanwhile, existing research on aspect-based recommendations often relies on separate aspect extraction models or assumes the aspects are given, without accounting for the fact the optimal set of aspects could be dependent on the recommendation task at hand. In this work, we propose to combine aspect extraction together with aspect-based recommendations in an end-to-end manner, achieving the two goals together in a single framework. For the aspect extraction component, we leverage the recent advances in large language models and design a new prompt learning mechanism to generate aspects for the end recommendation task. For the aspect-based recommendation component, the extracted aspects are concatenated with the usual user and item features used by the recommendation model. The recommendation task mediates the learning of the user embeddings and item embeddings, which are used as soft prompts to generate aspects. Therefore, the extracted aspects are personalized and contextualized by the recommendation task. We showcase the effectiveness of our proposed method through extensive experiments on three industrial datasets, where our proposed framework significantly outperforms state-of-the-art baselines in both the personalized aspect extraction and aspect-based recommendation tasks. In particular, we demonstrate that it is necessary and beneficial to combine the learning of aspect extraction and aspect-based recommendation together. We also conduct extensive ablation studies to understand the contribution of each design component in our framework.
IRNov 17, 2022
Latent User Intent Modeling for Sequential RecommendersBo Chang, Alexandros Karatzoglou, Yuyan Wang et al.
Sequential recommender models are essential components of modern industrial recommender systems. These models learn to predict the next items a user is likely to interact with based on his/her interaction history on the platform. Most sequential recommenders however lack a higher-level understanding of user intents, which often drive user behaviors online. Intent modeling is thus critical for understanding users and optimizing long-term user experience. We propose a probabilistic modeling approach and formulate user intent as latent variables, which are inferred based on user behavior signals using variational autoencoders (VAE). The recommendation policy is then adjusted accordingly given the inferred user intent. We demonstrate the effectiveness of the latent user intent modeling via offline analyses as well as live experiments on a large-scale industrial recommendation platform.
IRJun 2, 2023
Hierarchical Reinforcement Learning for Modeling User Novelty-Seeking Intent in Recommender SystemsPan Li, Yuyan Wang, Ed H. Chi et al.
Recommending novel content, which expands user horizons by introducing them to new interests, has been shown to improve users' long-term experience on recommendation platforms \cite{chen2021values}. Users however are not constantly looking to explore novel content. It is therefore crucial to understand their novelty-seeking intent and adjust the recommendation policy accordingly. Most existing literature models a user's propensity to choose novel content or to prefer a more diverse set of recommendations at individual interactions. Hierarchical structure, on the other hand, exists in a user's novelty-seeking intent, which is manifested as a static and intrinsic user preference for seeking novelty along with a dynamic session-based propensity. To this end, we propose a novel hierarchical reinforcement learning-based method to model the hierarchical user novelty-seeking intent, and to adapt the recommendation policy accordingly based on the extracted user novelty-seeking propensity. We further incorporate diversity and novelty-related measurement in the reward function of the hierarchical RL (HRL) agent to encourage user exploration \cite{chen2021values}. We demonstrate the benefits of explicitly modeling hierarchical user novelty-seeking intent in recommendations through extensive experiments on simulated and real-world datasets. In particular, we demonstrate that the effectiveness of our proposed hierarchical RL-based method lies in its ability to capture such hierarchically-structured intent. As a result, the proposed HRL model achieves superior performance on several public datasets, compared with state-of-art baselines.
CEApr 20Code
MFMDQwen: Multilingual Financial Misinformation Detection Based on Large Language ModelZhiwei Liu, Yuyan Wang, Yuechen Jiang et al.
Financial misinformation poses significant threats to financial market stability and individuals' investment decisions. The multilingual environment and the inherent complexity of financial information present substantial challenges for Multilingual Financial Misinformation Detection (MFMD). Existing LLM-based approaches for financial misinformation detection primarily focus on English and a single financial misinformation detection task, which limits their ability to capture multilingual contexts and complex features. In this paper, we propose MFMDQwen, the first open-source LLM designed for MFMD tasks. Furthermore, we introduce MFMD4Instruction, the first instruction dataset supporting MFMD with LLMs, covering English, Chinese, Greek, and Bengali. We also construct MFMDBench, a benchmark dataset for evaluating the MFMD capabilities of LLMs. Experimental results on MFMDBench demonstrate that our model outperforms existing open-source LLMs. The project is available at https://github.com/lzw108/FMD.
APDec 12, 2025Code
Neural Network-based Partial-Linear Single-Index Models for Environmental Mixtures AnalysisHyungrok Do, Yuyan Wang, Mengling Liu et al.
Evaluating the health effects of complex environmental mixtures remains a central challenge in environmental health research. Existing approaches vary in their flexibility, interpretability, scalability, and support for diverse outcome types, often limiting their utility in real-world applications. To address these limitations, we propose a neural network-based partial-linear single-index (NeuralPLSI) modeling framework that bridges semiparametric regression modeling interpretability with the expressive power of deep learning. The NeuralPLSI model constructs an interpretable exposure index via a learnable projection and models its relationship with the outcome through a flexible neural network. The framework accommodates continuous, binary, and time-to-event outcomes, and supports inference through a bootstrap-based procedure that yields confidence intervals for key model parameters. We evaluated NeuralPLSI through simulation studies under a range of scenarios and applied it to data from the National Health and Nutrition Examination Survey (NHANES) to demonstrate its practical utility. Together, our contributions establish NeuralPLSI as a scalable, interpretable, and versatile modeling tool for mixture analysis. To promote adoption and reproducibility, we release a user-friendly open-source software package that implements the proposed methodology and supports downstream visualization and inference (\texttt{https://github.com/hyungrok-do/NeuralPLSI}).
CVMay 14Code
From Sparse to Dense: Spatio-Temporal Fusion for Multi-View 3D Human Pose Estimation with DenseWarperLing Li, Changjie Chen, Yuyan Wang et al.
In multi-view 3D human pose estimation, models typically rely on images captured simultaneously from different camera views to predict a pose at a specific moment. While providing accurate spatial information, this traditional approach often overlooks the rich temporal dependencies between adjacent frames. We propose a novel 3D human pose estimation input method: the sparse interleaved input to address this. This method leverages images captured from different camera views at various time points (e.g., View 1 at time $t$ and View 2 at time $t+δ$), allowing our model to capture rich spatio-temporal information and effectively boost performance. More importantly, this approach offers two key advantages: First, it can theoretically increase the output pose frame rate by N times with N cameras, thereby breaking through single-view frame rate limitations and enhancing the temporal resolution of the production. Second, using a sparse subset of available frames, our method can reduce data redundancy and simultaneously achieve better performance. We introduce the DenseWarper model, which leverages epipolar geometry for efficient spatio-temporal heatmap exchange. We conducted extensive experiments on the Human3.6M and MPI-INF-3DHP datasets. Results demonstrate that our method, utilizing only sparse interleaved images as input, outperforms traditional dense multi-view input approaches and achieves state-of-the-art performance. The source code for this work is available at: https://github.com/lingli1724/DenseWarper-ICLR2026
LGMar 19, 2023
URM4DMU: an user represention model for darknet markets usersHongmeng Liu, Jiapeng Zhao, Yixuan Huo et al.
Darknet markets provide a large platform for trading illicit goods and services due to their anonymity. Learning an invariant representation of each user based on their posts on different markets makes it easy to aggregate user information across different platforms, which helps identify anonymous users. Traditional user representation methods mainly rely on modeling the text information of posts and cannot capture the temporal content and the forum interaction of posts. While recent works mainly use CNN to model the text information of posts, failing to effectively model posts whose length changes frequently in an episode. To address the above problems, we propose a model named URM4DMU(User Representation Model for Darknet Markets Users) which mainly improves the post representation by augmenting convolutional operators and self-attention with an adaptive gate mechanism. It performs much better when combined with the temporal content and the forum interaction of posts. We demonstrate the effectiveness of URM4DMU on four darknet markets. The average improvements on MRR value and Recall@10 are 22.5% and 25.5% over the state-of-the-art method respectively.
AIAug 12, 2025Code
OpenCUA: Open Foundations for Computer-Use AgentsXinyuan Wang, Bowen Wang, Dunjie Lu et al. · cmu
Vision-language models have demonstrated impressive capabilities as computer-use agents (CUAs) capable of automating diverse computer tasks. As their commercial potential grows, critical details of the most capable CUA systems remain closed. As these agents will increasingly mediate digital interactions and execute consequential decisions on our behalf, the research community needs access to open CUA frameworks to study their capabilities, limitations, and risks. To bridge this gap, we propose OpenCUA, a comprehensive open-source framework for scaling CUA data and foundation models. Our framework consists of: (1) an annotation infrastructure that seamlessly captures human computer-use demonstrations; (2) AgentNet, the first large-scale computer-use task dataset spanning 3 operating systems and 200+ applications and websites; (3) a scalable pipeline that transforms demonstrations into state-action pairs with reflective long Chain-of-Thought reasoning that sustain robust performance gains as data scales. Our end-to-end agent models demonstrate strong performance across CUA benchmarks. In particular, OpenCUA-72B achieves an average success rate of 45.0% on OSWorld-Verified, establishing a new state-of-the-art (SOTA) among open-source models. Further analysis confirms that our approach generalizes well across domains and benefits significantly from increased test-time computation. We release our annotation tool, datasets, code, and models to build open foundations for further CUA research.
IRMay 1
Can Explanations Improve Recommendations? Evidence from Prediction-Informed ExplanationsYuyan Wang, Pan Li, Minmin Chen
Recommender systems are central to digital platforms, yet they face a fundamental trade-off between accuracy and explainability. Black-box models achieve strong performance but lack interpretability needed for trust and adoption. Existing explainable AI approaches either treat explanations as post-hoc or at the cost of accuracy. We challenge this view, proposing that explanations, when designed as an integral component of a system and aligned with prediction outcomes, can improve both interpretability and performance. We introduce RecPIE (Recommendation with Prediction-Informed Explanations), a framework that jointly optimizes recommendation predictions and natural-language explanations generated by LLMs. RecPIE embeds explanation generation into the learning loop: predictions guide explanation generation (prediction-informed explanations), which are fed back to refine subsequent predictions (explanation-informed predictions) via alternating training. The LLM is fine-tuned using LoRA and reinforcement learning with a customized reward derived from recommendation accuracy. Drawing on multi-environment statistical learning theory, we formally ground why explanation generation and prediction can be mutually reinforcing. We evaluate RecPIE on large-scale point-of-interest recommendation data from Google Maps, where user preferences span diverse place categories. RecPIE improves predictive accuracy by 3-4% over state-of-the-art baselines and matches the best performing model using only 12% of the training data. In human evaluations with 566 participants, RecPIE explanations are preferred 61.5% of the time (versus 16.6% for the best baseline) and rated closer to human-generated explanations. These results reframe explainability not as a constraint on performance but as a design lever for improving AI systems, with implications for trust, data efficiency, and marketplace deployment.
AIMay 14
Herculean: An Agentic Benchmark for Financial IntelligenceXueqing Peng, Zhuohan Xie, Yupeng Cao et al.
As AI agents improve, the central question is no longer whether they can solve isolated well-defined financial tasks, but whether they can reliably carry out financial professional work. Existing financial benchmarks offer only a partial view of this ability, as they primarily evaluate static competencies such as question answering, retrieval, summarization, and classification. We introduce Herculean, the first skilled benchmark for agentic financial intelligence spanning four representative workflows, including Trading, Hedging, Market Insights, and Auditing. Each workflow is instantiated as a standardized MCP-based skill environment with its own tools, interaction dynamics, constraints, and success criteria, enabling consistent end-to-end assessment of heterogeneous agent systems. Across frontier agents, we find agents perform relatively well on Trading and Market Insights, but struggle substantially on Hedging and Auditing, where long-horizon coordination, state consistency, and structured verification are critical. Overall, our results point to a key gap in current agents in turning financial reasoning into dependable workflow execution in high-stakes financial workflows.
CEMay 9
AutoRedTrader: Autonomous Red Teaming of Trading Agents through Synthetic Misinformation InjectionZhiwei Liu, Yangyang Yu, Yupeng Cao et al.
LLM-based financial agents increasingly rely on both numerical market data and textual signals for sequential trading and stock prediction. However, financial misinformation often appears as subtle textual perturbations rather than explicit falsehoods, making it difficult to detect while still capable of significantly altering agent reasoning and decisions. To study this risk, we propose AutoRedTrader, an autonomous red-teaming framework that generates finance-specific misinformation through behavioral bias manipulation, minor textual perturbations, and rewriting strategies, with agent feedback used to strengthen attacks over time. We evaluate AutoRedTrader in a POMDP-based financial agent simulation environment, and further examine a time-series-informed grounding setting for robustness analysis. The framework enables systematic evaluation of how subtle misinformation affects financial agents and whether historical market evidence can stabilize decisions under misleading textual signals. We evaluate the framework on Bitcoin transaction data. The results show that AutoRedTrader achieves the strongest attack performance with 69.00% misinformation exposure rate and 26.67% attack success rate, outperforming general-purpose misinformation and red-teaming baselines. Ablation studies further show that all modules contribute to generating retrievable and decision-effective financial misinformation.
AIMay 3
Moira: Language-driven Hierarchical Reinforcement Learning for Pair TradingPolydoros Giannouris, Yuechen Jiang, Lingfei Qian et al.
Many sequential decision-making problems exhibit hierarchical structure, where high-level semantic choices constrain downstream actions and feedback is delayed and ambiguous. Learning in such settings is challenging due to credit assignment: performance degradation may arise from flawed abstractions, suboptimal execution, or their interaction. We study this challenge through pair trading, a domain that naturally combines long-horizon semantic reasoning for asset pair selection with short-horizon execution under partial observability. We formulate pair trading as a hierarchical reinforcement learning problem and propose a language-driven optimization framework in which both high-level and low-level policies are parameterized by large language models (LLMs) and optimized exclusively through prompt updates. Our approach leverages pretrained LLMs as hierarchical policies and uses trajectory- and episode-level textual feedback to adapt abstractions and execution without gradient-based fine-tuning. By explicitly separating abstraction selection from execution, the framework reduces non-stationarity across hierarchical levels and enables targeted adaptation under delayed feedback. Experiments on real-world market data show consistent improvements over traditional and LLM-based baselines, demonstrating the effectiveness of language-driven hierarchical reinforcement learning.
IRMay 20, 2024
Beyond Item Dissimilarities: Diversifying by Intent in Recommender SystemsYuyan Wang, Cheenar Banerjee, Samer Chucri et al.
It has become increasingly clear that recommender systems that overly focus on short-term engagement prevents users from exploring diverse interests, ultimately hurting long-term user experience. To tackle this challenge, numerous diversification algorithms have been proposed. These algorithms typically rely on measures of item similarity, aiming to maximize the dissimilarity across items in the final set of recommendations. However, in this work, we demonstrate the benefits of going beyond item-level similarities by utilizing higher-level user understanding--specifically, user intents that persist across multiple interactions--in diversification. Our approach is motivated by the observation that user behaviors on online platforms are largely driven by their underlying intents. Therefore, recommendations should ensure that diverse user intents are accurately represented. While intent has primarily been studied in the context of search, it is less clear how to incorporate real-time dynamic intent predictions into recommender systems. To address this gap, we develop a probabilistic intent-based whole-page diversification framework for the final stage of a recommender system. Starting with a prior belief of user intents, the proposed framework sequentially selects items for each position based on these beliefs and subsequently updates posterior beliefs about the intents. This approach ensures that different user intents are represented on a page, towards optimizing long-term user experience. We experiment with the intent diversification framework on YouTube, the world's largest video recommendation platform, serving billions of users daily. Live experiments on a diverse set of intents show that the proposed framework increases Daily Active Users (DAU) and overall user enjoyment, validating its effectiveness in facilitating long-term planning.
LGNov 16, 2025
Are LLMs The Way Forward? A Case Study on LLM-Guided Reinforcement Learning for Decentralized Autonomous DrivingTimur Anvar, Jeffrey Chen, Yuyan Wang et al.
Autonomous vehicle navigation in complex environments such as dense and fast-moving highways and merging scenarios remains an active area of research. A key limitation of RL is its reliance on well-specified reward functions, which often fail to capture the full semantic and social complexity of diverse, out-of-distribution situations. As a result, a rapidly growing line of research explores using Large Language Models (LLMs) to replace or supplement RL for direct planning and control, on account of their ability to reason about rich semantic context. However, LLMs present significant drawbacks: they can be unstable in zero-shot safety-critical settings, produce inconsistent outputs, and often depend on expensive API calls with network latency. This motivates our investigation into whether small, locally deployed LLMs (< 14B parameters) can meaningfully support autonomous highway driving through reward shaping rather than direct control. We present a case study comparing RL-only, LLM-only, and hybrid approaches, where LLMs augment RL rewards by scoring state-action transitions during training, while standard RL policies execute at test time. Our findings reveal that RL-only agents achieve moderate success rates (73-89%) with reasonable efficiency, LLM-only agents can reach higher success rates (up to 94%) but with severely degraded speed performance, and hybrid approaches consistently fall between these extremes. Critically, despite explicit efficiency instructions, LLM-influenced approaches exhibit systematic conservative bias with substantial model-dependent variability, highlighting important limitations of current small LLMs for safety-critical control tasks.
LGJul 24, 2025
Moving Out: Physically-grounded Human-AI CollaborationXuhui Kang, Sung-Wook Lee, Haolin Liu et al.
The ability to adapt to physical actions and constraints in an environment is crucial for embodied agents (e.g., robots) to effectively collaborate with humans. Such physically grounded human-AI collaboration must account for the increased complexity of the continuous state-action space and constrained dynamics caused by physical constraints. In this paper, we introduce Moving Out, a new human-AI collaboration benchmark that resembles a wide range of collaboration modes affected by physical attributes and constraints, such as moving heavy items together and maintaining consistent actions to move a big item around a corner. Using Moving Out, we designed two tasks and collected human-human interaction data to evaluate models' abilities to adapt to diverse human behaviors and unseen physical attributes. To address the challenges in physical environments, we propose a novel method, BASS (Behavior Augmentation, Simulation, and Selection), to enhance the diversity of agents and their understanding of the outcome of actions. Our experiments show that BASS outperforms state-of-the-art models in AI-AI and human-AI collaboration. The project page is available at https://live-robotics-uva.github.io/movingout_ai/.
LGJun 4, 2021
Understanding and Improving Fairness-Accuracy Trade-offs in Multi-Task LearningYuyan Wang, Xuezhi Wang, Alex Beutel et al.
As multi-task models gain popularity in a wider range of machine learning applications, it is becoming increasingly important for practitioners to understand the fairness implications associated with those models. Most existing fairness literature focuses on learning a single task more fairly, while how ML fairness interacts with multiple tasks in the joint learning setting is largely under-explored. In this paper, we are concerned with how group fairness (e.g., equal opportunity, equalized odds) as an ML fairness concept plays out in the multi-task scenario. In multi-task learning, several tasks are learned jointly to exploit task correlations for a more efficient inductive transfer. This presents a multi-dimensional Pareto frontier on (1) the trade-off between group fairness and accuracy with respect to each task, as well as (2) the trade-offs across multiple tasks. We aim to provide a deeper understanding on how group fairness interacts with accuracy in multi-task learning, and we show that traditional approaches that mainly focus on optimizing the Pareto frontier of multi-task accuracy might not perform well on fairness goals. We propose a new set of metrics to better capture the multi-dimensional Pareto frontier of fairness-accuracy trade-offs uniquely presented in a multi-task learning setting. We further propose a Multi-Task-Aware Fairness (MTA-F) approach to improve fairness in multi-task learning. Experiments on several real-world datasets demonstrate the effectiveness of our proposed approach.
LGAug 30, 2020
An Objective for Hierarchical Clustering in Euclidean Space and its Connection to Bisecting K-meansBenjamin Moseley, Yuyan Wang
This paper explores hierarchical clustering in the case where pairs of points have dissimilarity scores (e.g. distances) as a part of the input. The recently introduced objective for points with dissimilarity scores results in every tree being a 1/2 approximation if the distances form a metric. This shows the objective does not make a significant distinction between a good and poor hierarchical clustering in metric spaces. Motivated by this, the paper develops a new global objective for hierarchical clustering in Euclidean space. The objective captures the criterion that has motivated the use of divisive clustering algorithms: that when a split happens, points in the same cluster should be more similar than points in different clusters. Moreover, this objective gives reasonable results on ground-truth inputs for hierarchical clustering. The paper builds a theoretical connection between this objective and the bisecting k-means algorithm. This paper proves that the optimal 2-means solution results in a constant approximation for the objective. This is the first paper to show the bisecting k-means algorithm optimizes a natural global objective over the entire tree.
LGAug 17, 2020
Beyond Point Estimate: Inferring Ensemble Prediction Variation from Neuron Activation Strength in Recommender SystemsZhe Chen, Yuyan Wang, Dong Lin et al.
Despite deep neural network (DNN)'s impressive prediction performance in various domains, it is well known now that a set of DNN models trained with the same model specification and the same data can produce very different prediction results. Ensemble method is one state-of-the-art benchmark for prediction uncertainty estimation. However, ensembles are expensive to train and serve for web-scale traffic. In this paper, we seek to advance the understanding of prediction variation estimated by the ensemble method. Through empirical experiments on two widely used benchmark datasets MovieLens and Criteo in recommender systems, we observe that prediction variations come from various randomness sources, including training data shuffling, and parameter random initialization. By introducing more randomness into model training, we notice that ensemble's mean predictions tend to be more accurate while the prediction variations tend to be higher. Moreover, we propose to infer prediction variation from neuron activation strength and demonstrate the strong prediction power from activation strength features. Our experiment results show that the average R squared on MovieLens is as high as 0.56 and on Criteo is 0.81. Our method performs especially well when detecting the lowest and highest variation buckets, with 0.92 AUC and 0.89 AUC respectively. Our approach provides a simple way for prediction variation estimation, which opens up new opportunities for future work in many interesting areas (e.g.,model-based reinforcement learning) without relying on serving expensive ensemble models.
LGAug 13, 2020
Small Towers Make Big DifferencesYuyan Wang, Zhe Zhao, Bo Dai et al.
Multi-task learning aims at solving multiple machine learning tasks at the same time. A good solution to a multi-task learning problem should be generalizable in addition to being Pareto optimal. In this paper, we provide some insights on understanding the trade-off between Pareto efficiency and generalization as a result of parameterization in multi-task deep learning models. As a multi-objective optimization problem, enough parameterization is needed for handling task conflicts in a constrained solution space; however, from a multi-task generalization perspective, over-parameterization undermines the benefit of learning a shared representation which helps harder tasks or tasks with limited training examples. A delicate balance between multi-task generalization and multi-objective optimization is therefore needed for finding a better trade-off between efficiency and generalization. To this end, we propose a method of under-parameterized self-auxiliaries for multi-task models to achieve the best of both worlds. It is task-agnostic and works with other multi-task learning algorithms. Empirical results show that small towers of under-parameterized self-auxiliaries can make big differences in improving Pareto efficiency in various multi-task applications.
DSAug 1, 2020
Relational Algorithms for k-means ClusteringBenjamin Moseley, Kirk Pruhs, Alireza Samadian et al.
This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows represent the data points. The running time is potentially exponentially smaller than $N$, the number of data points to be clustered that the relational database represents. Few relational algorithms are known and this paper offers techniques for designing relational algorithms as well as characterizing their limitations. We show that given two data points as cluster centers, if we cluster points according to their closest centers, it is NP-Hard to approximate the number of points in the clusters on a general relational input. This is trivial for conventional data inputs and this result exemplifies that standard algorithmic techniques may not be directly applied when designing an efficient relational algorithm. This paper then introduces a new method that leverages rejection sampling and the $k$-means++ algorithm to construct an O(1)-approximate k-means solution.
DSJun 18, 2020
Fair Hierarchical ClusteringSara Ahmadian, Alessandro Epasto, Marina Knittel et al.
As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates over-representation in traditional clustering. In this paper we extend this notion to hierarchical clustering, where the goal is to recursively partition the data to optimize a specific objective. For various natural objectives, we obtain simple, efficient algorithms to find a provably good fair hierarchical clustering. Empirically, we show that our algorithms can find a fair hierarchical clustering, with only a negligible loss in the objective.